notebooks/neural_implicit_mf.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Approximating Implicit Matrix Factorization with Shallow Neural Networks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from collections import namedtuple\n",
    "from copy import deepcopy\n",
    "import random\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "from sklearn.manifold import TSNE\n",
    "from sklearn.metrics.pairwise import cosine_similarity\n",
    "from sqlalchemy import create_engine\n",
    "\n",
    "from dotify.config import DevelopmentConfig as Config\n",
    "from dotify.recommendation.implicit_mf.ratings_matrix import RatingsMatrix\n",
    "from dotify.recommendation.implicit_mf.implicit_mf import ImplicitMF\n",
    "from dotify.resources.countries import countries as countries_lookup\n",
    "\n",
    "ENGINE = create_engine(Config.SQLALCHEMY_DATABASE_URI)\n",
    "\n",
    "%matplotlib inline\n",
    "plt.style.use('seaborn')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Abstract"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implicit Matrix Factorization\n",
    "\n",
    "The Implicit Matrix Factorization (IMF) algorithm as presented by [Hu, Koren and Volinksy](http://yifanhu.net/PUB/cf.pdf) is a widely popular, effective method for recommending items to users. This approach was born from necessity: while explicit feedback as to our users' tastes - a questionnaire completed at user signup, for example - makes building a recommendation engine straightforward, we often have nothing more than *implicit feedback* data - view count, click count, time spent on page, for example - which serve instead as a proxy for these preferences. Crucially, the latter feedback is asymmetric: while a high view count might indicate positive preference for a given item, a low view count cannot be said to do the opposite. Perhaps, the user simply didn't know the item was there.\n",
    "\n",
    "IMF begins with a ratings matrix $R$, where $R_{u, i}$ gives the implicit feedback value observed for user $u$ and item $i$. Next, it constructs two other matrices defined as follows:\n",
    "\n",
    "$$\n",
    "p_{u, i} =\n",
    "\\begin{cases}\n",
    "1 & r_{u, i} \\gt 0\\\\\n",
    "0 & r_{u, i} = 0\n",
    "\\end{cases}\n",
    "$$\n",
    "<br>\n",
    "$$\n",
    "c_{u, i} = 1 + \\alpha r_{u, i}\n",
    "$$\n",
    "\n",
    "$P$ gives a binary matrix indicating our belief in the existence of each user's preference for each item. $C$ gives our *confidence* in the existence of each user's preference for each item where, trivially, larger values of $r_{u, i}$ give us higher confidence that user $u$ indeed likes item $i$.\n",
    "\n",
    "Next, IMF outlines its goal: let's embed each user and item into $\\mathbb{R}^f$ such that their dot product approximates the former's true preference for the latter. Finally, and naming user vectors $x_u \\in \\mathbb{R}^f$ and item vectors $y_i \\in \\mathbb{R}^f$, we compute the argmin of the following objective:\n",
    "\n",
    "$$\n",
    "\\underset{x_{*}, y_{*}}{\\arg\\min}\\sum\\limits_{u, i}c_{u, i}\\big(p_{u, i} - x_u^Ty_i\\big)^2 + \\lambda\\bigg(\\sum\\limits_u\\|x_u\\|^2 + \\sum\\limits_i\\|y_u\\|^2\\bigg)\n",
    "$$\n",
    "\n",
    "Once sufficiently minimized, we can compute expected preferences $\\hat{p}_{u, i} = x_u^Ty_i$ for unobserved $\\text{(user, item)}$ pairs; recommendation then becomes:\n",
    "1. For a given user $u$, compute predicted preferences $\\hat{p}_{u, i} = x_u^Ty_i$ for all items $i$.\n",
    "2. Sort the list in descending order.\n",
    "3. Returning the top $n$ items.\n",
    "\n",
    "## Shallow neural networks\n",
    "IMF effectively gives a function $f: u, i \\rightarrow \\hat{p}_{u, i}$. As before, our goal is to minimize the function above, which we can now rewrite as:\n",
    "\n",
    "$$\n",
    "\\underset{x_{*}, y_{*}}{\\arg\\min}\\sum\\limits_{u, i}c_{u, i}\\big(p_{u, i} - f(u, i)\\big)^2 + \\lambda\\bigg(\\sum\\limits_u\\|x_u\\|^2 + \\sum\\limits_i\\|y_u\\|^2\\bigg)\n",
    "$$\n",
    "\n",
    "To approximate this function, I turn to our favorite [universal function approximator](http://neuralnetworksanddeeplearning.com/chap4.html): neural networks optimized with stochastic gradient descent.\n",
    "\n",
    "This work is built around a toy web application I authored long ago: [dotify](http://dotify.herokuapp.com/). At present, dotify:\n",
    "- Pulls data nightly from [Spotify Charts](https://spotifycharts.com/regional). These data contain the number of streams for that day's top 200 songs for each of 55 countries.\n",
    "- Computes an implicit matrix factorization nightly, giving vectors for both countries and songs.\n",
    "- Allows the user to input a \"country-arithmetic\" expression, i.e. \"I want music like `Colombia x Turkey - Germany`.\" It then performs this arithmetic with the chosen vectors and recommends songs to the composite.\n",
    "\n",
    "In this work, I first fit and cross-validate an implicit matrix factorization model, establishing the three requisite parameters: $f$, the dimensionality of the latent vectors; $\\alpha$, the scalar multiple used in computing $C$; $\\lambda$ the regularization strength used in on our loss function.\n",
    "\n",
    "### Network architectures\n",
    "\n",
    "Next, I explore five different shallow neural network architectures in attempt to improve upon the observed results. These architectures are as follows:\n",
    "\n",
    "1. A trivially \"Siamese\" network which first embeds each country and song index into $\\mathbb{R}^f$ in parallel then computes a dot-product of the embeddings. This is roughly equivalent to what is being done by IMF.\n",
    "2. Same as previous, but with a bias embedding for each set, in $\\mathbb{R}$, added to the dot-product.\n",
    "3. Same as [#1](#network_1), but concatenate the vectors instead. Then, stack 3 fully-connected layers with ReLU activations, batch normalization after each, and dropout after the first. Finally, add a 1-unit dense layer on the end, and add bias embeddings to the result. (NB: I wanted to add the bias embeddings to the respective $\\mathbb{R}^f$ embeddings at the outset, but couldn't figure out how to do this in Keras.)\n",
    "4. Same as [#2](#network_2), except feed in the song title text as well. This text is first tokenized, then padded to a maximum sequence length, then embedded into a fixed-length vector by an LSTM, then reduced to a single value by a dense layer with a ReLU activation. Finally, this scalar is concatenated to the scalar output that [#2](#network_2) would produce, and the result is fed into a final dense layer with a linear activation - i.e. a linear combination of the two.\n",
    "5. Same as [#4](#network_4), except feed in the song artist index as well. This index is first embedded into a vector, then reduced to a scalar by a dense layer with a ReLU activation. Finally, this scalar is concatenated with the two scalars produced in the second-to-last layer of [#4](#network_4), then fed into a final dense layer with a linear activation. Like the previous, this is a linear combination of the three inputs.\n",
    "\n",
    "# Results\n",
    "\n",
    "While the various network architectures are intruiging for both the ease with which we can incorporate multiple, disparate inputs into our function, and the ability to then train this function end-to-end with respect to our main minimization objective, we find no reason to prefer them over the time-worn Implicit Matrix Factorization algorithm."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data preparation\n",
    "\n",
    "To construct our ratings matrix, I take the sum of total streams for each $\\text{(country, song)}$ pair. The data are limited to a given number of \"top songs,\" defined as a song that appeared on Spotify Charts *on a given date*.\n",
    "\n",
    "Because the values exist on wildly different orders of magnitude, I scale the results as follows:\n",
    "\n",
    "$$\\tilde{r}_{u, i} = \\log{\\bigg(\\frac{1 + r_{u, i}}{\\epsilon}\\bigg)}$$\n",
    "\n",
    "To start, let's build a ratings matrix for a small sample of the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>song_id</th>\n",
       "      <th>5552</th>\n",
       "      <th>5553</th>\n",
       "      <th>5557</th>\n",
       "      <th>5558</th>\n",
       "      <th>5560</th>\n",
       "      <th>5562</th>\n",
       "      <th>5565</th>\n",
       "      <th>5582</th>\n",
       "      <th>5583</th>\n",
       "      <th>5585</th>\n",
       "      <th>...</th>\n",
       "      <th>33062</th>\n",
       "      <th>33064</th>\n",
       "      <th>33065</th>\n",
       "      <th>33066</th>\n",
       "      <th>33067</th>\n",
       "      <th>33068</th>\n",
       "      <th>33069</th>\n",
       "      <th>33070</th>\n",
       "      <th>33071</th>\n",
       "      <th>33072</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>country_id</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.643437</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.546472</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.597833</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.175760</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.138153</td>\n",
       "      <td>0.961264</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 2110 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "song_id        5552   5553   5557      5558   5560   5562   5565      5582   \\\n",
       "country_id                                                                    \n",
       "1           0.000000    0.0    0.0  0.000000    0.0    0.0    0.0  0.000000   \n",
       "2           0.000000    0.0    0.0  0.000000    0.0    0.0    0.0  3.643437   \n",
       "4           2.546472    0.0    0.0  3.597833    0.0    0.0    0.0  0.000000   \n",
       "5           0.000000    0.0    0.0  3.175760    0.0    0.0    0.0  0.000000   \n",
       "6           0.000000    0.0    0.0  0.000000    0.0    0.0    0.0  0.000000   \n",
       "\n",
       "song_id     5583   5585   ...    33062     33064     33065  33066  33067  \\\n",
       "country_id                ...                                              \n",
       "1             0.0    0.0  ...      0.0  0.000000  0.000000    0.0    0.0   \n",
       "2             0.0    0.0  ...      0.0  0.000000  0.000000    0.0    0.0   \n",
       "4             0.0    0.0  ...      0.0  0.000000  0.000000    0.0    0.0   \n",
       "5             0.0    0.0  ...      0.0  0.000000  0.000000    0.0    0.0   \n",
       "6             0.0    0.0  ...      0.0  1.138153  0.961264    0.0    0.0   \n",
       "\n",
       "song_id     33068  33069  33070  33071  33072  \n",
       "country_id                                     \n",
       "1             0.0    0.0    0.0    0.0    0.0  \n",
       "2             0.0    0.0    0.0    0.0    0.0  \n",
       "4             0.0    0.0    0.0    0.0    0.0  \n",
       "5             0.0    0.0    0.0    0.0    0.0  \n",
       "6             0.0    0.0    0.0    0.0    0.0  \n",
       "\n",
       "[5 rows x 2110 columns]"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ratings_matrix = RatingsMatrix(n_top_songs=10000, eps=1e3)\n",
    "ratings_matrix.R_ui.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Next, let's get an idea of the sparsity of our data and how many songs each country has streamed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Our ratings matrix has 7.3999999999999995% non-zero entries.\n"
     ]
    }
   ],
   "source": [
    "sparsity = (ratings_matrix.R_ui == 0).mean().mean()\n",
    "non_zero_entries_percent = 100*np.round(1 - sparsity, 4)\n",
    "\n",
    "print('Our ratings matrix has {}% non-zero entries.'.format(non_zero_entries_percent))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Our ratings matrix contains 55 countries and 2110 unique songs.\n"
     ]
    }
   ],
   "source": [
    "print('Our ratings matrix contains {} countries and {} unique songs.'.format(*ratings_matrix.R_ui.shape))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlwAAAGDCAYAAAD+nM7XAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xd0FNX/xvFnU5CS8AUVRUUiAgkSWpBelWIQCB1CF0Gk\nKYKIQKT3KmCQYkRQICIlRBQEFEUMTQSJ9N4SkV4SQNLu7w8O+yOkos6GhPfrHM7JzszO/czcLQ93\nZmdsxhgjAAAAWMYpowsAAADI6ghcAAAAFiNwAQAAWIzABQAAYDECFwAAgMUIXAAAABYjcCFZtWrV\nkpeXl/1fiRIlVLt2bU2YMEHR0dH25bZt2yYvLy/99ddfaa7TGKPQ0FBdvHgxxWXuXV+tWrU0c+bM\nf7Utv//+u3bs2GF/7OXlpa+//vpfrfPfiI2NVd++fVW6dGlVq1ZNCQkJyS63YsUKdenSRZIUHx8v\nHx8fnTx58h+3O3r0aPn4+OjFF1/UhQsXksxPbb/c7z7L6H0sSVevXtXYsWP18ssvq0SJEqpatar6\n9ev3r/aho+zatUtdu3ZVuXLlVLJkSTVo0ECzZs1STEyMfZkrV65o2bJlGVjlf+evv/6Sl5eXtm3b\nltGlSJK2bNmi7t27q3LlyvLx8VGTJk305ZdfytFXUcpKfQwCF1LRtWtXhYWFKSwsTKtXr1a/fv20\natUqvfHGG/YPfh8fH4WFhemJJ55Ic307d+7UgAEDdPPmzRSXuZ/1pVf79u0TfcmGhYWpXr16/9n6\n79fmzZu1evVqTZ8+XUuXLpWTU/Jvw/DwcJUuXVqSdPjwYWXLlk0eHh7/qM0jR45owYIFGjBggL7+\n+ms9/vjj/7j+9MjofSxJ3bp10+7duzVhwgStXbtWH330kS5duqQ2bdro0qVLGVpbag4cOKCOHTuq\nePHi+vLLL7V69Wp169ZNn3/+uYYNG2ZfbvLkyRkearOiuXPnqmvXrvL09NRnn32m0NBQtW3bVpMm\nTUq0/x2BPs5aXDK6ADy4cubMqXz58tkfFyxYUB4eHmrevLmWL1+uNm3aKFu2bImWSU16/nd4P+tL\nr3vb/a/Xf7+uXr0qSapZs6ZsNluKy/3xxx/q3bu3/e+SJUv+6zarVq2qAgUK/OP1pFdG7+ODBw/q\n999/18qVK+Xl5SVJeuaZZzRjxgxVrVpV3377rTp27JihNaYkNDRURYoUUd++fe3Tnn32WcXGxmrw\n4MEaNGiQcufO7fDRlofBvn37NGXKFH3wwQdq166dfbqHh4fc3NzUt29fNW/e3P4fIavRx1kLI1y4\nL97e3nrxxRe1evVqSUkPAW7YsEFNmjRRqVKlVK1aNY0aNUq3bt1SRESE/QOsdu3aCgwM1LZt21Sy\nZEnNnDlTFSpUUIcOHZI9RHn27Fm9/vrrKlmypHx9ffXNN9/Y5wUGBqpu3bqJarx7Wq1atRQfH69B\ngwapQ4cOkpIe7lq2bJkaNmyoUqVKqW7dulq4cKF9XkhIiOrVq6evvvpKtWrVUokSJdS2bVsdPXo0\nxX108+ZNTZ48WbVq1VLJkiXVsmVLbdmyxV5b//79JUnFihVTYGBgoudGRETYD+Pu3btX3bp1k5eX\nl4YMGaJffvlFtWrVSrbNuLg4BQUF6ZVXXlHJkiXl5+dn76OQkBC1bdtWklSnTh0NHDgwxdrTIz37\n5O59nJCQoBkzZqhatWry8fHRsGHDFBAQYK8juT6/d1pMTIzGjx+vatWqqWzZsmrfvr127dqVYo3O\nzs6SpI0bNyb60sqVK5dCQ0PVuHFj+7TffvtN7du3l4+Pj6pUqaLRo0fbR2Hv9MfatWvVtGlTlShR\nQr6+vvrhhx/sz4+Li9OkSZNUpUoV+fj4aNCgQerXr599+27cuKFBgwapSpUqKlmypFq1amV/PSTH\nyclJp06dSvIaq1+/vr799lvlzJlTgYGBWrZsmX799Vd5eXkpIiJCAwcOVJ8+fdShQwe9+OKLCg4O\nliQtWbJEvr6+KlWqlPz8/LRixYpE6127dq2aN2+uUqVKqXTp0mrdurX++OOPRH25dOlStW7dWiVL\nllT9+vW1a9cuBQcHq2bNmipbtqzefffdRIc7f/vtN7Vu3VqlSpVS7dq1NWXKFN26dcs+PzIyUm++\n+aZ8fHxUq1Yt/fLLLynuD+n2+6ZTp06aOnWqypcvr4oVK2r06NGJ2jxz5ox69+6tsmXLqkqVKurb\nt6/Onj1rn9+hQwcNHTpUzZo1U/ny5fXjjz8maWfp0qXKkyePWrdunWRevXr1NH/+fHl6ekpK/T13\np+bUPpvSem2lp4/nzJkjLy+vRP0lSe3atdOYMWNS3afIAAZIxssvv2w+/vjjZOcNHz7cVKhQwRhj\nzNatW42np6c5c+aMuXjxovH29jZffvmliYiIMJs3bzaVKlUygYGBJi4uzvzwww/G09PThIeHm+jo\naPtzO3bsaE6cOGEOHDiQaH136ihWrJiZO3euOXbsmJk5c6bx8vIy4eHhxhhjPvroI1OnTp1E9d09\n7eLFi+aFF14w8+fPN5cvXzbGGOPp6WlCQ0ONMcZ89tlnplSpUmbJkiXm+PHj5ssvvzQlS5Y0c+fO\nNcYYs3z5cuPt7W3atWtndu/ebfbu3Wvq169vXnvttRT3Xbdu3UytWrXMxo0bzZEjR8yoUaNM8eLF\nza5du0x0dLRZuHCh8fT0NOfOnTPR0dGJnhsXF2fOnTtnfv75Z1OtWjVz7tw5c+7cOdOwYUMTEhJi\nLl68mGybo0aNMhUrVjTfffedOXbsmJk1a5bx8vIya9asMTdv3ky0769du5bsOu7eL6nNS88+uXv5\nGTNmmLJly5rVq1ebw4cPm3fffdeUKFHCDBgwwBhjkvR5ctPeeecd06xZM7N9+3Zz7NgxExgYaEqU\nKGGOHTuWaj94enqal19+2QwePNiEhoaaCxcuJFpm165dxtvb24wfP94cOXLEbNiwwbz00kumW7du\nxhhjTp8+bTw9PU2tWrXMzz//bE6cOGHeeecdU7ZsWXP9+nVjjDHjxo0zVapUMT/++KM5dOiQeffd\nd42Xl5d9+8aNG2datGhh9u3bZ06dOmWGDh2a6Pn3OnHihClfvrwpVqyYadOmjZk6darZvHmziYmJ\nsS8THR1t3n33XePv72/OnTtn4uLizIABA4ynp6f5/PPPzZEjR8y5c+fMokWLTKVKlcx3331nTp48\naUJDQ82LL75oQkJCjDHGhIeHm2LFipmFCxea06dPm/DwcOPv728aNWqUqC8rVapk1q9fb44ePWpa\ntmxpypcvbzp37mwOHjxo1qxZY7y9vc2iRYuMMcbs27fPlCpVynz66afmxIkTZvPmzaZBgwZm4MCB\nxhhjYmJiTL169Uz79u3N/v37zZYtW0ydOnWMp6en2bp1a7L75KOPPjLe3t6mQ4cOZv/+/WbDhg2m\natWqZsiQIcYYY65fv25q165t3nvvPXPw4EGzb98+06tXL+Pr62tu3bpljDGmffv2plixYua7774z\n+/fvN1FRUUnaadmypXnzzTdTfE3dLbX33J2aU/tsSuu1ld4+9vPzM6NGjbK3cfr0aePl5WX27duX\nru2A4xC4kKzUAteHH35oihcvboxJ/MW4d+9e4+npaX766Sf7snv27LF/KW7fvt14enqa06dPJ3ru\nxo0b7csnF7j69OmTqP327dubfv36GWPS/lAzxpgXXnjBLF++3P74ThhISEgwVapUMVOmTEn0/IkT\nJ5rKlSubhIQEs3z5cuPp6WmOHDlinz9//nxTunTpZPfN4cOHjaenp/nll18STW/ZsqV5++23jTHG\nhIaGGk9Pz2Sff8eSJUtMly5djDG3Q1jJkiXNqVOnkl02KirKFC9e3CxevDjR9DshxZik+z459xO4\n0tond+/jypUrm8DAQPu8W7dumRo1aqQ7cJ04ccJ4enqaQ4cOJaqpU6dO9i/c5MTGxpqFCxeali1b\nmmLFihlPT0/zwgsvmKFDh9rDS+/evY2/v3+i523YsMHe3p0vxTthwhhj9u/fbw+vN27cMKVKlTJL\nly5NtH3VqlWzb1/37t3Na6+9Zg+6169fN5s2bTJ///13irVHRkaakSNHmpo1axpPT0/j6elpqlat\natatW2dfJiAgwLRv397+eMCAAaZq1aqJ1lO9enWzcOHCRNNmzpxpXnnlFWPM7XD05ZdfJpq/bNky\nU6xYMftjT09P8+GHH9of3/kPw92vxxYtWpjhw4cbY4zp16+f/bV+x2+//WY8PT3N2bNnzYYNG4yX\nl5eJjIy0z7+zz1MLXKVKlUoUmJcuXWq8vb1NVFSUWbJkialSpYqJi4uzz79165YpU6aM+eabb4wx\ntz83WrVqlez673jllVfsny2pSc97Lr2BK6XXljHp6+N58+aZypUr27f9448/ThSY8eDgHC7ct+vX\nr8vd3T3J9BdeeEGvvvqqunXrpvz586tq1aqqU6eOXn755VTX9+yzz6Y638fHJ9HjkiVLatOmTfdf\n+D0uXbqkCxcuJFl/+fLl9emnn9p/TWmz2RKdrO7u7q7Y2Nhk13no0KFka37xxRe1YcOGdNd28OBB\n+7lHx48fV7Zs2VLcT8eOHVNcXFyy25HcYZOUuLi4JHvOyJ1fUbq6utqnpXefXL58WRcvXkx0/lm2\nbNnu6xyYffv2SZJatWqVaHpMTEyiQ0r3cnFxUbt27dSuXTtdu3ZNv/76q1auXKnFixfLzc1N/fv3\n1+HDh1WzZs1EzytXrpyk2z9UKFWqlCSpUKFC9vlubm6Sbv/a9OjRo/r7778T7fts2bIl2t4uXbqo\nZ8+e9l+8Va9eXY0aNdIjjzySYu1PP/20hgwZoiFDhuj48ePatGmTFixYoD59+igkJMT+2rjX3efn\nXbp0SWfPntWECRM0efJk+/S4uDjFx8crJiZGL7zwgtzd3TVnzhwdOXJEJ0+e1P79+5P8crZgwYL2\nv3PkyCEnJ6dEbWXPnt3eF/v379fJkycT7ZM7r6ujR4/q8OHDyps3r55++mn7/PS8Hp5//nk99thj\n9sdlypRRbGysjh8/rn379unSpUv2vrvj5s2biQ7NpnX+Yt68ee3nO6bmv3rPSSm/tlJy7zb4+flp\n0qRJCgsLU82aNfX111+rTZs291UDHIPAhfu2d+9eFS9ePMl0m82madOm6a233tLPP/+ssLAwvfXW\nW2rcuLHGjRuX4vqyZ8+eant3zse5wxijbNmypbh8XFxcGltwW0pfePHx8ZJuf2FLt8+pufP33TUk\nJ6VtSUhISLKO5Pz5559q0KCBbt26JScnJwUHB9u/HH18fPT0009r1apV6d6O9LR5R+7cuRUVFZVk\n+p0voP/973/2aendJ3dqu3fe3eEtOXf64O5lFy9enGT/pvQ6WLdunU6cOKE333xT0u1tq1OnjurU\nqaN+/frp559/Vv/+/ZPtrzu13r19ydVrjLEvk9KlPaTbAe7O+yEsLEyLFi3SrFmztGTJEhUtWjTJ\n8hMmTNBLL72kihUrSrr9hVyoUCE1bNhQL7/8ssLCwlIMXHdvz52ahwwZogoVKiRZ1sXFRVu2bNGb\nb76p2rVrq2zZsmrevLlOnDiR5Nd49/a1zWZL8Qcfrq6uatKkibp27ZpkXr58+bRv3777fj0kV8Od\n14iTk5NcXV1VpEgRzZgxI8nz7v7PYVqfNT4+PlqxYoUSEhKS/Ho4ISFB3bt3V7NmzRKFpHtrSu09\nl9xnU0qvrZTcuw2PPfaYatSooW+//VZ58+ZVRESE/Pz8Unw+Mg4nzeO+HDhwQL///nuyb+jdu3dr\n3LhxKlKkiLp06aJ58+apb9++9hNJU/tFXmrujHDcsXPnThUpUkTS7Q+r69evJ5p/73WWUmrXzc1N\n+fPn186dOxNN37Fjh/Lly5coYKTXnbruXefdNafmiSee0PLly+Xk5KR58+YpNDRUvr6+atWqlUJD\nQ/XJJ58keY6Hh4dcXV2T3Y70tHmHt7d3knXcWY+Tk1OyITstuXLlUoECBfT777/bpxljEvXpnS+c\nu6/vduLECfvfd0LJxYsX5eHhYf83f/58rV+/Ptl2//rrL82YMSPRSdN3uLu720dKChcunKg2SfZr\nthUuXDjN7fPw8FD27NkVHh5unxYbG5to+2bMmKGdO3eqbt26GjFihNatWydXV9cURzy3bt2qefPm\nJZmeM2dOubi42GtP6/3k7u6uJ598UhEREYn22+bNmzV37lw5OTnp888/V9WqVTVt2jR17NhRlSpV\nUmRkpKR//gu5IkWK6OjRo4navHTpkiZMmKDr16/rhRde0OXLlxP18Z49e9Jc77FjxxK918PDw5U9\ne3Y9//zzKlq0qCIiIpQnTx57m4899pjGjRtnH3VOj6ZNm+ratWv68ssvk8xbtWqVfv75Zz3++OPp\nes+l57MpLen9zGzWrJk2bNigNWvWqHr16olGAvHgIHAhRTdu3ND58+d1/vx5nT59WqtWrVKPHj1U\nvnx5NWrUKMny7u7uWrRokT788EOdOnVK+/fv108//WQ/LJMrVy5Jtw85JDeSkpKvv/5aCxcu1LFj\nxzRlyhTt2bNHb7zxhqTbhxUuXryo+fPnKyIiQsHBwdq4cWOi5+fKlUtHjhxJ9oKrPXr00BdffKGl\nS5fq5MmTWrJkiRYuXKhOnTr9o4BYsGBBNWjQQMOHD1dYWJiOHj2qcePGae/evem6DIGLi4v+/vtv\n5c6dW+XLl5eHh4dOnDih6tWry8PDQ88880yS52TPnl2vv/66pk2bpjVr1ujEiRP65JNPtG7dOr3+\n+uvprr1z585au3atpk6dqqNHj+r48eNauXKlRo4cqbZt2ypv3rz3tS/u6Nmzp7744guFhobq2LFj\nGjNmjI4dO2af7+npqZw5c2r27Nk6deqUNm7cmChweHh4qH79+hoyZIh+/vlnnTp1SlOnTtXixYtT\nDEXNmjXTM888o44dO2r16tWKiIjQ3r179emnn2rFihXq3r27pNvXmrtzra5jx47pl19+0YgRI1Sz\nZs10Ba4cOXKobdu2mjZtmjZs2KCjR49q6NChOnPmjP31ExkZqREjRmjbtm2KjIzUypUrFRUVleJh\ntL59+2rjxo167733tHPnTkVERGjLli165513lC9fPvv1zXLlyqWzZ8/q9OnTKY7q9ujRQ/Pnz9dX\nX32lU6dO6ZtvvtH48ePtl+3Inz+/Dhw4oF27dun06dNasGCBPv/8c0lK9XBtarp27ao//vhD48aN\n09GjR/Xrr79qwIABioqKUr58+VSxYkV5e3urf//+2r17t3bu3KnRo0enud7o6GgFBAToyJEj+umn\nnzRt2jS1bdtWOXLkkJ+fn/Lmzas+ffpo9+7dOnTokPr166fw8PBkRxFT4unpqbfeektjxozR1KlT\ndfDgQR09elSfffaZhgwZovbt26tcuXLpes+l57MpLenpY0l66aWX5OzsrEWLFqlZs2b31QYch0OK\nSFFQUJCCgoIk3X7jP/PMM2rVqpU6deqU5DCfJD333HP6+OOP9dFHH+mLL76Qq6urqlevrkGDBkm6\n/T9fX19f9e3bV23atFGdOnXSVUeXLl20evVqjR8/XoUKFdLs2bPtX4aVKlXS22+/raCgIE2dOlU1\natRQ7969tWjRIvvzu3btqpkzZ2rz5s0KDQ1NtO7WrVvr77//1pw5czRixAg9++yzGjhwoP0yCv/E\nqFGjNGnSJPXv3183btzQCy+8oLlz5yY53yMl4eHhKlOmjKTbX3r79++3P05J79695eTkpLFjx+ry\n5csqXLiwPvzwQ7366qvprrtKlSqaM2eOPvnkEwUHB+vWrVsqUKCAXnvttfsKbvdq3ry5oqKiNHXq\nVF29elW+vr6J9oWbm5smTZqkyZMnq379+ipWrJgGDBigXr162ZcZPXq0pkyZooCAAEVFRalw4cIK\nDAxU5cqVk23Tzc1NwcHBmjVrlqZNm6YzZ87I1dVVpUuXVlBQkP0Qm6enp2bPnq1p06ZpwYIFypMn\njxo0aKA+ffqke/v69u2rmJgYvf/++4qNjVXDhg3l4+NjH7kbPHiwJkyYoH79+unKlSvy8PDQuHHj\nkj3MJ0k1atTQggULFBQUpF69eikqKkqPPvqoateurTFjxtgPKTVr1kw//PCD6tevn+j1frc2bdoo\nJiZGc+fO1ahRo/Tkk0+qZ8+e9kOtvXv31rlz59SlSxc5OzvLy8tL48ePV9++fbV79+4k50Slh5eX\nl+bMmaPp06crODhY7u7uevnll/X+++9Lun2KQFBQkEaMGKGOHTvKzc1Nffr0UUBAQKrrLVCggAoW\nLKhWrVopZ86c8vf311tvvSXp9n865s2bp/Hjx+u1116TzWZTmTJl9Pnnn9/3aE/Pnj1VuHBhLViw\nQIsXL1ZMTIwKFSqkDz74QM2bN7cvl9Z7Lj2fTWlJTx9Lt0fTGjRooG+//VYvvfTSfW0vHMdm/um4\nMQD8Q506dVL+/Pk1fvz4jC7lX/vhhx/04osvJhoBrFevnvz8/BKFRvxzgYGBWrlypb7//vuMLuWB\n1bt3bz3xxBMaPHhwRpeCFDDCBQD/QlBQkJYtW6Z3331X2bNnV0hIiCIiIjL81kZ4OISFhenAgQP6\n8ccfuQ3QA47ABQD/wuTJkzV27Fi1b99eMTExKlasmD799NN0nQMG/FtLlizRpk2bNHDgQF5zDzgO\nKQIAAFiMXykCAABYjMAFAABgsQf6HK7z59N/rab7lTdvTl2+fMOy9cMx6MfMjz7M/OjDzI8+/G/k\ny5f0tnd3PLQjXC4uSa8jhcyHfsz86MPMjz7M/OhD61k2whUfH6/Bgwfr+PHjstlsGjFihB555BEN\nHDhQNptNRYsW1bBhw5LcrwoAACCrsSxw/fTTT5Ju33B227Ztmjp1qowx6tOnjypWrKihQ4dq/fr1\nqlu3rlUlAAAAPBAsvSxEXFycXFxctGLFCm3dulWbN2/Wxo0bZbPZ9MMPP2jTpk1J7kqf+PnxDHMC\nAIBMz9KT5l1cXDRgwAB9//33+uijj7Rp0yb7DV1z5cqV5g2MrTyBL18+d0tPyodj0I+ZH32Y+dGH\nmR99+N/I0JPmJ0yYoLVr12rIkCG6deuWffr169eVO3duq5sHAADIcJYFrtDQUM2ZM0eSlCNHDtls\nNpUoUULbtm2TJG3cuPEf3YkeAAAgs7HskOIrr7yiQYMGqV27doqLi1NAQIAKFy6sIUOG6MMPP9Tz\nzz8vX19fq5oHAAB4YFgWuHLmzKnp06cnmb5w4UKrmgQAAHggcREsAAAAixG4AAAALEbgAgAAsBiB\nCwAAwGIELgAAAItZeqV5AAAeRp3H/5jRJfwnPhtYK6NLyDIY4QIAALAYgQsAAMBiBC4AAACLEbgA\nAAAsRuACAACwGIELAADAYgQuAAAAixG4AAAALEbgAgAAsBiBCwAAwGIELgAAAIsRuAAAACxG4AIA\nALAYgQsAAMBiBC4AAACLEbgAAAAsRuACAACwGIELAADAYgQuAAAAixG4AAAALEbgAgAAsBiBCwAA\nwGIELgAAAIsRuAAAACxG4AIAALAYgQsAAMBiBC4AAACLEbgAAAAsRuACAACwGIELAADAYgQuAAAA\nixG4AAAALEbgAgAAsBiBCwAAwGIELgAAAIsRuAAAACxG4AIAALAYgQsAAMBiBC4AAACLuVix0tjY\nWAUEBCgyMlIxMTHq0aOHnnrqKXXr1k3PPfecJKlNmzaqX7++Fc0DAAA8UCwJXCtXrlSePHk0adIk\nXblyRU2aNFGvXr30+uuvq3PnzlY0CQAA8MCyJHDVq1dPvr6+kiRjjJydnbVnzx4dP35c69evl4eH\nhwICAuTm5mZF8wAAAA8UmzHGWLXy6Oho9ejRQ61atVJMTIy8vLxUokQJzZo1S9euXdOAAQNSfX5c\nXLxcXJytKg8AAEv49fs6o0v4T3wzpXFGl5BlWDLCJUlnzpxRr1691LZtW/n5+enatWvKnTu3JKlu\n3boaNWpUmuu4fPmGVeUpXz53nT8fZdn64Rj0Y+ZHH2Z+9GHWRb/en3z53FOcZ8mvFC9cuKDOnTur\nf//+atGihSSpS5cu+uOPPyRJW7Zskbe3txVNAwAAPHAsGeGaPXu2rl27ppkzZ2rmzJmSpIEDB2rs\n2LFydXXV448/nq4RLgAAgKzAksA1ePBgDR48OMn0xYsXW9EcAADAA40LnwIAAFiMwAUAAGAxAhcA\nAIDFCFwAAAAWI3ABAABYjMAFAABgMQIXAACAxQhcAAAAFiNwAQAAWIzABQAAYDECFwAAgMUIXAAA\nABYjcAEAAFiMwAUAAGAxAhcAAIDFCFwAAAAWI3ABAABYjMAFAABgMQIXAACAxQhcAAAAFiNwAQAA\nWIzABQAAYDECFwAAgMUIXAAAABYjcAEAAFiMwAUAAGAxAhcAAIDFCFwAAAAWI3ABAABYjMAFAABg\nMQIXAACAxQhcAAAAFiNwAQAAWIzABQAAYDECFwAAgMUIXAAAABYjcAEAAFiMwAUAAGAxAhcAAIDF\nCFwAAAAWI3ABAABYjMAFAABgMQIXAACAxQhcAAAAFiNwAQAAWIzABQAAYDEXK1YaGxurgIAARUZG\nKiYmRj169FCRIkU0cOBA2Ww2FS1aVMOGDZOTE3kPAABkfZYErpUrVypPnjyaNGmSrly5oiZNmqhY\nsWLq06ePKlasqKFDh2r9+vWqW7euFc0DAAA8UCwZYqpXr57eeecdSZIxRs7Oztq7d68qVKggSapR\no4Y2b95sRdMAAAAPHEtGuHLlyiVJio6OVu/evdWnTx9NmDBBNpvNPj8qKirN9eTNm1MuLs5WlChJ\nypfP3bJ1w3Hox8yPPsz86MOsiX7971gSuCTpzJkz6tWrl9q2bSs/Pz9NmjTJPu/69evKnTt3muu4\nfPmGVeUpXz53nT+fdujDg41+zPzow8yPPsy66Nf7k1pAteSQ4oULF9S5c2f1799fLVq0kCQVL15c\n27ZtkyRt3LhR5cqVs6JpAACAB44lgWv27Nm6du2aZs6cqQ4dOqhDhw7q06ePAgMD5e/vr9jYWPn6\n+lrRNADNnxqzAAAb9ElEQVQAwAPHkkOKgwcP1uDBg5NMX7hwoRXNAQAAPNC4EBYAAIDFCFwAAAAW\nI3ABAABYjMAFAABgMQIXAACAxQhcAAAAFiNwAQAAWIzABQAAYDECFwAAgMUIXAAAABa7r8B1+vRp\nbd++3apaAAAAsqQ076UYHBysHTt26IMPPlDr1q3l5uamV155Rf369XNEfQAAAJlemiNcy5Yt06BB\ng7RmzRrVrl1bq1at0qZNmxxRGwAAQJaQZuCy2Wx6/PHHtWXLFlWqVEkuLi5KSEhwRG0AAABZQpqB\nK1u2bAoKCtKvv/6qqlWrKjg4WDly5HBEbQAAAFlCmoFrzJgxOnHihCZMmKD//e9/2rFjh0aPHu2I\n2gAAALKENE+af/755zVkyBCdPHlSxhiNGTNG2bNnd0RtAAAAWUKaI1y7du1SnTp11K1bN509e1Y1\na9bUzp07HVEbAABAlpBm4Jo4caLmz5+vPHnyKH/+/Jo4caLGjBnjiNoAAACyhDQD199//60iRYrY\nH9esWVPx8fGWFgUAAJCVpBm4XFxcdPXqVdlsNknSsWPHLC8KAAAgK0nzpPnu3burffv2unDhgt59\n911t2rRJI0eOdERtAAAAWUKagatWrVoqXLiwNm3apISEBPXs2TPRIUYAAACkLsVDikePHpUk7d27\nV9HR0SpdurR8fHx069Yt7d2712EFAgAAZHYpjnBNnDhRc+bM0dtvv51kns1m0/r16y0tDAAAIKtI\nMXDNmTNHkhQQEKA6deo4rCAAAICsJs1fKU6dOtURdQAAAGRZaZ407+npqVmzZqlcuXLKmTOnfbq3\nt7elhQEAAGQVaQau8PBwhYeHa+nSpfZpnMMFAACQfmkGruDgYOXPnz/RtMOHD1tWEAAAQFaT4jlc\nV65c0ZUrV/Tmm2/q6tWrunLliq5evaoLFy6oV69ejqwRAAAgU0txhKtfv37atGmTJKlixYr26c7O\nzqpbt671lQEAAGQRKQauuXPnSpIGDRqkcePGOawgAACArCbNc7jGjRunyMhIXb16VcYY+3R+pQgA\nAJA+aQauyZMna8GCBXrsscfs0/iVIgAAQPqlGbhWr16tdevW6cknn3REPQAAAFlOmleaf+qppwhb\nAAAA/0KaI1yVK1fWxIkTVbt2bWXPnt0+nXO4AAAA0ifNwBUSEiJJWrNmjX0a53ABAACkX5qB68cf\nf3REHQAAAFlWmoFr3rx5yU5//fXX//NiAAAAsqI0A9ehQ4fsf8fExGjHjh2JrjwPAACA1KXrwqd3\nu3Tpkt5//33LCgIAAMhq0rwsxL0effRRRUZGWlELAABAlnRf53AZY7Rnz55EV50HAABA6u7rHC7p\n9oVQ03tIMTw83H5roH379qlbt2567rnnJElt2rRR/fr1779iAACATCbd53BFRkYqLi5OHh4e6Vpx\nUFCQVq5cqRw5ckiS9u7dq9dff12dO3f+F+UCAABkPmmew3Xy5Ek1aNBATZo0UbNmzVSnTh0dPXo0\nzRUXLFhQgYGB9sd79uzRhg0b1K5dOwUEBCg6OvrfVQ4AAJBJpDnCNXLkSL3xxhtq2rSpJGn58uUa\nMWKEvvjii1Sf5+vrq4iICPvjUqVKqWXLlipRooRmzZqljz/+WAMGDEh1HXnz5pSLi3N6tuMfyZfP\n3bJ1w3Hox8yPPsz86MOsiX7976QZuC5evGgPW5LUvHlzzZ8//74bqlu3rnLnzm3/e9SoUWk+5/Ll\nG/fdTnrly+eu8+ejLFs/HIN+zPzow8yPPsy66Nf7k1pATfOQYnx8vK5cuWJ/fOnSpX9URJcuXfTH\nH39IkrZs2cLNrwEAwEMjzRGu9u3by9/fX6+++qok6bvvvtNrr7123w0NHz5co0aNkqurqx5//PF0\njXABAABkBWkGLn9/fxUsWFBhYWFKSEjQsGHDVKVKlXStvECBAlqyZIkkydvbW4sXL/531QIAAGRC\nqQauy5cvKyEhQZUrV1blypW1ZcsWeXl5Oao2AACALCHFc7gOHz6sV199VTt37rRP+/7779WoUSMd\nO3bMIcUBAABkBSkGrilTpuiDDz5Q3bp17dOGDh2qd999V5MmTXJIcQAAAFlBioErMjJSfn5+SaY3\na9ZMp0+ftrQoAACArCTFwOXikvLpXa6urpYUAwAAkBWlGLgee+wx7d+/P8n0ffv22e+PCAAAgLSl\nOIzVs2dP9ezZU7169ZKPj4+MMfr99981c+ZMjR492pE1AgAAZGopBq6yZctq4sSJCgwM1NixY+Xk\n5KQyZcpo0qRJKleunCNrBAAAyNRSvQ5X+fLl07xJNQAAAFKX5r0UAQAA8O8QuAAAACyWYuAKDw93\nZB0AAABZVoqBa9iwYZKk1157zWHFAAAAZEUpnjQfHx+vzp07a9++ferevXuS+bNnz7a0MAAAgKwi\nxcAVFBSkrVu36vjx4/L19XVkTQAAAFlKioErf/78atKkiZ566ilVrFhRkZGRiouLk4eHhyPrAwAA\nyPRSvQ6XJD355JNq0KCBzp07p4SEBOXNm1dz5sxR4cKFHVEfAABAppfmZSFGjRqlN954Q9u3b9eO\nHTvUo0cPjRgxwhG1AQAAZAlpBq6LFy+qadOm9sfNmzfX5cuXLS0KAAAgK0kzcMXHx+vKlSv2x5cu\nXbK0IAAAgKwmzXO42rdvL39/f7366quSpO+++45rcwEAANyHNAOXv7+/ChYsqLCwMCUkJGjYsGGq\nUqWKI2oDAADIEtIMXJJUuXJlVa5c2epaAAAAsiRuXg0AAGAxAhcAAIDF0gxcwcHByf4NAACA9Ekx\ncPn6+ur999/XvHnzdODAAcXGxmrp0qWOrA0AACBLSDFwffvtt2rRooWio6P18ccfy8/PTydOnNCY\nMWP0/fffO7JGAACATC3FwBUREaEKFSroySefVGBgoNasWaMCBQqoYsWK2rlzpyNrBAAAyNRSvCzE\nmDFjdPr0aV27dk2ffPKJihcvLkmqU6eO6tSp47ACAQAAMrsUR7g+/fRTrVq1Srly5ZK7u7u+//57\nnT59Wg0bNtTQoUMdWSMAAECmluqFT11cXPT888+rTZs2kqQzZ85o2rRp2rVrl0OKAwAAyArSvNL8\nJ598kuRvbu0DAACQflz4FAAAwGIELgAAAIsRuAAAACxG4AIAALAYgQsAAMBiBC4AAACLEbgAAAAs\nRuACAACwGIELAADAYgQuAAAAixG4AAAALEbgAgAAsBiBCwAAwGKWBq7w8HB16NBBknTy5Em1adNG\nbdu21bBhw5SQkGBl0wAAAA8MywJXUFCQBg8erFu3bkmSxo0bpz59+ig4OFjGGK1fv96qpgEAAB4o\nlgWuggULKjAw0P547969qlChgiSpRo0a2rx5s1VNAwAAPFBcrFqxr6+vIiIi7I+NMbLZbJKkXLly\nKSoqKs115M2bUy4uzlaVqHz53C1bNxyHfsz86MPMjz7MmujX/45lgeteTk7/P5h2/fp15c6dO83n\nXL58w7J68uVz1/nzaYc+PNjox8yPPsz86MOsi369P6kFVIf9SrF48eLatm2bJGnjxo0qV66co5oG\nAADIUA4LXAMGDFBgYKD8/f0VGxsrX19fRzUNAACQoSw9pFigQAEtWbJEklSoUCEtXLjQyuYAAAAe\nSFz4FAAAwGIELgAAAIsRuAAAACxG4AIAALAYgQsAAMBiBC4AAACLEbgAAAAsRuACAACwGIELAADA\nYgQuAAAAixG4AAAALEbgAgAAsBiBCwAAwGIELgAAAIsRuAAAACxG4AIAALAYgQsAAMBiBC4AAACL\nEbgAAAAsRuACAACwGIELAADAYgQuAAAAixG4AAAALEbgAgAAsBiBCwAAwGIELgAAAIsRuAAAACxG\n4AIAALAYgQsAAMBiBC4AAACLEbgAAAAsRuACAACwGIELAADAYgQuAAAAixG4AAAALEbgAgAAsBiB\nCwAAwGIuGV0AAAB4MHUe/2NGl/Cf+WxgrQxtnxEuAAAAixG4AAAALEbgAgAAsBiBCwAAwGIELgAA\nAIsRuAAAACxG4AIAALCYw6/D1bRpU7m5uUmSChQooHHjxjm6BAAAAIdyaOC6deuWjDFasGCBI5sF\nAADIUA49pHjgwAHdvHlTnTt3VseOHbVr1y5HNg8AAJAhHDrClT17dnXp0kUtW7bUiRMn1LVrV61Z\ns0YuLsmXkTdvTrm4OFtWT7587patG45DP2Z+9GHmRx/iQZfRr1GHBq5ChQrJw8NDNptNhQoVUp48\neXT+/Hk99dRTyS5/+fINy2rJl89d589HWbZ+OAb9mPnRh5kffYjMwBGv0dRCnUMPKS5btkzjx4+X\nJJ09e1bR0dHKly+fI0sAAABwOIeOcLVo0UKDBg1SmzZtZLPZNHbs2BQPJwIAAGQVDk072bJl05Qp\nUxzZJAAAQIbjwqcAAAAWI3ABAABYjMAFAABgMQIXAACAxQhcAAAAFiNwAQAAWIyLYGUhncf/mNEl\nIBmfDayV0SUAADIYI1wAAAAWI3ABAABYjMAFAABgMQIXAACAxQhcAAAAFiNwAQAAWIzABQAAYDEC\nFwAAgMUIXAAAABYjcAEAAFiMW/sAQCaWlW7pxW2wkJUxwgUAAGAxAhcAAIDFCFwAAAAWI3ABAABY\njMAFAABgMQIXAACAxQhcAAAAFiNwAQAAWIzABQAAYDGuNK+sdaVmPHh4fQEAGOECAACwGIELAADA\nYgQuAAAAixG4AAAALEbgAgAAsBiBCwAAwGIELgAAAIsRuAAAACxG4AIAALAYgQsAAMBi3NoHAPBA\n4DZYyMoY4QIAALAYgQsAAMBiBC4AAACLEbgAAAAsRuACAACwGIELAADAYgQuAAAAizn0OlwJCQka\nPny4Dh48qGzZsmn06NHy8PBwZAkAAAAO59ARrh9++EExMTH66quv1K9fP40fP96RzQMAAGQIhwau\nHTt2qHr16pKkMmXKaM+ePY5sHgAAIEM49JBidHS03Nzc7I+dnZ0VFxcnF5fky8iXz93Seu6s/5sp\njS1tBwAAPNwcOsLl5uam69ev2x8nJCSkGLYAAACyCocGrrJly2rjxo2SpF27dsnT09ORzQMAAGQI\nmzHGOKqxO79SPHTokIwxGjt2rAoXLuyo5gEAADKEQwMXAADAw4gLnwIAAFiMwAUAAGCxh+4nglzt\nPnNr2rSp/dIiBQoUkL+/v8aMGSNnZ2dVq1ZNb731VgZXiJSEh4dr8uTJWrBggU6ePKmBAwfKZrOp\naNGiGjZsmJycnDRjxgxt2LBBLi4uCggIUKlSpTK6bNzl7j7ct2+funXrpueee06S1KZNG9WvX58+\nfEDFxsYqICBAkZGRiomJUY8ePVSkSBHeh45kHjJr1641AwYMMMYY8/vvv5vu3btncEVIr7///ts0\nbtw40bRGjRqZkydPmoSEBPPGG2+YvXv3ZlB1SM0nn3xiGjZsaFq2bGmMMaZbt25m69atxhhjhgwZ\nYtatW2f27NljOnToYBISEkxkZKRp1qxZRpaMe9zbh0uWLDFz585NtAx9+OBatmyZGT16tDHGmMuX\nL5uaNWvyPnSwh+6QIle7z7wOHDigmzdvqnPnzurYsaO2b9+umJgYFSxYUDabTdWqVdPmzZszukwk\no2DBggoMDLQ/3rt3rypUqCBJqlGjhjZv3qwdO3aoWrVqstlsevrppxUfH69Lly5lVMm4x719uGfP\nHm3YsEHt2rVTQECAoqOj6cMHWL169fTOO+9IkowxcnZ25n3oYA9d4Erpavd48GXPnl1dunTR3Llz\nNWLECA0aNEg5cuSwz8+VK5eioqIysEKkxNfXN9FFjo0xstlskv6/3+59b9KfD5Z7+7BUqVJ6//33\ntWjRIj377LP6+OOP6cMHWK5cueTm5qbo6Gj17t1bffr04X3oYA9d4OJq95lXoUKF1KhRI9lsNhUq\nVEju7u66cuWKff7169eVO3fuDKwQ6eXk9P8fPXf67d735vXr1+Xubu3tvfDP1a1bVyVKlLD/vW/f\nPvrwAXfmzBl17NhRjRs3lp+fH+9DB3voAhdXu8+8li1bpvHjx0uSzp49q5s3bypnzpw6deqUjDEK\nCwtTuXLlMrhKpEfx4sW1bds2SdLGjRtVrlw5lS1bVmFhYUpISNCff/6phIQEPfrooxlcKVLSpUsX\n/fHHH5KkLVu2yNvbmz58gF24cEGdO3dW//791aJFC0m8Dx3toRvaqVu3rjZt2qTWrVvbr3aPzKFF\nixYaNGiQ2rRpI5vNprFjx8rJyUnvvfee4uPjVa1aNZUuXTqjy0Q6DBgwQEOGDNGHH36o559/Xr6+\nvnJ2dla5cuXk7++vhIQEDR06NKPLRCqGDx+uUaNGydXVVY8//rhGjRolNzc3+vABNXv2bF27dk0z\nZ87UzJkzJUkffPCBRo8ezfvQQbjSPAAAgMUeukOKAAAAjkbgAgAAsBiBCwAAwGIELgAAAIsRuAAA\nACxG4AIeQl5eXklu17FmzRp16NAhzed27dpVR44csao0u9jYWE2cOFF+fn5q1KiR/Pz8NHv2bGX0\nD6tDQkLUrFkzNWrUSA0aNNAHH3xgvxL36dOn9fbbb2dofWm5dOmSvLy8MroM4KHz0F2HC8C/ExQU\n5JB2Pv/8c0VERGjFihVycXFRVFSUXnvtNeXNm1f+/v4OqeFef/zxhz7++GMtX75cefLkUXx8vEaM\nGKHhw4drypQp+vPPP3X8+PEMqQ3Ag43ABSCJwMBARUZG6vz584qMjNSjjz6qqVOn6sknn1StWrU0\nffp0lSxZUtOnT9c333yjvHnzqly5ctqzZ48WLFiggQMHqmjRourSpYskJXp89uxZjRw5UmfOnFFs\nbKwaNGig7t27J6nh/Pnzio2NVUxMjFxcXOTu7q6JEycqISFBkvTXX39p+PDhioyMlDFGTZo00Rtv\nvKGIiAh16tRJNWvWVHh4uK5evaq+ffuqfv36unnzpoYNG6bw8HC5u7urSJEikqTx48crODhYixcv\nlqurqx555BGNHDnSPv/umowx+vvvvyXdvhfrO++8o8OHDys+Pl6DBw/W2bNn1aVLF40YMULt2rVT\n4cKFFRkZqQULFigiIkKTJ0/WzZs3ZbPZ9Pbbb+vll1/WjRs3NHz4cJ04cUJXr15Vrly5NHnyZD3/\n/PPq0KGDvL29tXXrVl28eFEdO3bUxYsX9euvv+rmzZuaNm2avLy8FBUVpTFjxujQoUOKjY1V5cqV\n9f7778vFxUXr1q3T1KlTlSNHDvvteAA4FocUASTrt99+0/Tp07VmzRrlzp1bX331VaL569at07p1\n6xQaGqrg4OB0H2bs37+/mjdvrpCQEC1btkybN2/W6tWrkyz3+uuv6+zZs6pUqZI6dOigqVOnKiYm\nxn47rvfee08VK1bUN998oy+//FIrV67UqlWrJN0+tFetWjUtW7ZM7733niZNmiRJmjlzpuLj4/Xd\nd99p/vz52rdvnyQpPj5eY8eO1aeffqrly5erVatW2rFjR5KaatSoIR8fH9WqVUtNmzbVyJEjtXv3\nblWsWFHOzs4aPXq0ChYsqLlz50q6HQp79uyptWvX6pFHHtGgQYM0ceJErVixQrNmzdLw4cP1559/\nauPGjcqdO7eWLFmitWvXqkSJElq0aJG93cjISIWGhmrGjBmaPHmyKlSooJCQEFWvXl0LFy6UJI0d\nO1be3t4KCQlRaGioLl++rHnz5unChQsKCAhQYGCgQkJC9Mwzz6SrnwD8txjhAh5CNpstybSEhIRE\nN7OtUKGC3NzcJN2+59rVq1cTLb9161bVrVvXvoy/v78+//zzVNu9ceOGtm/frqtXr2r69On2aQcO\nHFD9+vUTLZs/f36FhIToyJEj2rZtm7Zt2yZ/f38NHDhQTZs21c6dO/XZZ59Jktzd3dWsWTNt3LhR\npUuXlqurq2rWrGmv/c5Nzn/++WcNGjRITk5OcnNzU9OmTXXw4EE5OzurXr16at26tV566SVVrVpV\nfn5+Sep3dXXVlClT9P7772vbtm3avn27BgwYoMqVK2vatGlJlndxcVGZMmUk3b536/nz59WrVy/7\nfJvNpoMHD6pevXp69tlntWDBAp08eVK//vqrfHx87MvVrVtXkvTss89KkqpXry5JKliwoH799VdJ\n0oYNG7R7924tW7ZMkuyjcDt27JCnp6d9tM7f318ffvhhqv0E4L9H4AIeQnnz5tWVK1cS3ZT24sWL\nypMnj/1x9uzZ7X/bbLYkJ6s/8sgjiaa5urqmuHxsbKyk26HOGKPFixcrR44ckm6fxP3II48kqXHi\nxIlq2bKlihQpoiJFiqhdu3b6+uuvFRQUpMaNGyepJyEhQXFxcfZa7oTHu8Oli4tLoufdHTAnT56s\nQ4cOafPmzQoKCtKyZcs0a9asRG0sW7ZMefPmVe3atdWoUSM1atRIPXr0UK1atZL8CEGSsmXLJheX\n2x+z8fHxKly4sJYuXWqff/bsWT366KMKDg7WkiVL1K5dO/n5+SlPnjyKiIhItJ673b2v797+6dOn\nq3DhwpKka9euyWazacuWLYm2+U49AByLQ4rAQ6hGjRpasGCB/Xyoq1evasWKFfZRofR46aWXtGbN\nGl29elUJCQkKDQ21z8ubN6/27Nkj6Xag+u233yRJbm5uKlOmjObNmyfpdiho06aN1q9fn2T9ly5d\n0vTp03Xz5k1JkjFGx48fV/HixeXm5qbSpUvbD7tFRUUpNDRUVapUSbXmmjVravny5UpISNDNmzf1\n7bffymaz6dKlS6pZs6by5MmjTp06qU+fPjp48GCS5zs5OWny5Mn666+/7NNOnDihZ555Rv/73//k\n7OxsD5f3KlOmjE6ePKnt27dLkvbv3y9fX1+dO3dOYWFhatq0qVq2bKlChQrpxx9/VHx8fKrbcq9q\n1app/vz5MsYoJiZGPXr00MKFC1WuXDkdOXJEBw4ckHT7V5YAHI//6gAPoQ8++EDjx49Xw4YN5ezs\nLElq3LixmjZtmu51VKxYUR07dlTbtm31yCOPJDo3qEOHDnrvvffk6+urAgUKqEKFCvZ5kydP1qhR\no+Tn56eYmBg1bNhQjRo1SrL+YcOGaerUqWrUqJGyZcumuLg4VapUSUOHDrWvZ+TIkQoJCVFMTIz8\n/PzUrFkzRUZGplhzt27dNHLkSPn5+cnd3V2PPfaYsmfPrkcffVQ9evRQp06dlD17dvv5WPdq1qyZ\nbt68qa5duyomJkY2m03PPfecPv30Uzk7O6to0aJydnZWixYtNHXq1ETPffTRR/XRRx9p4sSJunXr\nlowxmjhxop555hl17txZQ4cOVUhIiJydneXt7a1Dhw6luy+k2306ZswY+fn5KTY2VlWqVNEbb7wh\nV1dXTZ48We+9955cXV1Vvnz5+1ovgP+GzWT0RW0AZAlr1qzRokWLtGDBgowuJUWrVq2Sm5ubatas\nqYSEBL399tuqWrWq2rZtm9GlAcjiOKQI4KFRtGhRzZo1S40bN1bDhg31xBNPqGXLlhldFoCHACNc\nAAAAFmOECwAAwGIELgAAAIsRuAAAACxG4AIAALAYgQsAAMBiBC4AAACL/R8WAdOG/jmsrQAAAABJ\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b8bec18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "\n",
    "songs_rated_by_country = (ratings_matrix.R_ui > 0).sum(axis=1)\n",
    "plt.hist(songs_rated_by_country)\n",
    "plt.title('Distribution of # of Unique Songs Streamed per Country', fontsize=15)\n",
    "plt.xlabel('Unique Songs Streamed', fontsize=12)\n",
    "_ = plt.ylabel('# of Countries', fontsize=12)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Construct training, validation sets\n",
    "\n",
    "In reviewing literature on recommender engine evaluation, it seems common to create training and validation sets as follows:\n",
    "1. Filter your ratings matrix for users (countries) that meet some criterion, i.e. they've streamed above a certain threshold of songs.\n",
    "2. Select a random $x\\%$ of their items (songs).\n",
    "3. \"Move\" these items into a validation matrix; set them to 0 in the training matrix.\n",
    "\n",
    "To construct this split, I first compute a sensible threshold for Step #1, then \"move\" a random 20% of songs from the training matrix to the validation matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The 15th percentile of songs rated by country is 54.5.\n"
     ]
    }
   ],
   "source": [
    "print('The 15th percentile of songs rated by country is {}.'.format(\n",
    "    np.percentile(songs_rated_by_country, 15)\n",
    "))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's choose 50 songs as our cutoff, and move 20% of the songs in qualifying rows to a validation set.\n",
    "\n",
    "NB: The actual ratings matrix is located at `RatingsMatrix.R_ui`. This reflects an API choice I made when first starting this project."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def split_ratings_matrix_into_training_and_validation(ratings_matrix, eligibility_mask, fraction_to_drop=.2):\n",
    "    training_matrix = ratings_matrix\n",
    "    validation_matrix = deepcopy(training_matrix)\n",
    "    validation_matrix.R_ui = pd.DataFrame(0., index=training_matrix.R_ui.index, columns=training_matrix.R_ui.columns)\n",
    "\n",
    "    for country_id, ratings in training_matrix.R_ui[eligibility_mask].iterrows():\n",
    "        \n",
    "        rated_songs_mask = training_matrix.R_ui.ix[country_id] > 0\n",
    "        rated_songs = training_matrix.R_ui.ix[country_id][rated_songs_mask].index.tolist()\n",
    "        n_songs_to_drop = int( len(rated_songs)*fraction_to_drop )\n",
    "        songs_to_drop = set( random.sample(rated_songs, n_songs_to_drop) )\n",
    "        \n",
    "        validation_matrix.R_ui.ix[country_id][songs_to_drop] = training_matrix.R_ui.ix[country_id][songs_to_drop]\n",
    "        training_matrix.R_ui.ix[country_id][songs_to_drop] = 0.\n",
    "\n",
