k_means.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# K Means Clustering: An Iterative Approach\n",
    "\n",
    "Given a dataset *d*, automatically segment *d* such that data points fall into *k* number distinct clusters. \n",
    "\n",
    "A cluster is defined as any data group which demonstrates greater in-group similarity than out-of-group similarity. In other words, members of a cluster share commonalities among features which do not necessarily extend to members of other clusters. \n",
    "\n",
    "How does one measure feature \"commonalities\"? There are various methods. In this notebook, Euclidean distance among data points plotted in feature space will be used as the similarity metric. \n",
    "\n",
    "First, some housekeeping. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Reset the workspace, forcibly deleting all existing variables \n",
    "%reset -f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd \n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.pyplot import figure\n",
    "from random import randint\n",
    "from math import sqrt\n",
    "from IPython import display"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Importing the Data\n",
    "\n",
    "The set that will be used in this demo is a .csv file located in a subdirectory named Data. This script would theroretically work with any two-dimensional dataset, that is, any .csv containing data points plottable using two coordinates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load data into a pandas dataframe\n",
    "df = pd.read_csv('Data/mall_customers.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Shall we shuffle the dataset? This is not strictly necessary for k means clustering. \n",
    "shuffle_on = False\n",
    "if shuffle_on:\n",
    "    df = df.sample(frac=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dataframe shape: (200, 5)\n",
      "Number of data examples: 200\n",
      "Number of data featrues: 5\n",
      "Number of dimensions: 2\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CustomerID</th>\n",
       "      <th>Gender</th>\n",
       "      <th>Age</th>\n",
       "      <th>Annual Income (k$)</th>\n",
       "      <th>Spending Score (1-100)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>Male</td>\n",
       "      <td>19</td>\n",
       "      <td>15</td>\n",
       "      <td>39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>Male</td>\n",
       "      <td>21</td>\n",
       "      <td>15</td>\n",
       "      <td>81</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>Female</td>\n",
       "      <td>20</td>\n",
       "      <td>16</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>Female</td>\n",
       "      <td>23</td>\n",
       "      <td>16</td>\n",
       "      <td>77</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>Female</td>\n",
       "      <td>31</td>\n",
       "      <td>17</td>\n",
       "      <td>40</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   CustomerID  Gender  Age  Annual Income (k$)  Spending Score (1-100)\n",
       "0           1    Male   19                  15                      39\n",
       "1           2    Male   21                  15                      81\n",
       "2           3  Female   20                  16                       6\n",
       "3           4  Female   23                  16                      77\n",
       "4           5  Female   31                  17                      40"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Print data dimensionality to get our bearings. Then display first few rows\n",
    "print('Dataframe shape:', df.shape)\n",
    "print('Number of data examples:', df.shape[0])\n",
    "print('Number of data featrues:', df.shape[1])\n",
    "print('Number of dimensions:', df.ndim)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CustomerID</th>\n",
       "      <th>Age</th>\n",
       "      <th>Annual Income (k$)</th>\n",
       "      <th>Spending Score (1-100)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>100.500000</td>\n",
       "      <td>38.850000</td>\n",
       "      <td>60.560000</td>\n",
       "      <td>50.200000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>57.879185</td>\n",
       "      <td>13.969007</td>\n",
       "      <td>26.264721</td>\n",
       "      <td>25.823522</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>18.000000</td>\n",
       "      <td>15.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>50.750000</td>\n",
       "      <td>28.750000</td>\n",
       "      <td>41.500000</td>\n",
       "      <td>34.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>100.500000</td>\n",
       "      <td>36.000000</td>\n",
       "      <td>61.500000</td>\n",
       "      <td>50.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>150.250000</td>\n",