    "    return training_matrix, validation_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "more_than_50_ratings_mask = songs_rated_by_country > 50\n",
    "\n",
    "training_matrix, validation_matrix = split_ratings_matrix_into_training_and_validation(\n",
    "    ratings_matrix=ratings_matrix, \n",
    "    eligibility_mask=more_than_50_ratings_mask\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Evaluation\n",
    "\n",
    "Evaluating recommender systems is an inexact science because there is no \"right\" answer. In production, this evaluation is often done via the A/B test of a proxy metric important to the business - revenue, for example. In training, the process is less clear. To this end, the authors of the IMF paper offer the following:\n",
    "\n",
    "> Evaluation of implicit-feedback recommender requires appropriate measures. In the traditional setting where a user is specifying a numeric score, there are clear metrics such as mean squared error to measure success in prediction. However with implicit models we have to take into account availability of the item, competition for the item with other items, and repeat feedback. For example, if we gather data on television viewing, it is unclear how to evaluate a show that has been watched more than once, or how to compare two shows that are on at the same time, and hence cannot both be watched by the user.\n",
    "\n",
    "Additionally, they state:\n",
    "\n",
    "> It is important to realize that we do not have a reliable feedback regarding which programs are unloved, as not watching a program can stem from multiple different reasons. In addition, we are currently unable to track user reactions to our recommendations. Thus, precision based metrics are not very appropriate, as they require knowing which programs are undesired to a user. However, watching a program is an indication of liking it, making recall-oriented measures applicable.\n",
    "\n",
    "In solution, they propose evaluating the \"expected percentile ranking\" defined as follows:\n",
    "\n",
    "$$\n",
    "\\overline{\\text{rank}} = \\frac{\\sum_{u, i}\\tilde{r}_{u, i}^t\\text{rank}_{u, i}}{\\sum_{u, i}\\tilde{r}_{u, i}^t}\n",
    "$$\n",
    "\n",
    "Here, $\\text{rank}_{u, i}$ gives the percentile-ranking of the predicted preference, i.e. if $\\hat{p}_{u = 17, i = 34}$ is the largest of all predicted preferences, then $\\text{rank}_{u = 17, i = 34} = 0\\%$. Similarly, the smallest of the predicted preferences, i.e. the last on the list, equals $100\\%$.\n",
    "\n",
    "The following class accepts a training matrix, validation matrix and a matrix of predicted preferences. It then exposes the mean expected percentile ranking for both training and validation sets as properties on the instance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class ExpectedPercentileRankingsEvaluator:\n",
    "    \n",
    "    def __init__(self, training_matrix, validation_matrix, eligibility_mask, predicted_preferences):\n",
    "        self.training_matrix = training_matrix\n",
    "        self.validation_matrix = validation_matrix\n",
    "        self.eligibility_mask = eligibility_mask\n",
    "        self.predicted_preferences = predicted_preferences\n",
    "        self._expected_percentile_rankings_train = []\n",
    "        self._expected_percentile_rankings_validation = []\n",
    "        \n",
    "    def run(self):\n",
    "        self._evaluate_train()\n",
    "        self._evaluate_validation()\n",
    "\n",
    "    def _evaluate_train(self):\n",
    "        self._expected_percentile_rankings_train = self._evaluate(matrix=self.training_matrix)\n",
    "        \n",
    "    def _evaluate_validation(self):\n",
    "        self._expected_percentile_rankings_validation = self._evaluate(matrix=self.validation_matrix)\n",
    "        \n",
    "    def _evaluate(self, matrix):\n",
    "        expected_percentile_rankings = []\n",
    "        for country_id, preferences in self.predicted_preferences[self.eligibility_mask].iterrows():\n",
    "            predictions = pd.DataFrame({\n",
    "                'predicted_preference': preferences.sort_values(ascending=False),\n",
    "                'rank': np.arange( len(preferences) ),\n",
    "                'percentile_rank': np.arange( len(preferences) ) / len(preferences)\n",
    "            })\n",
    "            ground_truth = matrix.R_ui.ix[country_id][ matrix.R_ui.ix[country_id] > 0 ]\n",
    "            numerator = (ground_truth * predictions['percentile_rank'][ground_truth.index]).sum()\n",
    "            denominator = ground_truth.sum()\n",
    "            expected_percentile_rankings.append( numerator / denominator )\n",
    "\n",
    "        return expected_percentile_rankings\n",
    "\n",
    "    @property\n",
    "    def mean_expected_percentile_rankings_train(self):\n",
    "        return np.mean(self._expected_percentile_rankings_train)\n",
    "    \n",
    "    @property\n",
    "    def mean_expected_percentile_rankings_validation(self):\n",
    "        return np.mean(self._expected_percentile_rankings_validation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Grid search\n",
    "\n",
    "Next, we perform a basic grid search to find reasonable values for $\\alpha$ and $\\lambda$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "F = 30\n",
    "grid_search_results = {}\n",
    "result = namedtuple('Result', 'alpha lmbda')\n",
    "alpha_values = [1e-1, 1e0, 1e1, 1e2]\n",
    "lmbda_values = [1e-1, 1e0, 1e1, 1e2]\n",
    "\n",
    "for alpha in alpha_values:\n",
    "    for lmbda in lmbda_values:\n",
    "        implicit_mf = ImplicitMF(ratings_matrix=training_matrix, f=F, alpha=alpha, lmbda=lmbda)\n",
    "        implicit_mf.run()\n",
    "        predicted_preferences = implicit_mf.country_vectors.vectors.dot( implicit_mf.song_vectors.vectors.T )\n",
    "        \n",
    "        evaluator = ExpectedPercentileRankingsEvaluator(\n",
    "            training_matrix=training_matrix,\n",
    "            validation_matrix=validation_matrix,\n",
    "            eligibility_mask=more_than_50_ratings_mask,\n",
    "            predicted_preferences=predicted_preferences\n",
    "        )\n",
    "        evaluator.run()\n",
    "        grid_search_results[result(alpha=alpha, lmbda=lmbda)] = {\n",
    "            'train': evaluator.mean_expected_percentile_rankings_train,\n",
    "            'validation': evaluator.mean_expected_percentile_rankings_validation\n",
    "        }\n",
    "        print(grid_search_results)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's visualize the results for clarity. I plot the opposite of the validation score such that the parameters corresponding to the *darkest* square are most favorable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAyQAAAJSCAYAAAAyBgFsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x122032b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "grid_search_items = [(params, results) for params, results in grid_search_results.items()]\n",
    "grid_search_items.sort(key=lambda tup: tup[0].alpha)\n",
    "\n",
    "params, results = zip(*grid_search_items)\n",
    "validation_results = np.array([result['validation'] for result in results]).reshape(4, 4)\n",
    "\n",
    "plt.figure(figsize=(15, 10))\n",
    "plt.xticks([])\n",
    "plt.yticks([])\n",
    "plt.pcolormesh(-validation_results, cmap='Reds')\n",
    "plt.colorbar()\n",
    "for alpha_index, alpha in enumerate(alpha_values):\n",
    "    for lbmda_index, lmbda in enumerate(lmbda_values):\n",
    "        plt.text(\n",
    "            x = lbmda_index + 0.5,\n",
    "            y = alpha_index + 0.5,\n",
    "            s = r'$\\alpha$ = {}'.format(alpha) + '\\n' + r'$\\lambda$ = {}'.format(lmbda), \n",
    "            ha='center', \n",
    "            va='center', \n",
    "            size=15, \n",
    "            color='w'\n",
    "        )\n",
    "plt.title('Grid Search Results', fontsize=15)\n",
    "plt.xlabel(r'$\\lambda$ Values', fontsize=14)\n",
    "_ = plt.ylabel(r'$\\alpha$ Values', fontsize=14)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The best parameters were found to be: Result(alpha=0.1, lmbda=10.0).\n"
     ]
    }
   ],
   "source": [
    "best_params = min(grid_search_results, key=lambda key: grid_search_results.get(key)['validation'])\n",
    "print('The best parameters were found to be: {}.'.format(best_params))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Train a final model\n",
    "\n",
    "Using these parameters, let's train a final implicit matrix factorization model using 1,000,000 top songs. Additionally, we'll choose $\\epsilon = 1,000$ which seemed to work best in simple experimentation. This experimentation is not shown here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ratings_matrix = RatingsMatrix(n_top_songs=1000000, eps=1e3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Our ratings matrix contains 55 countries and 8663 unique songs.\n"
     ]
    }
   ],
   "source": [
    "print('Our ratings matrix contains {} countries and {} unique songs.'.format(*ratings_matrix.R_ui.shape))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "implicit_mf = ImplicitMF(ratings_matrix=ratings_matrix, f=F, alpha=best_params.alpha, lmbda=best_params.lmbda)\n",
    "implicit_mf.run()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Visualize\n",
    "\n",
    "Let's plot the cosine similarities between all pairs of countries to confirm that things make sense. Intuitively, I'd think that countries in the following groups should be similar:\n",
    "- United States, United Kingdom, Canada, Australia, New Zealand\n",
    "- Latin American countries\n",
    "- Sweden, Finland, Norway, Denmark"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First let's replace the index of our vectors such that it contains the country names."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>dim_0</th>\n",
       "      <th>dim_1</th>\n",
       "      <th>dim_2</th>\n",
       "      <th>dim_3</th>\n",
       "      <th>dim_4</th>\n",
       "      <th>dim_5</th>\n",
       "      <th>dim_6</th>\n",
       "      <th>dim_7</th>\n",
       "      <th>dim_8</th>\n",
       "      <th>dim_9</th>\n",
       "      <th>...</th>\n",
       "      <th>dim_20</th>\n",
       "      <th>dim_21</th>\n",
       "      <th>dim_22</th>\n",
       "      <th>dim_23</th>\n",
       "      <th>dim_24</th>\n",
       "      <th>dim_25</th>\n",
       "      <th>dim_26</th>\n",
       "      <th>dim_27</th>\n",
       "      <th>dim_28</th>\n",
       "      <th>dim_29</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>country_name</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>United States</th>\n",
       "      <td>-1.276051</td>\n",
       "      <td>-1.058583</td>\n",
       "      <td>-0.622779</td>\n",
       "      <td>0.430231</td>\n",
       "      <td>0.306830</td>\n",
       "      <td>0.966786</td>\n",
       "      <td>0.190530</td>\n",
       "      <td>-0.549356</td>\n",
       "      <td>0.538788</td>\n",
       "      <td>-0.722162</td>\n",
       "      <td>...</td>\n",
       "      <td>0.057478</td>\n",
       "      <td>0.500288</td>\n",
       "      <td>0.799253</td>\n",
       "      <td>0.383243</td>\n",
       "      <td>0.575051</td>\n",
       "      <td>0.247066</td>\n",
       "      <td>0.548018</td>\n",
       "      <td>-0.238643</td>\n",
       "      <td>0.114481</td>\n",
       "      <td>0.731294</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>United Kingdom</th>\n",
       "      <td>0.106521</td>\n",
       "      <td>0.346207</td>\n",
       "      <td>-0.276669</td>\n",
       "      <td>-0.003249</td>\n",
       "      <td>-1.294024</td>\n",
       "      <td>-0.090318</td>\n",
       "      <td>0.666301</td>\n",
       "      <td>-0.533962</td>\n",
       "      <td>0.281620</td>\n",
       "      <td>-0.268332</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.803658</td>\n",
       "      <td>-0.498773</td>\n",
       "      <td>-0.041302</td>\n",
       "      <td>-0.705815</td>\n",
       "      <td>0.624482</td>\n",
       "      <td>-0.007293</td>\n",
       "      <td>1.335080</td>\n",
       "      <td>-0.717667</td>\n",
       "      <td>0.019507</td>\n",
       "      <td>-1.700016</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Argentina</th>\n",
       "      <td>-0.871966</td>\n",
       "      <td>0.678408</td>\n",
       "      <td>0.343354</td>\n",
       "      <td>-0.968614</td>\n",
       "      <td>-1.099471</td>\n",
       "      <td>0.014175</td>\n",
       "      <td>0.031833</td>\n",
       "      <td>-0.370821</td>\n",
       "      <td>-0.114270</td>\n",
       "      <td>-0.982766</td>\n",
       "      <td>...</td>\n",
       "      <td>0.435942</td>\n",
       "      <td>-0.170878</td>\n",
       "      <td>-0.172491</td>\n",
       "      <td>-0.158596</td>\n",
       "      <td>0.445267</td>\n",
       "      <td>-0.949628</td>\n",
       "      <td>0.542433</td>\n",
       "      <td>-0.157643</td>\n",
       "      <td>0.765119</td>\n",
       "      <td>0.587947</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Australia</th>\n",
       "      <td>-1.129085</td>\n",
       "      <td>0.212391</td>\n",
       "      <td>0.136416</td>\n",
       "      <td>-0.665215</td>\n",
       "      <td>0.452084</td>\n",
       "      <td>-0.418566</td>\n",
       "      <td>-0.187979</td>\n",
       "      <td>0.807976</td>\n",
       "      <td>-0.693282</td>\n",
       "      <td>-0.723989</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.961785</td>\n",
       "      <td>-0.064047</td>\n",
       "      <td>-0.161033</td>\n",
       "      <td>0.211444</td>\n",
       "      <td>0.180285</td>\n",
       "      <td>0.597487</td>\n",
       "      <td>-0.143220</td>\n",
       "      <td>0.336241</td>\n",
       "      <td>-0.251201</td>\n",
       "      <td>-1.057264</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Austria</th>\n",
       "      <td>-0.094485</td>\n",
       "      <td>0.870111</td>\n",
       "      <td>-0.328650</td>\n",
       "      <td>-0.594735</td>\n",
       "      <td>-0.429165</td>\n",
       "      <td>-0.955718</td>\n",
       "      <td>0.151173</td>\n",
       "      <td>0.250305</td>\n",
       "      <td>-0.302996</td>\n",
       "      <td>0.718965</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.409435</td>\n",
       "      <td>-0.381884</td>\n",
       "      <td>-0.144373</td>\n",
       "      <td>0.340587</td>\n",
       "      <td>0.006711</td>\n",
       "      <td>0.870717</td>\n",
       "      <td>0.067101</td>\n",
       "      <td>-0.361675</td>\n",
       "      <td>0.742727</td>\n",
       "      <td>1.341254</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 30 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                   dim_0     dim_1     dim_2     dim_3     dim_4     dim_5  \\\n",
       "country_name                                                                 \n",
       "United States  -1.276051 -1.058583 -0.622779  0.430231  0.306830  0.966786   \n",
       "United Kingdom  0.106521  0.346207 -0.276669 -0.003249 -1.294024 -0.090318   \n",
       "Argentina      -0.871966  0.678408  0.343354 -0.968614 -1.099471  0.014175   \n",
       "Australia      -1.129085  0.212391  0.136416 -0.665215  0.452084 -0.418566   \n",
       "Austria        -0.094485  0.870111 -0.328650 -0.594735 -0.429165 -0.955718   \n",
       "\n",
       "                   dim_6     dim_7     dim_8     dim_9    ...       dim_20  \\\n",
       "country_name                                              ...                \n",
       "United States   0.190530 -0.549356  0.538788 -0.722162    ...     0.057478   \n",
       "United Kingdom  0.666301 -0.533962  0.281620 -0.268332    ...    -0.803658   \n",
       "Argentina       0.031833 -0.370821 -0.114270 -0.982766    ...     0.435942   \n",
       "Australia      -0.187979  0.807976 -0.693282 -0.723989    ...    -0.961785   \n",
       "Austria         0.151173  0.250305 -0.302996  0.718965    ...    -0.409435   \n",
       "\n",
       "                  dim_21    dim_22    dim_23    dim_24    dim_25    dim_26  \\\n",
       "country_name                                                                 \n",
       "United States   0.500288  0.799253  0.383243  0.575051  0.247066  0.548018   \n",
       "United Kingdom -0.498773 -0.041302 -0.705815  0.624482 -0.007293  1.335080   \n",
       "Argentina      -0.170878 -0.172491 -0.158596  0.445267 -0.949628  0.542433   \n",
       "Australia      -0.064047 -0.161033  0.211444  0.180285  0.597487 -0.143220   \n",
       "Austria        -0.381884 -0.144373  0.340587  0.006711  0.870717  0.067101   \n",
       "\n",
       "                  dim_27    dim_28    dim_29  \n",
       "country_name                                  \n",
       "United States  -0.238643  0.114481  0.731294  \n",
       "United Kingdom -0.717667  0.019507 -1.700016  \n",
       "Argentina      -0.157643  0.765119  0.587947  \n",
       "Australia       0.336241 -0.251201 -1.057264  \n",
       "Austria        -0.361675  0.742727  1.341254  \n",
       "\n",
       "[5 rows x 30 columns]"
      ]
     },
     "execution_count": 165,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "country_vectors_df = implicit_mf.country_vectors.vectors.copy()\n",
    "\n",
    "country_id_to_name = {countries_lookup[name]['id']: name for name in countries_lookup}\n",
    "country_ids = country_vectors_df.index\n",
    "country_names = pd.Index([country_id_to_name[c_id] for c_id in country_ids], name='country_name')\n",
    "country_vectors_df.index = country_names\n",
    "\n",
    "country_vectors_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, we'll plot the cosine similarities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sns.set(style=\"white\")\n",
    "\n",
    "def plot_cosine_similarities(country_vectors_df):\n",
    "\n",
    "    similarities_df = pd.DataFrame(\n",
    "        data=cosine_similarity(country_vectors_df),\n",
    "        index=country_vectors_df.index,\n",
    "        columns=country_vectors_df.index\n",
    "    )\n",
    "    \n",
    "    lower_triangle_mask = np.zeros_like(similarities_df, dtype=np.bool)\n",
    "    lower_triangle_mask[np.triu_indices_from(lower_triangle_mask)] = True\n",
    "\n",
    "    f, ax = plt.subplots(figsize=(21, 21))\n",
    "    cmap = sns.diverging_palette(220, 10, as_cmap=True)\n",
    "\n",
    "    sns.heatmap(\n",
    "        similarities_df, \n",
    "        mask=lower_triangle_mask, \n",
    "        cmap=cmap, \n",
    "        vmax=.5,\n",
    "        square=True, \n",
    "        xticklabels=True, \n",
    "        yticklabels=True,\n",
    "        linewidths=1, \n",
    "        cbar_kws={\"shrink\": .5}, \n",
    "        ax=ax,\n",
    "    )\n",
    "    ax.set_title('Cosine Similarity Matrix', fontsize=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABJEAAAQ6CAYAAAD0leyfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ndwfdM93TubkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ae08a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_cosine_similarities(country_vectors_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I first turn to my favorite country - Colombia - to inspect its similarity with other Latin American countries. The numbers are high for: Peru, Paraguay, Panama, Nicaragua, Gautemala, Ecuador, Dominican Republic and Costa Rica.\n",
    "\n",
    "Next, I turn to the United Kingdom: it is most similar with Switzerland, New Zealand, Ireland, Hungary, Belgium and Australia.\n",
    "\n",
    "Finally, we see that Sweden is similar enough to Norway, yet not Finland (who, incidentally, seems to have nothing in common with anyone at all).\n",
    "\n",
    "Overall, this looks very good to me."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Visualize with TSNE\n",
    "\n",
    "To further inspect similarities between countries, let's explore the 2-dimensional TSNE space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "tsne = TSNE(perplexity=30, n_components=2, init='pca', n_iter=5000, random_state=12345)\n",
    "\n",
    "country_embeddings = pd.DataFrame(\n",
    "    data=tsne.fit_transform(country_vectors_df),\n",
    "    index=country_vectors_df.index,\n",
    "    columns=['dim_1', 'dim_2']\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_tsne_embeddings(country_embeddings):\n",
    "\n",
    "    plt.figure(figsize=(15,15))\n",
    "\n",
    "    for country_name, country_embedding in country_embeddings.iterrows():\n",
    "        dim_1, dim_2 = country_embedding\n",
    "        plt.scatter(dim_1, dim_2)\n",
    "        plt.annotate(country_name, xy=(dim_1, dim_2), xytext=(5, 2), textcoords='offset points', ha='right', va='bottom')\n",
    "        plt.title('Two-Dimensional TSNE Embeddings of Latent Country Vectors', fontsize=16)\n",
    "        plt.xlabel('Dimension 1', fontsize=12)\n",
    "        plt.ylabel('Dimension 2', fontsize=12)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA34AAANtCAYAAADPa6khAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nBwAAAAAG938I1U9urWdMGwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ab54cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_tsne_embeddings(country_embeddings)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is not particularly useful. Furthermore, and perhaps most importantly, the plot varies immensely when changing the random seed. This is a worthwhile step nonetheless."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Inspect predicted preferences\n",
    "\n",
    "Crucially, we'll now inspect predicted preferences for select countries and confirm that they make sense. I first normalize each of the country and song vectors, then compute predicted preferences via the dot product."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "SONG_METADATA_QUERY = \"\"\"\n",
    "    SELECT \n",
    "        songs.title as song_title, \n",
    "        songs.artist as song_artist,\n",
    "        songs.id as song_id\n",
    "    FROM songs\n",
    "\"\"\"\n",
    "\n",
    "song_metadata_df = pd.read_sql(SONG_METADATA_QUERY, ENGINE, index_col=['song_id'])\n",
    "\n",
    "song_vectors_df = song_metadata_df.join(implicit_mf.song_vectors.vectors, how='inner')\\\n",
    "    .set_index(['song_title', 'song_artist'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "song_vectors_df_norm = song_vectors_df.apply(lambda vec: vec / np.linalg.norm(vec), axis=1)\n",
    "country_vectors_df_norm = country_vectors_df.apply(lambda vec: vec / np.linalg.norm(vec), axis=1)\n",
    "\n",
    "assert song_vectors_df_norm.apply(np.linalg.norm, axis=1).mean() == 1.\n",
    "assert country_vectors_df_norm.apply(np.linalg.norm, axis=1).mean() == 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## United States"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pd.set_option('display.max_colwidth', 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>song_title</th>\n",
       "      <th>song_artist</th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Dab of Ranch - Recorded at Spotify Studios NYC</td>\n",
       "      <td>Migos</td>\n",
       "      <td>0.899299</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Massage In My Room</td>\n",
       "      <td>Future</td>\n",
       "      <td>0.899299</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Father Stretch My Hands Pt. 1</td>\n",
       "      <td>Kanye West</td>\n",
       "      <td>0.899299</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Keep On</td>\n",
       "      <td>Kehlani</td>\n",
       "      <td>0.899299</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>First Day Out</td>\n",
       "      <td>Tee Grizzley</td>\n",
       "      <td>0.899299</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>When I Was Broke</td>\n",
       "      <td>Future</td>\n",
       "      <td>0.899299</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Star Of The Show</td>\n",
       "      <td>Thomas Rhett</td>\n",
       "      <td>0.899299</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Rose Golden</td>\n",
       "      <td>Kid Cudi</td>\n",
       "      <td>0.899299</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>oui</td>\n",
       "      <td>Jeremih</td>\n",
       "      <td>0.899299</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Everyday We Lit</td>\n",
       "      <td>YFN Lucci</td>\n",
       "      <td>0.899299</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                       song_title   song_artist         0\n",
       "0  Dab of Ranch - Recorded at Spotify Studios NYC         Migos  0.899299\n",
       "1                              Massage In My Room        Future  0.899299\n",
       "2                   Father Stretch My Hands Pt. 1    Kanye West  0.899299\n",
       "3                                         Keep On       Kehlani  0.899299\n",
       "4                                   First Day Out  Tee Grizzley  0.899299\n",
       "5                                When I Was Broke        Future  0.899299\n",
       "6                                Star Of The Show  Thomas Rhett  0.899299\n",
       "7                                     Rose Golden      Kid Cudi  0.899299\n",
       "8                                             oui       Jeremih  0.899299\n",
       "9                                 Everyday We Lit     YFN Lucci  0.899299"
      ]
     },
     "execution_count": 211,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "country_vec = country_vectors_df_norm.ix['United States']\n",
    "song_vectors_df_norm.dot(country_vec).sort_values(ascending=False).reset_index().head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Colombia"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>song_title</th>\n",
       "      <th>song_artist</th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Ya No Me Duele Más</td>\n",
       "      <td>Silvestre Dangond</td>\n",
       "      <td>0.941204</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Bajo el agua</td>\n",
       "      <td>Manuel Medrano</td>\n",
       "      <td>0.919997</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Si No Te Quiere</td>\n",
       "      <td>Ozuna</td>\n",
       "      <td>0.916971</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>El Ganador</td>\n",
       "      <td>Nicky Jam</td>\n",
       "      <td>0.898030</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Oiga, Mira, Vea</td>\n",
       "      <td>Guayacán Orquesta</td>\n",
       "      <td>0.897944</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Mil Lágrimas</td>\n",
       "      <td>Nicky Jam</td>\n",
       "      <td>0.897863</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Déjame Te Explico</td>\n",
       "      <td>Reykon</td>\n",
       "      <td>0.897396</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Quédate</td>\n",
       "      <td>Manuel Medrano</td>\n",
       "      <td>0.896307</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Afuera del planeta</td>\n",
       "      <td>Manuel Medrano</td>\n",
       "      <td>0.895686</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Materialista</td>\n",
       "      <td>Silvestre Dangond</td>\n",
       "      <td>0.895501</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           song_title        song_artist         0\n",
       "0  Ya No Me Duele Más  Silvestre Dangond  0.941204\n",
       "1        Bajo el agua     Manuel Medrano  0.919997\n",
       "2     Si No Te Quiere              Ozuna  0.916971\n",
       "3          El Ganador          Nicky Jam  0.898030\n",
       "4     Oiga, Mira, Vea  Guayacán Orquesta  0.897944\n",
       "5        Mil Lágrimas          Nicky Jam  0.897863\n",
       "6   Déjame Te Explico             Reykon  0.897396\n",
       "7             Quédate     Manuel Medrano  0.896307\n",
       "8  Afuera del planeta     Manuel Medrano  0.895686\n",
       "9        Materialista  Silvestre Dangond  0.895501"
      ]
     },
     "execution_count": 212,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "country_vec = country_vectors_df_norm.ix['Colombia']\n",
    "song_vectors_df_norm.dot(country_vec).sort_values(ascending=False).reset_index().head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Turkey"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>song_title</th>\n",
       "      <th>song_artist</th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Dudak</td>\n",
       "      <td>Edis</td>\n",
       "      <td>0.943574</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Benim Karanlık Yanım</td>\n",
       "      <td>Sezen Aksu</td>\n",
       "      <td>0.943574</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Affection</td>\n",
       "      <td>Cigarettes After Sex</td>\n",
       "      <td>0.943574</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Ateş Böceği</td>\n",
       "      <td>Mithat Can Özer</td>\n",
       "      <td>0.943574</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Beni Öyle Bilme</td>\n",
       "      <td>Ceylan Ertem</td>\n",
       "      <td>0.943574</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Keyfim Kaçık Acık</td>\n",
       "      <td>Can Bonomo</td>\n",
       "      <td>0.943574</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Seni Unutmaya Ömrüm Yeter mi</td>\n",
       "      <td>Ümit Besen</td>\n",
       "      <td>0.943574</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Vazgeçtim</td>\n",
       "      <td>Sezen Aksu</td>\n",
       "      <td>0.943574</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Yanımda Kal</td>\n",
       "      <td>Harun Kolçak</td>\n",
       "      <td>0.943574</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Stanga</td>\n",
       "      <td>Sagi Abitbul</td>\n",
       "      <td>0.943574</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                     song_title           song_artist         0\n",
       "0                         Dudak                  Edis  0.943574\n",
       "1          Benim Karanlık Yanım            Sezen Aksu  0.943574\n",
       "2                     Affection  Cigarettes After Sex  0.943574\n",
       "3                   Ateş Böceği       Mithat Can Özer  0.943574\n",
       "4               Beni Öyle Bilme          Ceylan Ertem  0.943574\n",
       "5             Keyfim Kaçık Acık            Can Bonomo  0.943574\n",
       "6  Seni Unutmaya Ömrüm Yeter mi            Ümit Besen  0.943574\n",
       "7                     Vazgeçtim            Sezen Aksu  0.943574\n",
       "8                   Yanımda Kal          Harun Kolçak  0.943574\n",
       "9                        Stanga          Sagi Abitbul  0.943574"
      ]
     },
     "execution_count": 213,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "country_vec = country_vectors_df_norm.ix['Turkey']\n",
    "song_vectors_df_norm.dot(country_vec).sort_values(ascending=False).reset_index().head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Germany"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>song_title</th>\n",
       "      <th>song_artist</th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Skandale</td>\n",
       "      <td>Bonez MC</td>\n",
       "      <td>0.908499</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Ahnma</td>\n",
       "      <td>Beginner</td>\n",
       "      <td>0.906591</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Am schönsten</td>\n",
       "      <td>SDP</td>\n",
       "      <td>0.906250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Tage wie diese</td>\n",
       "      <td>Die Toten Hosen</td>\n",
       "      <td>0.906250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Kartell (feat. Azet &amp; Nash)</td>\n",
       "      <td>Zuna</td>\n",
       "      <td>0.906250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Chill mal dein Leben (feat. Moe Phoenix)</td>\n",
       "      <td>Kianush</td>\n",
       "      <td>0.906250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Neuanfang</td>\n",
       "      <td>Clueso</td>\n",
       "      <td>0.906250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Neben der Spur</td>\n",
       "      <td>Maxwell</td>\n",
       "      <td>0.906250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Hochspannung</td>\n",
       "      <td>Maxwell</td>\n",
       "      <td>0.906250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Intro</td>\n",
       "      <td>Capital Bra</td>\n",
       "      <td>0.906250</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                 song_title      song_artist         0\n",
       "0                                  Skandale         Bonez MC  0.908499\n",
       "1                                     Ahnma         Beginner  0.906591\n",
       "2                              Am schönsten              SDP  0.906250\n",
       "3                            Tage wie diese  Die Toten Hosen  0.906250\n",
       "4               Kartell (feat. Azet & Nash)             Zuna  0.906250\n",
       "5  Chill mal dein Leben (feat. Moe Phoenix)          Kianush  0.906250\n",
       "6                                 Neuanfang           Clueso  0.906250\n",
       "7                            Neben der Spur          Maxwell  0.906250\n",
       "8                              Hochspannung          Maxwell  0.906250\n",
       "9                                     Intro      Capital Bra  0.906250"
      ]
     },
     "execution_count": 214,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "country_vec = country_vectors_df_norm.ix['Germany']\n",
    "song_vectors_df_norm.dot(country_vec).sort_values(ascending=False).reset_index().head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Taiwan"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 215,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>song_title</th>\n",
       "      <th>song_artist</th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>如果的事</td>\n",
       "      <td>王藍茵</td>\n",
       "      <td>0.954455</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>小小的</td>\n",
       "      <td>思衛</td>\n",
       "      <td>0.954455</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Heathens (feat. MUTEMATH)</td>\n",
       "      <td>Twenty One Pilots</td>\n",
       "      <td>0.954455</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>其實都沒有</td>\n",
       "      <td>楊宗緯</td>\n",
       "      <td>0.954455</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>對摺 - 國語</td>\n",
       "      <td>任賢齊</td>\n",
       "      <td>0.954455</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>最難的是相遇</td>\n",
       "      <td>Valen Hsu</td>\n",
       "      <td>0.954455</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>안녕 못해 I'm Not Okay (From “MISSING 9”)</td>\n",
       "      <td>CHEN</td>\n",
       "      <td>0.954455</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>未接來電</td>\n",
       "      <td>楊乃文</td>\n",
       "      <td>0.954455</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>飛機 - feat. 林俊峰</td>\n",
       "      <td>林俊傑</td>\n",
       "      <td>0.954455</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>All On Me</td>\n",
       "      <td>Devin Dawson</td>\n",
       "      <td>0.954455</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                              song_title        song_artist         0\n",
       "0                                   如果的事                王藍茵  0.954455\n",
       "1                                    小小的                 思衛  0.954455\n",
       "2              Heathens (feat. MUTEMATH)  Twenty One Pilots  0.954455\n",
       "3                                  其實都沒有                楊宗緯  0.954455\n",
       "4                                對摺 - 國語                任賢齊  0.954455\n",