       "      <td>49.000000</td>\n",
       "      <td>78.000000</td>\n",
       "      <td>73.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>200.000000</td>\n",
       "      <td>70.000000</td>\n",
       "      <td>137.000000</td>\n",
       "      <td>99.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       CustomerID         Age  Annual Income (k$)  Spending Score (1-100)\n",
       "count  200.000000  200.000000          200.000000              200.000000\n",
       "mean   100.500000   38.850000           60.560000               50.200000\n",
       "std     57.879185   13.969007           26.264721               25.823522\n",
       "min      1.000000   18.000000           15.000000                1.000000\n",
       "25%     50.750000   28.750000           41.500000               34.750000\n",
       "50%    100.500000   36.000000           61.500000               50.000000\n",
       "75%    150.250000   49.000000           78.000000               73.000000\n",
       "max    200.000000   70.000000          137.000000               99.000000"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Display summary statistics of the data. This includes basics like mean, min, max, and standard deviation\n",
    "df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'numpy.ndarray'> <class 'numpy.ndarray'>\n"
     ]
    }
   ],
   "source": [
    "# Define dataset from existing dataframe\n",
    "x = df['Age'].to_numpy()\n",
    "y = df['Annual Income (k$)'].to_numpy()\n",
    "\n",
    "print(type(x), type(y)) # Resultant variables are numpy arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set desired number of clusters (any positive integer > 0)\n",
    "k = 4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step I: Initialize Centroids\n",
    "Randomly select the starting locations of the cluster centers (a.k.a., \"centroids\"). \n",
    "\n",
    "There will be as many centroids as desired clusters (equal to *k*, defined above). \n",
    "\n",
    "We will also visualize the centroids (see below). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Centroid coordinates:\n",
      "29.6, 51.2\n",
      "45.6, 82.4\n",
      "30.400000000000002, 23.200000000000003\n",
      "52.0, 16.8\n",
      "<class 'list'> <class 'list'>\n",
      "4\n"
     ]
    }
   ],
   "source": [
    "def initialize_centroids(x_data, y_data, k):\n",
    "    \"\"\"\n",
    "    Randomly instantiate centroids and return their coordinates in separate lists containing x and y components.\n",
    "    \n",
    "    Generates k number centroids at random locations within range of the data, which is \n",
    "    calculated and then reduced by 20%. This reduction is specified by the local variable\n",
    "    'margin' and prevents cluster centroids from instantiating at the edge of the set, which \n",
    "    is less than optimal for the k means algorithm. \n",
    "\n",
    "    Args:\n",
    "        x_data (numpy.ndarray): data for independent variable.\n",
    "        y_data (numpy.ndarray): data for dependent variable.\n",
    "        k (int): desired number of centroids/clusters.\n",
    "\n",
    "    Returns:\n",
    "        initial_centroids_x_coords: a list of length k, where each element is the x-coordinate of a centroid.\n",
    "        initial_centroids_y_coords: a list of length k, where each element is the y-coordinate of a centroid.\n",
    "\n",
    "    \"\"\"\n",
    "    x_max = np.amax(x_data) \n",
    "    x_min = np.amin(x_data)\n",
    "    y_max = np.amax(y_data)\n",
    "    y_min = np.amin(y_data)\n",
    "    margin = 0.20 # Precludes centroids at edge of data range\n",
    "    \n",
    "    initial_centroids_x_coords = [] # List of all centroids' x coordinates\n",
    "    initial_centroids_y_coords = [] # List of all centroids' y coordinates\n",
    "\n",
    "    for i in range(k):\n",
    "        initial_centroids_x_coords.append(randint(x_min, x_max)*(1-margin))\n",
    "        initial_centroids_y_coords.append(randint(y_min, y_max)*(1-margin))\n",
    "\n",
    "    return initial_centroids_x_coords, initial_centroids_y_coords\n",
    "\n",
    "# Set number of clusters \n",
    "initial_centroids_x, initial_centroids_y = initialize_centroids(x, y, k)\n",
    "print('Centroid coordinates:')\n",
    "for j in range(k):\n",
    "    print(initial_centroids_x[j],', ', initial_centroids_y[j], sep='')\n",
    "    \n",
    "print(type(initial_centroids_x), type(initial_centroids_y))\n",
    "print(len(initial_centroids_x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step II: Assign Each Data Point to its Nearest Centroid\n",
    "Remember, in this notebook, our metric will be Euclidean Distance. \n",
    "\n",
    "i. First find the distance between every combination of points and centroids.\n",
    "\n",
    "ii. For each data point, identify the centroid whose distance is smallest.\n",
    "\n",
    "iii. Assign every data point to its nearest centroid (identified in ii). Centroids and their member data points will be stored in a dictionary, to be returned by the function make_clusters. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def find_distance(x1, y1, x2, y2):\n",
    "    \"\"\"\n",
    "    Find Euclidean distance between a point (x1, y1) and another point (x2, y2).\n",
    "    \n",
    "    In the context of k means clustering, for a given set containing data points of the form (x1, y1),\n",
    "    find the distance between every point in that set and every centroid (x2, y2).\n",
    "\n",
    "    Args:\n",
    "        x1 (int or float): x coordinate of first point.\n",
    "        y1 (int or float): y coordinate of first point.\n",
    "        x2 (int or float): x coordinate of second point.\n",
    "        y2 (int or float): y coordinate of second point.\n",
    "\n",
    "    Returns:\n",
    "        distance: as a float. \n",
    "\n",
    "    \"\"\"\n",
    "    distance = sqrt((x1 - x2)**2 + (y1 - y2)**2)\n",
    "    return distance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TYPE of clusters: <class 'dict'>\n",
      "dict_keys([(30.400000000000002, 23.200000000000003), (52.0, 16.8), (29.6, 51.2), (45.6, 82.4)])\n"
     ]
    }
   ],
   "source": [
    "def make_clusters(x, y, k_x, k_y):\n",
    "    \"\"\"\n",
    "    Create clusters by assigning each data point to its nearest centroid. \n",
    "    \n",
    "    1. Find the Euclidean distance between every point described by (x,y) and every centroid (k_x, k_y).\n",
    "    2. For each point, compare distances to find the nearest centroid. \n",
    "    3. Assign each point to the nearest centroid. \n",
    "    4. Return clusters as a dictionary, where keys are centroid coords and values are lists of member coords. \n",
    "    \n",
    "    Args:\n",
    "        x (numpy.ndarray): contains x coordinate of every data point\n",
    "        y (numpy.ndarray): contains y coordinate of every data point\n",
    "        k_x (list): contains x coordinate of every centroid\n",
    "        k_y (list): contains y coordinate of every centroid \n",
    "        d (numpy.ndarray): null array of size (k+1, len(x)). Will store centroid distances\n",
    "\n",
    "    Returns:\n",
    "        clusters (dict): \n",
    "            keys: tuples containing centroid coordinates in the form (k_x, k_y)\n",
    "            values: lists containing assigned member points' coordinates as tuples of the form (x, y)\n",
    "\n",
    "    \"\"\"\n",
    "    k = len(initial_centroids_x) # Number of centroids \n",
    "    \n",
    "    clusters = {}\n",
    "    for j in range(len(x)): #200\n",
    "        min_distance = 9999999999 # Arbitrarily large number \n",
    "        x_i, y_i = x[j], y[j] # Select (x, y) coords of one data point at a time\n",
    "        for i in range(0, k): # k = number of clusters\n",
    "            k_xi, k_yi = k_x[i], k_y[i] # Coordinates of each centroid  \n",
    "            distance = find_distance(x_i, y_i, k_xi, k_yi)\n",
    "            if distance < min_distance:\n",
    "                min_distance = distance \n",
    "                centroid_coords = k_xi, k_yi\n",
    "        try: \n",
    "            clusters[centroid_coords].append(tuple([x_i, y_i]))\n",
    "        except KeyError:\n",
    "            clusters[centroid_coords] = [tuple([x_i, y_i])]\n",
    "       \n",
    "    return clusters\n",
    "\n",
    "clusters = make_clusters(x, y, initial_centroids_x, initial_centroids_y)\n",
    "print('TYPE of clusters:',type(clusters))\n",
    "print(clusters.keys())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of entries in clusters dict: 4\n",
      "Keys: dict_keys([(30.400000000000002, 23.200000000000003), (52.0, 16.8), (29.6, 51.2), (45.6, 82.4)])\n",
      "Centroid coords:\n",
      "(29.6, 51.2)\n",
      "(45.6, 82.4)\n",
      "(30.400000000000002, 23.200000000000003)\n",
      "(52.0, 16.8)\n"
     ]
    }
   ],
   "source": [
    "# Print data characteristics as a 'sanity check.'\n",
    "print(\"Number of entries in clusters dict:\", len(clusters))\n",
    "print(\"Keys:\", clusters.keys())\n",
    "print(\"Centroid coords:\")\n",
    "for i in range(k):\n",
    "    print('(',initial_centroids_x[i],', ',initial_centroids_y[i], ')', sep ='')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step III: Reassign Cluster Centers\n",
    "In Step II, we created ad-hoc clusters by assigning each data point to the nearest randomly-initialized centroid. \n",
    "\n",
    "Since the centroid was initialized randomly, it is not located in the \"true\" center of its cluster. Rather, it approximates the center of a bunch of points who could not be assigned to another, nearer, centroid. \n",