       "5                                 最難的是相遇          Valen Hsu  0.954455\n",
       "6  안녕 못해 I'm Not Okay (From “MISSING 9”)               CHEN  0.954455\n",
       "7                                   未接來電                楊乃文  0.954455\n",
       "8                         飛機 - feat. 林俊峰                林俊傑  0.954455\n",
       "9                              All On Me       Devin Dawson  0.954455"
      ]
     },
     "execution_count": 215,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "country_vec = country_vectors_df_norm.ix['Taiwan']\n",
    "song_vectors_df_norm.dot(country_vec).sort_values(ascending=False).reset_index().head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These look great.\n",
    "\n",
    "One interesting thing to note is the significance of the length of the vectors. To this point, [Schakel and Wilson](https://arxiv.org/abs/1508.02297) offer the following:\n",
    "\n",
    "> A word that is consistently used in a similar context will be represented by a longer vector than a word of the same frequency that is used in different contexts.\n",
    "\n",
    "> Not only the direction, but also the length of word vectors carries important information.\n",
    "\n",
    "> Word vector length furnishes, in combination with term frequency, a useful measure of word significance.\n",
    "\n",
    "In our case, my guess is that length indicates something like popularity - at least for songs. Let's see which songs and countries have the largest L2 norms."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>song_title</th>\n",
       "      <th>song_artist</th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Shape of You</td>\n",
       "      <td>Ed Sheeran</td>\n",
       "      <td>0.687497</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Starboy</td>\n",
       "      <td>The Weeknd</td>\n",
       "      <td>0.684529</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>I Don’t Wanna Live Forever (Fifty Shades Darker) - From \"Fifty Shades Darker (Original Motion Pi...</td>\n",
       "      <td>ZAYN</td>\n",
       "      <td>0.682996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Despacito (Featuring Daddy Yankee)</td>\n",
       "      <td>Luis Fonsi</td>\n",
       "      <td>0.682941</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Rockabye (feat. Sean Paul &amp; Anne-Marie)</td>\n",
       "      <td>Clean Bandit</td>\n",
       "      <td>0.682918</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Paris</td>\n",
       "      <td>The Chainsmokers</td>\n",
       "      <td>0.682878</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Call On Me - Ryan Riback Extended Remix</td>\n",
       "      <td>Starley</td>\n",
       "      <td>0.682799</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Castle on the Hill</td>\n",
       "      <td>Ed Sheeran</td>\n",
       "      <td>0.682442</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>I Feel It Coming</td>\n",
       "      <td>The Weeknd</td>\n",
       "      <td>0.682225</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Closer</td>\n",
       "      <td>The Chainsmokers</td>\n",
       "      <td>0.682175</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                                                            song_title  \\\n",
       "0                                                                                         Shape of You   \n",
       "1                                                                                              Starboy   \n",
       "2  I Don’t Wanna Live Forever (Fifty Shades Darker) - From \"Fifty Shades Darker (Original Motion Pi...   \n",
       "3                                                                   Despacito (Featuring Daddy Yankee)   \n",
       "4                                                              Rockabye (feat. Sean Paul & Anne-Marie)   \n",
       "5                                                                                                Paris   \n",
       "6                                                              Call On Me - Ryan Riback Extended Remix   \n",
       "7                                                                                   Castle on the Hill   \n",
       "8                                                                                     I Feel It Coming   \n",
       "9                                                                                               Closer   \n",
       "\n",
       "        song_artist         0  \n",
       "0        Ed Sheeran  0.687497  \n",
       "1        The Weeknd  0.684529  \n",
       "2              ZAYN  0.682996  \n",
       "3        Luis Fonsi  0.682941  \n",
       "4      Clean Bandit  0.682918  \n",
       "5  The Chainsmokers  0.682878  \n",
       "6           Starley  0.682799  \n",
       "7        Ed Sheeran  0.682442  \n",
       "8        The Weeknd  0.682225  \n",
       "9  The Chainsmokers  0.682175  "
      ]
     },
     "execution_count": 216,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "song_vectors_df.apply(np.linalg.norm, axis=1).sort_values(ascending=False).reset_index().head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>country_name</th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Taiwan</td>\n",
       "      <td>4.842656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Sweden</td>\n",
       "      <td>4.602653</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Finland</td>\n",
       "      <td>4.415459</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>France</td>\n",
       "      <td>4.399233</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>United Kingdom</td>\n",
       "      <td>4.374870</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Netherlands</td>\n",
       "      <td>4.330190</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Denmark</td>\n",
       "      <td>4.232457</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Italy</td>\n",
       "      <td>4.218088</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Norway</td>\n",
       "      <td>4.084380</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Germany</td>\n",
       "      <td>4.076692</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     country_name         0\n",
       "0          Taiwan  4.842656\n",
       "1          Sweden  4.602653\n",
       "2         Finland  4.415459\n",
       "3          France  4.399233\n",
       "4  United Kingdom  4.374870\n",
       "5     Netherlands  4.330190\n",
       "6         Denmark  4.232457\n",
       "7           Italy  4.218088\n",
       "8          Norway  4.084380\n",
       "9         Germany  4.076692"
      ]
     },
     "execution_count": 217,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "country_vectors_df.apply(np.linalg.norm, axis=1).sort_values(ascending=False).reset_index().head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To reference Taiwan and Colombia, let's inspect predictions using unnormalized vectors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>song_title</th>\n",
       "      <th>song_artist</th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Bad Things - With Camila Cabello</td>\n",
       "      <td>Machine Gun Kelly</td>\n",
       "      <td>0.958864</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Just Hold On</td>\n",
       "      <td>Steve Aoki</td>\n",
       "      <td>0.958692</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Shape of You</td>\n",
       "      <td>Ed Sheeran</td>\n",
       "      <td>0.958325</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Side To Side</td>\n",
       "      <td>Ariana Grande</td>\n",
       "      <td>0.957497</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Closer</td>\n",
       "      <td>The Chainsmokers</td>\n",
       "      <td>0.957290</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Starboy</td>\n",
       "      <td>The Weeknd</td>\n",
       "      <td>0.957090</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Paris</td>\n",
       "      <td>The Chainsmokers</td>\n",
       "      <td>0.957001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>I Don’t Wanna Live Forever (Fifty Shades Darker) - From \"Fifty Shades Darker (Original Motion Pi...</td>\n",
       "      <td>ZAYN</td>\n",
       "      <td>0.956933</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Something Just Like This</td>\n",
       "      <td>The Chainsmokers</td>\n",
       "      <td>0.956803</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>The Greatest</td>\n",
       "      <td>Sia</td>\n",
       "      <td>0.956746</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                                                            song_title  \\\n",
       "0                                                                     Bad Things - With Camila Cabello   \n",
       "1                                                                                         Just Hold On   \n",
       "2                                                                                         Shape of You   \n",
       "3                                                                                         Side To Side   \n",
       "4                                                                                               Closer   \n",
       "5                                                                                              Starboy   \n",
       "6                                                                                                Paris   \n",
       "7  I Don’t Wanna Live Forever (Fifty Shades Darker) - From \"Fifty Shades Darker (Original Motion Pi...   \n",
       "8                                                                             Something Just Like This   \n",
       "9                                                                                         The Greatest   \n",
       "\n",
       "         song_artist         0  \n",
       "0  Machine Gun Kelly  0.958864  \n",
       "1         Steve Aoki  0.958692  \n",
       "2         Ed Sheeran  0.958325  \n",
       "3      Ariana Grande  0.957497  \n",
       "4   The Chainsmokers  0.957290  \n",
       "5         The Weeknd  0.957090  \n",
       "6   The Chainsmokers  0.957001  \n",
       "7               ZAYN  0.956933  \n",
       "8   The Chainsmokers  0.956803  \n",
       "9                Sia  0.956746  "
      ]
     },
     "execution_count": 218,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "country_vec = country_vectors_df.ix['Taiwan']\n",
    "song_vectors_df.dot(country_vec).sort_values(ascending=False).reset_index().head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>song_title</th>\n",
       "      <th>song_artist</th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>I Got You</td>\n",
       "      <td>Bebe Rexha</td>\n",
       "      <td>1.019838</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Party Monster</td>\n",
       "      <td>The Weeknd</td>\n",
       "      <td>0.993647</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Hello</td>\n",
       "      <td>Adele</td>\n",
       "      <td>0.993421</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>I Would Like</td>\n",
       "      <td>Zara Larsson</td>\n",
       "      <td>0.987099</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Scars To Your Beautiful</td>\n",
       "      <td>Alessia Cara</td>\n",
       "      <td>0.987036</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Weak</td>\n",
       "      <td>AJR</td>\n",
       "      <td>0.986642</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Too Good</td>\n",
       "      <td>Drake</td>\n",
       "      <td>0.982179</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Nancy Mulligan</td>\n",
       "      <td>Ed Sheeran</td>\n",
       "      <td>0.979373</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Supermarket Flowers</td>\n",
       "      <td>Ed Sheeran</td>\n",
       "      <td>0.978706</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Hearts Don't Break Around Here</td>\n",
       "      <td>Ed Sheeran</td>\n",
       "      <td>0.978494</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                       song_title   song_artist         0\n",
       "0                       I Got You    Bebe Rexha  1.019838\n",
       "1                   Party Monster    The Weeknd  0.993647\n",
       "2                           Hello         Adele  0.993421\n",
       "3                    I Would Like  Zara Larsson  0.987099\n",
       "4         Scars To Your Beautiful  Alessia Cara  0.987036\n",
       "5                            Weak           AJR  0.986642\n",
       "6                        Too Good         Drake  0.982179\n",
       "7                  Nancy Mulligan    Ed Sheeran  0.979373\n",
       "8             Supermarket Flowers    Ed Sheeran  0.978706\n",
       "9  Hearts Don't Break Around Here    Ed Sheeran  0.978494"
      ]
     },
     "execution_count": 219,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "country_vec = country_vectors_df.ix['Colombia']\n",
    "song_vectors_df.dot(country_vec).sort_values(ascending=False).reset_index().head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Respectively, there is not a song with Chinese nor Spanish letters in each set of recommendations. Additionally, it seems like the world is fond of Ed Sheeran. It is clear that the global popularity of songs dominates our recommendations when computing the dot product with unnormalized vectors.\n",
    "\n",
    "When we do normalize, our predicted preferences can be defined thus:\n",
    "\n",
    "$$\n",
    "\\hat{x}_u = \\frac{x_u}{\\|x_u\\|} \\quad \\hat{y}_i = \\frac{y_i}{\\|y_i\\|}\\\\\n",
    "\\hat{p}_{u, i} = \\hat{x}_u \\cdot \\hat{y}_i\n",
    "$$\n",
    "\n",
    "One idea might be to scale the song vectors by their respective lengths, leaving our predicted preferences as:\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\hat{p}_{u, i} &= \\hat{x}_u \\cdot \\big(\\hat{y}_i \\cdot c\\|y_i\\|\\big)\\\\\n",
    "&= \\hat{x}_u \\cdot \\Bigg(\\hat{y}_i \\cdot c\\frac{y_i}{\\hat{y_i}}\\Bigg)\\\\\n",
    "&= \\hat{x}_u \\cdot c y_i\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "Let's briefly see what this looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>song_title</th>\n",
       "      <th>song_artist</th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Bad Things - With Camila Cabello</td>\n",
       "      <td>Machine Gun Kelly</td>\n",
       "      <td>0.039601</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Just Hold On</td>\n",
       "      <td>Steve Aoki</td>\n",
       "      <td>0.039594</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Shape of You</td>\n",
       "      <td>Ed Sheeran</td>\n",
       "      <td>0.039578</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Side To Side</td>\n",
       "      <td>Ariana Grande</td>\n",
       "      <td>0.039544</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Closer</td>\n",
       "      <td>The Chainsmokers</td>\n",
       "      <td>0.039536</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Starboy</td>\n",
       "      <td>The Weeknd</td>\n",
       "      <td>0.039528</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Paris</td>\n",
       "      <td>The Chainsmokers</td>\n",
       "      <td>0.039524</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>I Don’t Wanna Live Forever (Fifty Shades Darker) - From \"Fifty Shades Darker (Original Motion Pi...</td>\n",
       "      <td>ZAYN</td>\n",
       "      <td>0.039521</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Something Just Like This</td>\n",
       "      <td>The Chainsmokers</td>\n",
       "      <td>0.039516</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>The Greatest</td>\n",
       "      <td>Sia</td>\n",
       "      <td>0.039513</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                                                            song_title  \\\n",
       "0                                                                     Bad Things - With Camila Cabello   \n",
       "1                                                                                         Just Hold On   \n",
       "2                                                                                         Shape of You   \n",
       "3                                                                                         Side To Side   \n",
       "4                                                                                               Closer   \n",
       "5                                                                                              Starboy   \n",
       "6                                                                                                Paris   \n",
       "7  I Don’t Wanna Live Forever (Fifty Shades Darker) - From \"Fifty Shades Darker (Original Motion Pi...   \n",
       "8                                                                             Something Just Like This   \n",
       "9                                                                                         The Greatest   \n",
       "\n",
       "         song_artist         0  \n",
       "0  Machine Gun Kelly  0.039601  \n",
       "1         Steve Aoki  0.039594  \n",
       "2         Ed Sheeran  0.039578  \n",
       "3      Ariana Grande  0.039544  \n",
       "4   The Chainsmokers  0.039536  \n",
       "5         The Weeknd  0.039528  \n",
       "6   The Chainsmokers  0.039524  \n",
       "7               ZAYN  0.039521  \n",
       "8   The Chainsmokers  0.039516  \n",
       "9                Sia  0.039513  "
      ]
     },
     "execution_count": 220,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C = .2\n",
    "\n",
    "country_vec = country_vectors_df_norm.ix['Taiwan']\n",