    "\n",
    "The \"true\" center is the mean of the dataset. This is where the centroid will be moved. In our 2D dataset, the mean is the point (x, y), where x is the mean of all x coordinates, and y is the mean of all y coordinates. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Centers_x (x coordinates of centers): [28.20689655172414, 59.36842105263158, 34.71875, 40.93181818181818]\n",
      "Centers_y (y coordinates of centers): [23.551724137931036, 34.73684210526316, 53.640625, 83.36363636363636]\n"
     ]
    }
   ],
   "source": [
    "def make_centers(clusters):\n",
    "    \"\"\"\n",
    "    Given 2D data clusters, find each cluster's mean. \n",
    "\n",
    "    Args:\n",
    "        clusters (dict): \n",
    "            keys: tuples containing centroid coordinates in the form (k_x, k_y)\n",
    "            values: lists containing assigned member points' coordinates as tuples of the form (x, y) \n",
    "\n",
    "    Returns:\n",
    "        centers (list): \n",
    "\n",
    "    \"\"\"\n",
    "    centers_x = []\n",
    "    centers_y = []\n",
    "    \n",
    "    for centroid in clusters.keys():\n",
    "        x_mean = 0\n",
    "        y_mean = 0\n",
    "        items = 0\n",
    "        for coord in clusters[centroid]:\n",
    "            items +=1 \n",
    "            x_mean += coord[0]\n",
    "            y_mean += coord[1]\n",
    "        x_mean = x_mean/items\n",
    "        y_mean = y_mean/items\n",
    "        centers_x.append(x_mean)\n",
    "        centers_y.append(y_mean)\n",
    "\n",
    "    return centers_x, centers_y\n",
    "\n",
    "centers_x, centers_y = make_centers(clusters)\n",
    "\n",
    "print('Centers_x (x coordinates of centers):', centers_x)\n",
    "print('Centers_y (y coordinates of centers):', centers_y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Setting Up Visualizations\n",
    "The next two cells set up cluster plotting and the styles to be used by Matplotlib. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_clusters(clusters, centroids_x, centroids_y): # TODO: output of get_individual_cluster will output a key, val pair\n",
    "    \"\"\"\n",
    "    Plots data as assigned to different clusters (demarcated with differing colors), and cluster centroids.\n",
    "\n",
    "    Args:\n",
    "        output_of_get_individual_cluster (key, val): should be a coord of form (x, y). Keep i, replace 'for coord in...'\n",
    "\n",
    "    Returns:\n",
    "        None \n",
    "        \n",
    "    \"\"\"\n",
    "    ax.clear()\n",
    "    \n",
    "    colors = ['turquoise', 'blueviolet', 'gold', 'pink'] # TODO: update with more colors in case of k > 4.\n",
    "\n",
    "    for i in range(4):\n",
    "        for coord in clusters[centroids_x[i], centroids_y[i]]:\n",
    "            ax.scatter(coord[0], coord[1], color = colors[i], edgecolor = 'grey')\n",
    "            ax.scatter(centroids_x[i], centroids_y[i], s= 30, color = 'red', marker='x')\n",
    "    ax.set_title('Income vs. Age')\n",
    "    ax.set_xlabel('Age')\n",
    "    ax.set_ylabel('Income')\n",
    "    fig.canvas.draw()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support. ' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
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     "output_type": "display_data"
    },
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "\n",
    "fig = plt.figure()\n",
    "\n",
    "ax = fig.add_subplot(111)\n",
    "plt.ion()\n",
    "\n",
    "fig.show()\n",
    "fig.canvas.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step IV: Repeat II and III Until Convergence\n",
    "We repeat calculation of cluster means, placement of centroids, and reassignment of member points to clusters until we reach 'MAX_ITERATIONS', which specifies the maximum number of iterations to execute before stopping. \n",
    "    \n",
    "We will also re-draw the cluster visualization upon each iteration. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "MAX_ITERATIONS = 20 # Set desired number. A larger value will take longer to complete. \n",
    "\n",
    "# Centroid will, at first, be located at the random, initialized locations.\n",
    "centroids_x = initial_centroids_x\n",
    "centroids_y = initial_centroids_y\n",
    "\n",
    "for i in range(MAX_ITERATIONS):\n",
    "    clusters = make_clusters(x, y, centroids_x, centroids_y)\n",
    "    plot_clusters(clusters, centroids_x, centroids_y)\n",
    "    centroids_x, centroids_y = make_centers(clusters)\n",
    "    # print(centroids_x, centroids_y)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And that's it! We have now segmented the original data set into *k* clusters. "
   ]
  }
 ],
 "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}