    "(C * song_vectors_df).dot(country_vec).sort_values(ascending=False).reset_index().head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "About the same. Nevertheless, the length of our vectors can likely offer some value when balancing local recommendations with globally popular songs. I leave this to the reader to explore further for now."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Approximating IMF with neural networks\n",
    "\n",
    "Again, IMF gives a function $f: u, i \\rightarrow \\hat{p}_{u, i}$ and the following objective function to minimize:\n",
    "\n",
    "$$\n",
    "\\underset{x_{*}, y_{*}}{\\arg\\min}\\sum\\limits_{u, i}c_{u, i}\\big(p_{u, i} - f(u, i)\\big)^2 + \\lambda\\bigg(\\sum\\limits_u\\|x_u\\|^2 + \\sum\\limits_i\\|y_u\\|^2\\bigg)\n",
    "$$\n",
    "\n",
    "Let's try to do this with neural networks. I'll use the $\\alpha$ and $\\lambda$ parameters found above, and keep the same dimensionality, $F = 30$, for our latent vectors. This number was chosen in separate experimentation not shown here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true,
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "from itertools import product\n",
    "\n",
    "from keras import backend as K\n",
    "from keras.layers import Input, Embedding, Flatten, Lambda, Dense, BatchNormalization, Dropout, LSTM\n",
    "from keras.layers.merge import add, dot, concatenate\n",
    "from keras.models import Model\n",
    "from keras.optimizers import Adam\n",
    "from keras.preprocessing.sequence import pad_sequences\n",
    "from keras.preprocessing.text import Tokenizer\n",
    "from keras.regularizers import l2\n",
    "from keras.utils import plot_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAe4AAAFoCAYAAACR/hiTAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRCQj/wf3B/4faiP+LAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1173dca20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "songs_rated_by_country = (ratings_matrix.R_ui > 0).sum(axis=1)\n",
    "\n",
    "plt.hist(songs_rated_by_country)\n",
    "plt.title('Distribution of # of Unique Songs Streamed per Country', fontsize=15)\n",
    "plt.xlabel('Unique Songs Streamed', fontsize=12)\n",
    "_ = plt.ylabel('# of Countries', fontsize=12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The 15th percentile of songs rated by country is 218.20000000000002.\n"
     ]
    }
   ],
   "source": [
    "print('The 15th percentile of songs rated by country is {}.'.format(\n",
    "    np.percentile(songs_rated_by_country, 15)\n",
    "))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's set our eligibility cutoff at 200 songs and create training and validation matrices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "more_than_200_ratings_mask = songs_rated_by_country > 20\n",
    "\n",
    "training_matrix, validation_matrix = split_ratings_matrix_into_training_and_validation(\n",
    "    ratings_matrix=ratings_matrix,\n",
    "    eligibility_mask=more_than_200_ratings_mask\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Arrange our data\n",
    "\n",
    "To interact with Keras, we'll need to change our data from wide format to long. Additionally, so as to create our embeddings, we'll need to give each country and song a unique, contiguous index. Finally, I'll do the same with the song artist, as well as tokenize the song title, for later use."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>song_title</th>\n",
       "      <th>song_artist</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>song_id</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>5552</th>\n",
       "      <td>El Perdón</td>\n",
       "      <td>Nicky Jam</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5553</th>\n",
       "      <td>Lean On (feat. MØ &amp; DJ Snake)</td>\n",
       "      <td>Major Lazer</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5555</th>\n",
       "      <td>Love Me Like You Do - From \"Fifty Shades Of Grey\"</td>\n",
       "      <td>Ellie Goulding</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5556</th>\n",
       "      <td>Uptown Funk</td>\n",
       "      <td>Mark Ronson</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5557</th>\n",
       "      <td>Loquita</td>\n",
       "      <td>Marama</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                song_title     song_artist\n",
       "song_id                                                                   \n",
       "5552                                             El Perdón       Nicky Jam\n",
       "5553                         Lean On (feat. MØ & DJ Snake)     Major Lazer\n",
       "5555     Love Me Like You Do - From \"Fifty Shades Of Grey\"  Ellie Goulding\n",
       "5556                                           Uptown Funk     Mark Ronson\n",
       "5557                                               Loquita          Marama"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "song_metadata_df = song_metadata_df.ix[ratings_matrix.R_ui.columns]\n",
    "song_metadata_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>song_title</th>\n",
       "      <th>song_artist</th>\n",
       "      <th>song_index</th>\n",
       "      <th>song_artist_index</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>song_id</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>33068</th>\n",
       "      <td>Affection</td>\n",
       "      <td>Cigarettes After Sex</td>\n",
       "      <td>8658</td>\n",
       "      <td>3699</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33069</th>\n",
       "      <td>Istemem Soz Sevmeni</td>\n",
       "      <td>Ferman Akgül</td>\n",
       "      <td>8659</td>\n",
       "      <td>3106</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33070</th>\n",
       "      <td>Skammekroken 2017</td>\n",
       "      <td>TIX</td>\n",
       "      <td>8660</td>\n",
       "      <td>1677</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33071</th>\n",
       "      <td>Wiosna</td>\n",
       "      <td>Organek</td>\n",
       "      <td>8661</td>\n",
       "      <td>3716</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33072</th>\n",
       "      <td>Fuckt.</td>\n",
       "      <td>Strapo</td>\n",
       "      <td>8662</td>\n",
       "      <td>3717</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  song_title           song_artist  song_index  \\\n",
       "song_id                                                          \n",
       "33068              Affection  Cigarettes After Sex        8658   \n",
       "33069    Istemem Soz Sevmeni          Ferman Akgül        8659   \n",
       "33070      Skammekroken 2017                   TIX        8660   \n",
       "33071                 Wiosna               Organek        8661   \n",
       "33072                 Fuckt.                Strapo        8662   \n",
       "\n",
       "         song_artist_index  \n",
       "song_id                     \n",
       "33068                 3699  \n",
       "33069                 3106  \n",
       "33070                 1677  \n",
       "33071                 3716  \n",
       "33072                 3717  "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "country_id_to_index = {c_id: index for index, c_id in enumerate(ratings_matrix.R_ui.index)}\n",
    "song_id_to_index = {s_id: index for index, s_id in enumerate(ratings_matrix.R_ui.columns)}\n",
    "song_artist_to_index = {artist: index for index, artist in enumerate(song_metadata_df['song_artist'].unique())}\n",
    "\n",
    "song_metadata_df['song_index'] = song_metadata_df.index.map(song_id_to_index.get)\n",
    "song_metadata_df['song_artist_index'] = song_metadata_df['song_artist'].map(song_artist_to_index.get).astype(int)\n",
    "song_metadata_df.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Tokenize song title"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "NUM_WORDS = 5000\n",
    "\n",
    "tokenizer = Tokenizer(num_words=NUM_WORDS, lower=True, split=\" \")\n",
    "tokenizer.fit_on_texts(song_metadata_df['song_title'])\n",
    "song_metadata_df['title_sequence'] = tokenizer.texts_to_sequences(song_metadata_df['song_title'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Convert ratings to long format"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "input_tuples = list( product(ratings_matrix.R_ui.index, ratings_matrix.R_ui.columns) )\n",
    "country_ids, song_ids = zip(*input_tuples)\n",
    "\n",
    "ratings_df = pd.DataFrame({\n",
    "    'country_id': country_ids,\n",
    "    'song_id': song_ids,\n",
    "    'train_rating': training_matrix.R_ui.values.flatten(),\n",
    "    'validation_rating': validation_matrix.R_ui.values.flatten(),\n",
    "})\n",
    "\n",
    "ratings_df = ratings_df.join(song_metadata_df, on='song_id', how='inner').sort_index()\n",
    "ratings_df['country_index'] = ratings_df['country_id'].map(country_id_to_index.get)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define network parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n_countries = ratings_df['country_index'].nunique()\n",
    "n_songs = ratings_df['song_index'].nunique()\n",
    "n_artists = ratings_df['song_artist_index'].nunique()\n",
    "\n",
    "alpha = best_params.alpha\n",
    "lmbda = best_params.lmbda\n",
    "F = 30\n",
    "LEARNING_RATE = .001"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define a loss function\n",
    "\n",
    "This is simply the IMF objective we'd like to minimize."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def implicit_cf_loss(y_true, y_pred, alpha=alpha):\n",
    "    P = y_true > 0\n",
    "    C = 1 + alpha*y_true\n",
    "    return K.mean( C*(P - y_pred)**2 )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define functions to generate, evaluate and visualize predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def generate_predictions(model, inputs, ratings_df=ratings_df):\n",
    "    predictions = model.predict(x=inputs)\n",
    "    return pd.DataFrame({\n",
    "        'prediction': predictions.flatten(),\n",
    "        'country_id': ratings_df['country_id'],\n",
    "        'song_id': ratings_df['song_id']\n",
    "    }).pivot('country_id', 'song_id', 'prediction')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def evaluate_predictions(predictions, eligibility_mask=more_than_200_ratings_mask, \n",
    "                         training_matrix=training_matrix, validation_matrix=validation_matrix):\n",
    "    evaluator = ExpectedPercentileRankingsEvaluator(\n",
    "        training_matrix=training_matrix,\n",
    "        validation_matrix=validation_matrix,\n",
    "        eligibility_mask=eligibility_mask,\n",
    "        predicted_preferences=predictions\n",
    "    )\n",
    "    evaluator.run()\n",
    "    print('Train: {}'.format(evaluator.mean_expected_percentile_rankings_train))\n",
    "    print('Validation: {}'.format(evaluator.mean_expected_percentile_rankings_validation))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def visualize_predictions(predictions):\n",
    "    plt.figure(figsize=(10, 6))\n",
    "\n",
    "    plt.hist(predictions.values.flatten(), bins=25)\n",
    "    plt.title('Predicted Preferences Histogram', fontsize=15)\n",
    "    plt.xlabel('Predicted Prefence', fontsize=12)\n",
    "    _ = plt.ylabel('Count', fontsize=12)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"network_1\"></a>\n",
    "# Network \\#1\n",
    "\n",
    "A trivially \"Siamese\" network which first embeds each country and song index into $\\mathbb{R}^f$ in parallel then computes a dot-product of the embeddings. This is roughly equivalent to what is being done by IMF."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "country_input = Input(shape=(1,), dtype='int64', name='country')\n",
    "song_input = Input(shape=(1,), dtype='int64', name='song')\n",
    "\n",
    "country_embedding = Embedding(input_dim=n_countries, output_dim=F, embeddings_regularizer=l2(lmbda))(country_input)\n",
    "song_embedding = Embedding(input_dim=n_songs, output_dim=F, embeddings_regularizer=l2(lmbda))(song_input)\n",
    "\n",
    "predicted_preference = dot(inputs=[country_embedding, song_embedding], axes=2)\n",
    "predicted_preference = Flatten()(predicted_preference)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model = Model(inputs=[country_input, song_input], outputs=predicted_preference)\n",
    "model.compile(loss=implicit_cf_loss, optimizer=Adam(lr=LEARNING_RATE))\n",
    "\n",
    "plot_model(model, to_file='figures/network_1.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![network 1](../figures/network_1.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 476465 samples, validate on 476465 samples\n",
      "Epoch 1/5\n",
      "476465/476465 [==============================] - 2s - loss: 64.9000 - val_loss: 0.0185\n",
      "Epoch 2/5\n",
      "476465/476465 [==============================] - 8s - loss: 0.0744 - val_loss: 0.0185\n",
      "Epoch 3/5\n",
      "476465/476465 [==============================] - 3s - loss: 0.0744 - val_loss: 0.0185\n",
      "Epoch 4/5\n",
      "476465/476465 [==============================] - 10s - loss: 0.0745 - val_loss: 0.0185\n",
      "Epoch 5/5\n",
      "476465/476465 [==============================] - 8s - loss: 0.0745 - val_loss: 0.0186\n"
     ]
    }
   ],
   "source": [
    "inputs = [ratings_df['country_index'], ratings_df['song_index']]\n",
    "\n",
    "network_1 = model.fit(\n",
    "    x=inputs,\n",
    "    y=ratings_df['train_rating'],\n",
    "    batch_size=1024, \n",
    "    epochs=5,\n",
    "    validation_data=(inputs, ratings_df['validation_rating'])\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train: 0.5053388101677021\n",
      "Validation: 0.49071882278215817\n"
     ]
    }
   ],
   "source": [
    "predictions = generate_predictions(model=model, inputs=inputs)\n",
    "evaluate_predictions(predictions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For reference, let's recall the results we computed when validation our model with `best_params`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'train': 0.04479720392806505, 'validation': 0.18543168148626762}"
      ]
     },
     "execution_count": 166,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grid_search_results[best_params]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Additionally, a *random* model should return an expected percentile ranking of ~50%, as noted in [Hu, Koren and Volinksy](http://yifanhu.net/PUB/cf.pdf). So, this is really bad. Let's visualize the distribution of predictions before moving on to another model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAnIAAAGDCAYAAACvCP20AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nI1yu2QjYhF4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x124ce2208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "visualize_predictions(predictions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"network_2\"></a>\n",
    "# Network \\#2\n",
    "\n",
    "Same as previous, but with a bias embedding for each set, in $\\mathbb{R}$, added to the dot-product."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "country_bias = Embedding(input_dim=n_countries, output_dim=1, name='country_bias', input_length=1)(country_input)\n",
    "song_bias = Embedding(input_dim=n_songs, output_dim=1, name='song_bias', input_length=1)(song_input)\n",
    "\n",
    "predicted_preference = add(inputs=[predicted_preference, song_bias, country_bias])\n",
    "predicted_preference = Flatten()(predicted_preference)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model = Model(inputs=[country_input, song_input], outputs=predicted_preference)\n",
    "model.compile(loss=implicit_cf_loss, optimizer=Adam(lr=LEARNING_RATE))\n",
    "\n",
    "plot_model(model, to_file='figures/network_2.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![network 2](../figures/network_2.png?)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 476465 samples, validate on 476465 samples\n",
      "Epoch 1/5\n",
      "476465/476465 [==============================] - 2s - loss: 0.0734 - val_loss: 0.0204\n",
      "Epoch 2/5\n",
      "476465/476465 [==============================] - 2s - loss: 0.0563 - val_loss: 0.0216\n",
      "Epoch 3/5\n",
      "476465/476465 [==============================] - 2s - loss: 0.0534 - val_loss: 0.0236\n",
      "Epoch 4/5\n",
      "476465/476465 [==============================] - 2s - loss: 0.0515 - val_loss: 0.0252\n",
      "Epoch 5/5\n",
      "476465/476465 [==============================] - 2s - loss: 0.0502 - val_loss: 0.0269\n"
     ]
    }
   ],
   "source": [
    "inputs = [ratings_df['country_index'], ratings_df['song_index']]\n",
    "\n",
    "network_2 = model.fit(\n",
    "    x=inputs,\n",
    "    y=ratings_df['train_rating'],\n",
    "    batch_size=1024, \n",
    "    epochs=5,\n",
    "    validation_data=(inputs, ratings_df['validation_rating'])\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train: 0.10900494586591782\n",
      "Validation: 0.1906236846450195\n"
     ]
    }
   ],
   "source": [
    "predictions = generate_predictions(model=model, inputs=inputs)\n",
    "evaluate_predictions(predictions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This looks a lot better. Now let's visualize our ground-truth and predictions side-by-side."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA7MAAAFyCAYAAAAnNY1XAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nKRMqaLIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12a668048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = pd.DataFrame({\n",
    "    'predictions': predictions.values.flatten(),\n",
    "    'ratings': ratings_df['train_rating'].values.flatten()\n",
    "}).hist(figsize=(16, 6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This model approximates the training distribution much better than the others. Key to this task is delineating between items with 0 ratings, and those with high ratings. Remember, we first down-scaled our ratings with the following transformation to shrink the domain:\n",
    "\n",
    "$$\\tilde{r}_{u, i} = \\log{\\bigg(\\frac{1 + r_{u, i}}{\\epsilon}\\bigg)}$$\n",
    "\n",
    "Furthermore, the model scores worse on the training distribution, yet similarly on the validation set. The bias term was clearly helpful.\n",
    "\n",
    "Let's try a similar model, but *concatenate* the country and song embeddings, then stack fully connected layers, then compute the final linear combination as before."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"network_3\"></a>\n",
    "# Network \\#3\n",
    "\n",
    "Same as [#1](#network_1), but concatenate the latent vectors instead. Then, stack 3 fully-connected layers with ReLU activations, batch normalization after each, and dropout after the first. Finally, add a 1-unit dense layer on the end, and add bias embeddings to the result. (NB: I wanted to add the bias embeddings to the respective $\\mathbb{R}^f$ embeddings at the outset, but couldn't figure out how to do this in Keras.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "country_input = Input(shape=(1,), dtype='int64', name='country')\n",
    "song_input = Input(shape=(1,), dtype='int64', name='song')\n",
    "\n",
    "country_embedding = Embedding(input_dim=n_countries, output_dim=F, embeddings_regularizer=l2(lmbda))(country_input)\n",
    "song_embedding = Embedding(input_dim=n_songs, output_dim=F, embeddings_regularizer=l2(lmbda))(song_input)\n",
    "\n",
    "country_bias = Embedding(input_dim=n_countries, output_dim=1, name='country_bias', input_length=1)(country_input)\n",
    "song_bias = Embedding(input_dim=n_songs, output_dim=1, name='song_bias', input_length=1)(song_input)\n",
    "\n",
    "concatenation = concatenate([country_embedding, song_embedding])\n",
    "\n",
    "dense_layer = Dense(activation='relu', units=10)(concatenation)\n",
    "dropout = Dropout(.5)(dense_layer)\n",
    "batch_norm = BatchNormalization()(dropout)\n",
    "dense_layer = Dense(activation='relu', units=10)(batch_norm)\n",
    "batch_norm = BatchNormalization()(dense_layer)\n",
    "dense_layer = Dense(activation='relu', units=10)(batch_norm)\n",
    "batch_norm = BatchNormalization()(dense_layer)\n",
    "\n",
    "predicted_preference = Dense(units=1, name='predicted_preference')(batch_norm)\n",
    "predicted_preference = Flatten()(predicted_preference)\n",
    "\n",
    "predicted_preference = add(inputs=[predicted_preference, country_bias, song_bias])\n",
    "predicted_preference = Flatten()(predicted_preference)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model = Model(inputs=[country_input, song_input], outputs=predicted_preference)\n",
    "model.compile(loss=implicit_cf_loss, optimizer=Adam(lr=LEARNING_RATE))\n",
    "\n",
    "plot_model(model, to_file='figures/network_3.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![network 3](../figures/network_3.png?)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 476465 samples, validate on 476465 samples\n",
      "Epoch 1/5\n",
      "476465/476465 [==============================] - 5s - loss: 0.0702 - val_loss: 0.0830\n",
      "Epoch 2/5\n",
      "476465/476465 [==============================] - 5s - loss: 0.0472 - val_loss: 0.0601\n",
      "Epoch 3/5\n",
      "476465/476465 [==============================] - 5s - loss: 0.0477 - val_loss: 0.0667\n",
      "Epoch 4/5\n",
      "476465/476465 [==============================] - 5s - loss: 0.0483 - val_loss: 0.0508\n",
      "Epoch 5/5\n",
      "476465/476465 [==============================] - 5s - loss: 0.0491 - val_loss: 0.0513\n"
     ]
    }
   ],
   "source": [
    "inputs = [ratings_df['country_index'], ratings_df['song_index']]\n",
    "\n",
    "network_3 = model.fit(\n",
    "    x=inputs,\n",
    "    y=ratings_df['train_rating'],\n",
    "    batch_size=1024, \n",
    "    epochs=5,\n",
    "    validation_data=(inputs, ratings_df['validation_rating'])\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train: 0.11102242413459021\n",
      "Validation: 0.1899202531334214\n"
     ]
    }
   ],
   "source": [
    "predictions = generate_predictions(model=model, inputs=inputs)\n",
    "evaluate_predictions(predictions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These results are roughly identical to the previous. Choosing between the models, we'd certainly go with the simpler of the two.\n",
    "\n",
    "Now, let's try some architectures that benefit from other data sources altogether: the song title, and the song artist."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"network_4\"></a>\n",
    "# Network \\#4\n",
    "\n",
    "Same as [#2](#network_2), except feed in the song title text as well. This text is first tokenized, then padded to a maximum sequence length, then embedded into a fixed-length vector by an LSTM, then reduced to a single value by a dense layer with a ReLU activation. Finally, this scalar is concatenated to the scalar output that [#2](#network_2) would produce, and the result is fed into a final dense layer with a linear activation - i.e. a linear combination of the two."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "MAX_SEQUENCE_LENGTH = ratings_df['title_sequence'].map(len).max()\n",
    "\n",
    "padded_title_sequences = pad_sequences(sequences=ratings_df['title_sequence'], maxlen=MAX_SEQUENCE_LENGTH)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "country_input = Input(shape=(1,), dtype='int64', name='country')\n",
    "song_input = Input(shape=(1,), dtype='int64', name='song')\n",
    "title_input = Input(shape=(MAX_SEQUENCE_LENGTH,), dtype='int32', name='song_title_sequence')\n",
    "\n",
    "country_embedding = Embedding(input_dim=n_countries, output_dim=F, embeddings_regularizer=l2(lmbda))(country_input)\n",
    "song_embedding = Embedding(input_dim=n_songs, output_dim=F, embeddings_regularizer=l2(lmbda))(song_input)\n",
    "title_embedding = Embedding(output_dim=F, input_dim=NUM_WORDS, input_length=MAX_SEQUENCE_LENGTH)(title_input)\n",
    "\n",
    "country_bias = Embedding(input_dim=n_countries, output_dim=1, name='country_bias', input_length=1)(country_input)\n",
    "song_bias = Embedding(input_dim=n_songs, output_dim=1, name='song_bias', input_length=1)(song_input)\n",
    "\n",
    "predicted_preference = dot(inputs=[country_embedding, song_embedding], axes=2)\n",
    "predicted_preference = add(inputs=[predicted_preference, country_bias, song_bias])\n",
    "predicted_preference = Flatten()(predicted_preference)\n",
    "\n",
    "title_lstm = LSTM(F)(title_embedding)\n",
    "dense_title_lstm = Dense(units=1, activation='relu')(title_lstm)\n",
    "\n",
    "predicted_preference_merge = concatenate(inputs=[predicted_preference, dense_title_lstm])\n",
    "final_output = Dense(activation='linear', units=1)(predicted_preference_merge)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model = Model(inputs=[country_input, song_input, title_input], outputs=final_output)\n",
    "model.compile(loss=implicit_cf_loss, optimizer=Adam(lr=LEARNING_RATE))\n",
    "\n",
    "plot_model(model, to_file='figures/network_4.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![network 4](../figures/network_4.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 476465 samples, validate on 476465 samples\n",
      "Epoch 1/5\n",
      "476465/476465 [==============================] - 124s - loss: 65.4419 - val_loss: 0.0215\n",
      "Epoch 2/5\n",
      "476465/476465 [==============================] - 126s - loss: 0.0506 - val_loss: 0.0256\n",
      "Epoch 3/5\n",
      "476465/476465 [==============================] - 120s - loss: 0.0476 - val_loss: 0.0282\n",
      "Epoch 4/5\n",
      "476465/476465 [==============================] - 119s - loss: 0.0472 - val_loss: 0.0288\n",
      "Epoch 5/5\n",
      "476465/476465 [==============================] - 119s - loss: 0.0471 - val_loss: 0.0291\n"
     ]
    }
   ],
   "source": [
    "inputs = [ratings_df['country_index'], ratings_df['song_index'], padded_title_sequences]\n",
    "\n",
    "network_4 = model.fit(\n",
    "    x=inputs,\n",
    "    y=ratings_df['train_rating'],\n",
    "    batch_size=1024, \n",
    "    epochs=5,\n",
    "    validation_data=(inputs, ratings_df['validation_rating'])\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train: 0.11471700578472085\n",
      "Validation: 0.18885209182480478\n"
     ]
    }
   ],
   "source": [
    "predictions = generate_predictions(model=model, inputs=inputs)\n",
    "evaluate_predictions(predictions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We seem to get a pinch of lift from the song title, though we're still underfitting our training set. Perhaps we could make our model bigger, or run it for more epochs.\n",
    "\n",
    "Let's plot our ground-truth vs. prediction distributions side-by-side just to make sure we're still on the right track."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA7MAAAFyCAYAAAAnNY1XAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12cd0f8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = pd.DataFrame({\n",
    "    'predictions': predictions.values.flatten(),\n",
    "    'ratings': ratings_df['train_rating'].values.flatten()\n",
    "}).hist(figsize=(16, 6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, let's add the artist."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"network_5\"></a>\n",
    "# Network \\#5\n",
    "\n",
    "Same as [#4](#network_4), except feed in the song artist index as well. This index is first embedded into a vector, then reduced to a scalar by a dense layer with a ReLU activation. Finally, this scalar is concatenated with the two scalars produced in the second-to-last layer of [#4](#network_4), then fed into a final dense layer with a linear activation. Like the previous, this is a linear combination of the three inputs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "artist_input = Input(shape=(1,), dtype='int64', name='artist')\n",
    "artist_embedding = Embedding(input_dim=n_artists, output_dim=F, embeddings_regularizer=l2(lmbda))(artist_input)\n",
    "dense_artist_embedding = Dense(units=1, activation='relu')(artist_embedding)\n",
    "dense_artist_embedding = Flatten()(dense_artist_embedding)\n",
    "\n",
    "predicted_preference_merge = concatenate(inputs=[predicted_preference, dense_title_lstm, dense_artist_embedding])\n",
    "final_output = Dense(activation='linear', units=1)(predicted_preference_merge)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model = Model(inputs=[country_input, song_input, title_input, artist_input], outputs=final_output)\n",
    "model.compile(loss=implicit_cf_loss, optimizer=Adam(lr=LEARNING_RATE))\n",
    "\n",
    "plot_model(model, to_file='figures/network_5.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![network 5](../figures/network_5.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 476465 samples, validate on 476465 samples\n",
      "Epoch 1/5\n",
      "476465/476465 [==============================] - 122s - loss: 28.0315 - val_loss: 0.0224\n",
      "Epoch 2/5\n",
      "476465/476465 [==============================] - 129s - loss: 0.0484 - val_loss: 0.0269\n",
      "Epoch 3/5\n",
      "476465/476465 [==============================] - 121s - loss: 0.0473 - val_loss: 0.0310\n",
      "Epoch 4/5\n",
      "476465/476465 [==============================] - 134s - loss: 0.0489 - val_loss: 0.0333\n",
      "Epoch 5/5\n",
      "476465/476465 [==============================] - 131s - loss: 0.0485 - val_loss: 0.0300\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x12ee912b0>"
      ]
     },
     "execution_count": 219,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inputs = [\n",
    "    ratings_df['country_index'], \n",
    "    ratings_df['song_index'], \n",
    "    padded_title_sequences, \n",
    "    ratings_df['song_artist_index']\n",
    "]\n",
    "\n",
    "model.fit(\n",
    "    x=inputs,\n",
    "    y=ratings_df['train_rating'],\n",
    "    batch_size=1024, \n",
    "    epochs=5,\n",
    "    validation_data=(inputs, ratings_df['validation_rating'])\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train: 0.11092262775206822\n",
      "Validation: 0.19037930919362725\n"
     ]
    }
   ],
   "source": [
    "predictions = generate_predictions(model=model, inputs=inputs)\n",
    "evaluate_predictions(predictions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This seems a bit worse than the last, though similar all the same. I'm a bit surprised we didn't get more lift from artists. Nevertheless, we're still underfitting. Bigger model, more epochs, etc."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# What went wrong?\n",
    "\n",
    "Our best neural network in terms of performance and complexity is network [#2](#network_2). Let's refit this model and inspect a few predictions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 409,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "country_input = Input(shape=(1,), dtype='int64', name='country')\n",
    "song_input = Input(shape=(1,), dtype='int64', name='song')\n",
    "\n",
    "country_embedding = Embedding(input_dim=n_countries, output_dim=F, embeddings_regularizer=l2(lmbda))(country_input)\n",
    "song_embedding = Embedding(input_dim=n_songs, output_dim=F, embeddings_regularizer=l2(lmbda))(song_input)\n",
    "\n",
    "country_bias = Embedding(input_dim=n_countries, output_dim=1, name='country_bias', input_length=1)(country_input)\n",
    "song_bias = Embedding(input_dim=n_songs, output_dim=1, name='song_bias', input_length=1)(song_input)\n",
    "\n",
    "predicted_preference = dot(inputs=[country_embedding, song_embedding], axes=2)\n",
    "predicted_preference = Flatten()(predicted_preference)\n",
    "\n",
    "predicted_preference = add(inputs=[predicted_preference, song_bias, country_bias])\n",
    "predicted_preference = Flatten()(predicted_preference)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 410,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model = Model(inputs=[country_input, song_input], outputs=predicted_preference)\n",
    "model.compile(loss=implicit_cf_loss, optimizer=Adam(lr=LEARNING_RATE))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 411,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 476465 samples, validate on 476465 samples\n",
      "Epoch 1/5\n",
      "476465/476465 [==============================] - 3s - loss: 65.2042 - val_loss: 0.0205\n",
      "Epoch 2/5\n",
      "476465/476465 [==============================] - 8s - loss: 0.0559 - val_loss: 0.0212\n",
      "Epoch 3/5\n",
      "476465/476465 [==============================] - 3s - loss: 0.0519 - val_loss: 0.0225\n",
      "Epoch 4/5\n",
      "476465/476465 [==============================] - 2s - loss: 0.0496 - val_loss: 0.0235\n",
      "Epoch 5/5\n",
      "476465/476465 [==============================] - 2s - loss: 0.0482 - val_loss: 0.0248\n"
     ]
    }
   ],
   "source": [
    "inputs = [ratings_df['country_index'], ratings_df['song_index']]\n",
    "\n",
    "network_2 = model.fit(\n",
    "    x=inputs,\n",
    "    y=ratings_df['train_rating'],\n",
    "    batch_size=1024, \n",
    "    epochs=5,\n",
    "    validation_data=(inputs, ratings_df['validation_rating'])\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 412,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train: 0.10905118689288228\n",
      "Validation: 0.19050085125816704\n"
     ]
    }
   ],
   "source": [
    "predictions = generate_predictions(model=model, inputs=inputs)\n",
    "evaluate_predictions(predictions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 441,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "predictions_unstack = predictions.unstack()\n",
    "\n",
    "predictions_unstack = pd.DataFrame({\n",
    "    'song_title': song_metadata_df.ix[predictions_unstack.index.get_level_values('song_id')]['song_title'],\n",
    "    'song_artist': song_metadata_df.ix[predictions_unstack.index.get_level_values('song_id')]['song_artist'],\n",
    "    'country': unstack.index.get_level_values('country_id').map(country_id_to_name.get),\n",
    "    'rating': predictions_unstack.values\n",
    "})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Colombia"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 443,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>country</th>\n",
       "      <th>rating</th>\n",
       "      <th>song_artist</th>\n",
       "      <th>song_title</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>song_id</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>30519</th>\n",
       "      <td>Colombia</td>\n",
       "      <td>0.715299</td>\n",
       "      <td>Katy Perry</td>\n",
       "      <td>Chained To The Rhythm</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31060</th>\n",
       "      <td>Colombia</td>\n",
       "      <td>0.704788</td>\n",
       "      <td>Ed Sheeran</td>\n",
       "      <td>Perfect</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30137</th>\n",
       "      <td>Colombia</td>\n",
       "      <td>0.683443</td>\n",
       "      <td>Ed Sheeran</td>\n",
       "      <td>Castle on the Hill</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31043</th>\n",
       "      <td>Colombia</td>\n",
       "      <td>0.681572</td>\n",
       "      <td>Zedd</td>\n",
       "      <td>Stay (with Alessia Cara)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31041</th>\n",
       "      <td>Colombia</td>\n",
       "      <td>0.680419</td>\n",
       "      <td>The Chainsmokers</td>\n",
       "      <td>Something Just Like This</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18894</th>\n",
       "      <td>Colombia</td>\n",
       "      <td>0.674962</td>\n",
       "      <td>Calvin Harris</td>\n",
       "      <td>My Way</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30487</th>\n",
       "      <td>Colombia</td>\n",
       "      <td>0.674799</td>\n",
       "      <td>Major Lazer</td>\n",
       "      <td>Run Up (feat. PARTYNEXTDOOR &amp; Nicki Minaj)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20131</th>\n",
       "      <td>Colombia</td>\n",
       "      <td>0.672363</td>\n",
       "      <td>The Weeknd</td>\n",
       "      <td>I Feel It Coming</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20222</th>\n",
       "      <td>Colombia</td>\n",
       "      <td>0.671484</td>\n",
       "      <td>Bruno Mars</td>\n",
       "      <td>That's What I Like</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31045</th>\n",
       "      <td>Colombia</td>\n",
       "      <td>0.669374</td>\n",
       "      <td>Clean Bandit</td>\n",
       "      <td>Symphony (feat. Zara Larsson)</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          country    rating       song_artist  \\\n",
       "song_id                                         \n",
       "30519    Colombia  0.715299        Katy Perry   \n",
       "31060    Colombia  0.704788        Ed Sheeran   \n",
       "30137    Colombia  0.683443        Ed Sheeran   \n",
       "31043    Colombia  0.681572              Zedd   \n",
       "31041    Colombia  0.680419  The Chainsmokers   \n",
       "18894    Colombia  0.674962     Calvin Harris   \n",
       "30487    Colombia  0.674799       Major Lazer   \n",
       "20131    Colombia  0.672363        The Weeknd   \n",
       "20222    Colombia  0.671484        Bruno Mars   \n",
       "31045    Colombia  0.669374      Clean Bandit   \n",
       "\n",
       "                                         song_title  \n",
       "song_id                                              \n",
       "30519                         Chained To The Rhythm  \n",
       "31060                                       Perfect  \n",
       "30137                            Castle on the Hill  \n",
       "31043                      Stay (with Alessia Cara)  \n",
       "31041                      Something Just Like This  \n",
       "18894                                        My Way  \n",
       "30487    Run Up (feat. PARTYNEXTDOOR & Nicki Minaj)  \n",
       "20131                              I Feel It Coming  \n",
       "20222                            That's What I Like  \n",
       "31045                 Symphony (feat. Zara Larsson)  "
      ]
     },
     "execution_count": 443,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predictions_unstack[predictions_unstack['country'] == 'Colombia'].sort_values(by='rating', ascending=False).head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## United States"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 444,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>country</th>\n",
       "      <th>rating</th>\n",
       "      <th>song_artist</th>\n",
       "      <th>song_title</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>song_id</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>30519</th>\n",
       "      <td>United States</td>\n",
       "      <td>0.752865</td>\n",
       "      <td>Katy Perry</td>\n",
       "      <td>Chained To The Rhythm</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31060</th>\n",
       "      <td>United States</td>\n",
       "      <td>0.742354</td>\n",
       "      <td>Ed Sheeran</td>\n",
       "      <td>Perfect</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30137</th>\n",
       "      <td>United States</td>\n",
       "      <td>0.721009</td>\n",
       "      <td>Ed Sheeran</td>\n",
       "      <td>Castle on the Hill</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31043</th>\n",
       "      <td>United States</td>\n",
       "      <td>0.719138</td>\n",
       "      <td>Zedd</td>\n",
       "      <td>Stay (with Alessia Cara)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31041</th>\n",
       "      <td>United States</td>\n",
       "      <td>0.717985</td>\n",
       "      <td>The Chainsmokers</td>\n",
       "      <td>Something Just Like This</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18894</th>\n",
       "      <td>United States</td>\n",
       "      <td>0.712528</td>\n",
       "      <td>Calvin Harris</td>\n",
       "      <td>My Way</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30487</th>\n",
       "      <td>United States</td>\n",
       "      <td>0.712365</td>\n",
       "      <td>Major Lazer</td>\n",
       "      <td>Run Up (feat. PARTYNEXTDOOR &amp; Nicki Minaj)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20131</th>\n",
       "      <td>United States</td>\n",
       "      <td>0.709929</td>\n",
       "      <td>The Weeknd</td>\n",
       "      <td>I Feel It Coming</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20222</th>\n",
       "      <td>United States</td>\n",
       "      <td>0.709051</td>\n",
       "      <td>Bruno Mars</td>\n",
       "      <td>That's What I Like</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31045</th>\n",
       "      <td>United States</td>\n",
       "      <td>0.706940</td>\n",
       "      <td>Clean Bandit</td>\n",
       "      <td>Symphony (feat. Zara Larsson)</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               country    rating       song_artist  \\\n",
       "song_id                                              \n",
       "30519    United States  0.752865        Katy Perry   \n",
       "31060    United States  0.742354        Ed Sheeran   \n",
       "30137    United States  0.721009        Ed Sheeran   \n",
       "31043    United States  0.719138              Zedd   \n",
       "31041    United States  0.717985  The Chainsmokers   \n",
       "18894    United States  0.712528     Calvin Harris   \n",
       "30487    United States  0.712365       Major Lazer   \n",
       "20131    United States  0.709929        The Weeknd   \n",
       "20222    United States  0.709051        Bruno Mars   \n",
       "31045    United States  0.706940      Clean Bandit   \n",
       "\n",
       "                                         song_title  \n",
       "song_id                                              \n",
       "30519                         Chained To The Rhythm  \n",
       "31060                                       Perfect  \n",
       "30137                            Castle on the Hill  \n",
       "31043                      Stay (with Alessia Cara)  \n",
       "31041                      Something Just Like This  \n",
       "18894                                        My Way  \n",
       "30487    Run Up (feat. PARTYNEXTDOOR & Nicki Minaj)  \n",
       "20131                              I Feel It Coming  \n",
       "20222                            That's What I Like  \n",
       "31045                 Symphony (feat. Zara Larsson)  "
      ]
     },
     "execution_count": 444,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predictions_unstack[predictions_unstack['country'] == 'United States'].sort_values(by='rating', ascending=False).head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Turkey"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 445,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>country</th>\n",
       "      <th>rating</th>\n",
       "      <th>song_artist</th>\n",
       "      <th>song_title</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>song_id</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>30519</th>\n",
       "      <td>Turkey</td>\n",
       "      <td>0.728861</td>\n",
       "      <td>Katy Perry</td>\n",
       "      <td>Chained To The Rhythm</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31060</th>\n",
       "      <td>Turkey</td>\n",
       "      <td>0.718350</td>\n",
       "      <td>Ed Sheeran</td>\n",
       "      <td>Perfect</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30137</th>\n",
       "      <td>Turkey</td>\n",
       "      <td>0.697005</td>\n",
       "      <td>Ed Sheeran</td>\n",
       "      <td>Castle on the Hill</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31043</th>\n",
       "      <td>Turkey</td>\n",
       "      <td>0.695134</td>\n",
       "      <td>Zedd</td>\n",
       "      <td>Stay (with Alessia Cara)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31041</th>\n",
       "      <td>Turkey</td>\n",
       "      <td>0.693981</td>\n",
       "      <td>The Chainsmokers</td>\n",
       "      <td>Something Just Like This</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18894</th>\n",
       "      <td>Turkey</td>\n",
       "      <td>0.688524</td>\n",
       "      <td>Calvin Harris</td>\n",
       "      <td>My Way</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30487</th>\n",
       "      <td>Turkey</td>\n",
       "      <td>0.688361</td>\n",
       "      <td>Major Lazer</td>\n",
       "      <td>Run Up (feat. PARTYNEXTDOOR &amp; Nicki Minaj)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20131</th>\n",
       "      <td>Turkey</td>\n",
       "      <td>0.685925</td>\n",
       "      <td>The Weeknd</td>\n",
       "      <td>I Feel It Coming</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20222</th>\n",
       "      <td>Turkey</td>\n",
       "      <td>0.685046</td>\n",
       "      <td>Bruno Mars</td>\n",
       "      <td>That's What I Like</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31045</th>\n",
       "      <td>Turkey</td>\n",
       "      <td>0.682936</td>\n",
       "      <td>Clean Bandit</td>\n",
       "      <td>Symphony (feat. Zara Larsson)</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        country    rating       song_artist  \\\n",
       "song_id                                       \n",
       "30519    Turkey  0.728861        Katy Perry   \n",
       "31060    Turkey  0.718350        Ed Sheeran   \n",
       "30137    Turkey  0.697005        Ed Sheeran   \n",
       "31043    Turkey  0.695134              Zedd   \n",
       "31041    Turkey  0.693981  The Chainsmokers   \n",
       "18894    Turkey  0.688524     Calvin Harris   \n",
       "30487    Turkey  0.688361       Major Lazer   \n",
       "20131    Turkey  0.685925        The Weeknd   \n",
       "20222    Turkey  0.685046        Bruno Mars   \n",
       "31045    Turkey  0.682936      Clean Bandit   \n",
       "\n",
       "                                         song_title  \n",
       "song_id                                              \n",
       "30519                         Chained To The Rhythm  \n",
       "31060                                       Perfect  \n",
       "30137                            Castle on the Hill  \n",
       "31043                      Stay (with Alessia Cara)  \n",
       "31041                      Something Just Like This  \n",
       "18894                                        My Way  \n",
       "30487    Run Up (feat. PARTYNEXTDOOR & Nicki Minaj)  \n",
       "20131                              I Feel It Coming  \n",
       "20222                            That's What I Like  \n",
       "31045                 Symphony (feat. Zara Larsson)  "
      ]
     },
     "execution_count": 445,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predictions_unstack[predictions_unstack['country'] == 'Turkey'].sort_values(by='rating', ascending=False).head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Taiwan"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 446,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>country</th>\n",
       "      <th>rating</th>\n",
       "      <th>song_artist</th>\n",
       "      <th>song_title</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>song_id</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>30519</th>\n",
       "      <td>Taiwan</td>\n",
       "      <td>0.789601</td>\n",
       "      <td>Katy Perry</td>\n",
       "      <td>Chained To The Rhythm</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31060</th>\n",
       "      <td>Taiwan</td>\n",
       "      <td>0.779090</td>\n",
       "      <td>Ed Sheeran</td>\n",
       "      <td>Perfect</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30137</th>\n",
       "      <td>Taiwan</td>\n",
       "      <td>0.757745</td>\n",
       "      <td>Ed Sheeran</td>\n",
       "      <td>Castle on the Hill</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31043</th>\n",
       "      <td>Taiwan</td>\n",
       "      <td>0.755874</td>\n",
       "      <td>Zedd</td>\n",
       "      <td>Stay (with Alessia Cara)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31041</th>\n",
       "      <td>Taiwan</td>\n",
       "      <td>0.754721</td>\n",
       "      <td>The Chainsmokers</td>\n",
       "      <td>Something Just Like This</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18894</th>\n",
       "      <td>Taiwan</td>\n",
       "      <td>0.749264</td>\n",
       "      <td>Calvin Harris</td>\n",
       "      <td>My Way</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30487</th>\n",
       "      <td>Taiwan</td>\n",
       "      <td>0.749101</td>\n",
       "      <td>Major Lazer</td>\n",
       "      <td>Run Up (feat. PARTYNEXTDOOR &amp; Nicki Minaj)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20131</th>\n",
       "      <td>Taiwan</td>\n",
       "      <td>0.746664</td>\n",
       "      <td>The Weeknd</td>\n",
       "      <td>I Feel It Coming</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20222</th>\n",
       "      <td>Taiwan</td>\n",
       "      <td>0.745786</td>\n",
       "      <td>Bruno Mars</td>\n",
       "      <td>That's What I Like</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31045</th>\n",
       "      <td>Taiwan</td>\n",
       "      <td>0.743676</td>\n",
       "      <td>Clean Bandit</td>\n",
       "      <td>Symphony (feat. Zara Larsson)</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        country    rating       song_artist  \\\n",
       "song_id                                       \n",
       "30519    Taiwan  0.789601        Katy Perry   \n",
       "31060    Taiwan  0.779090        Ed Sheeran   \n",
       "30137    Taiwan  0.757745        Ed Sheeran   \n",
       "31043    Taiwan  0.755874              Zedd   \n",
       "31041    Taiwan  0.754721  The Chainsmokers   \n",
       "18894    Taiwan  0.749264     Calvin Harris   \n",
       "30487    Taiwan  0.749101       Major Lazer   \n",
       "20131    Taiwan  0.746664        The Weeknd   \n",
       "20222    Taiwan  0.745786        Bruno Mars   \n",
       "31045    Taiwan  0.743676      Clean Bandit   \n",
       "\n",
       "                                         song_title  \n",
       "song_id                                              \n",
       "30519                         Chained To The Rhythm  \n",
       "31060                                       Perfect  \n",
       "30137                            Castle on the Hill  \n",
       "31043                      Stay (with Alessia Cara)  \n",
       "31041                      Something Just Like This  \n",
       "18894                                        My Way  \n",
       "30487    Run Up (feat. PARTYNEXTDOOR & Nicki Minaj)  \n",
       "20131                              I Feel It Coming  \n",
       "20222                            That's What I Like  \n",
       "31045                 Symphony (feat. Zara Larsson)  "
      ]
     },
     "execution_count": 446,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predictions_unstack[predictions_unstack['country'] == 'Taiwan'].sort_values(by='rating', ascending=False).head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As is abundantly clear, the model is simply converging to a popularity baseline. I tried extracting the vectors outright, normalizing as before then computing dot products, but the results made little sense."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Future work\n",
    "\n",
    "At this stage, Implicit Matrix Factorization is the clear winner. The algorithm is popular for several good reasons - it's simple, relatively scalable, intuitive (especially given the significance of the interplay between $C$ and $P$, which I did not expressedly discuss) and effective. Herein, I did not produce a neural network approximating this algorithm with superior results.\n",
    "\n",
    "My intuition tells me I'm missing something simple; why shouldn't a non-linear function approximator be able to approximate $f(u, i)$ better than a linear matrix decomposition? At this stage, I'm not sure. My best guess is that we should seek to optimize a different loss function. Here, we've mirrored that of IMF; why not optimize a *ranking* loss function instead, since that's what's ultimately important? The IMF objective makes the actual optimization process easy for ratings matrices with billions of items; in our case, with far fewer items, we're simply using stochastic gradient descent. To this effect, I did experiment with some composite loss functions; on one side, `implicit_mf_loss`, and on the other, a `cutoff_loss`, which seeks to enforce that songs which received a rating $\\tilde{r}_{u, i}$ above a certain cutoff should be indeed predicted at above that cutoff. It's a crude, binary absolute error. This was unsuccessful.\n",
    "\n",
    "Finally, if there is in fact some value in using neural networks for this type of problem, I'm extremely intrigued by the ease and intuitiveness with which we can incorporate multiple inputs into our function. Encoding our song title with an LSTM, and training that LSTM end-to-end with our main minimization objective, is one example of this. Furthermore, Keras makes the construction of these networks straightforward.\n",
    "\n",
    "Thanks for reading this work. Your feedback is welcome, and I do hope this serves as a point of inspiration, trial and error should this question interest you."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}