#6.모델기반 협업필터링 및 협업필터링 성능 비교 분석.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "모델 기반 협업 필터링- 협업필터링 성능 비교 분석.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyNeRCTWWMjFMXYL7PHYsvlk",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/moch1996/Vaycold/blob/main/Recommend_Algorithm/%EB%AA%A8%EB%8D%B8_%EA%B8%B0%EB%B0%98_%ED%98%91%EC%97%85_%ED%95%84%ED%84%B0%EB%A7%81_%ED%98%91%EC%97%85%ED%95%84%ED%84%B0%EB%A7%81_%EC%84%B1%EB%8A%A5_%EB%B9%84%EA%B5%90_%EB%B6%84%EC%84%9D.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "duz57tVOT1VU"
      },
      "source": [
        "# Matrix Factorization\n",
        " - Train matrix factorization from scratch\n",
        " - SGD를 사용한 matrix factorization 기법"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "t6xWAVH0Wj8Z"
      },
      "source": [
        "## 라이브러리 불러오기"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YOzs5CYqT3CY"
      },
      "source": [
        "import os\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "from math import sqrt\n",
        "from tqdm import tqdm_notebook as tqdm\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.metrics import mean_squared_error\n",
        "from google.colab import drive"
      ],
      "execution_count": 36,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SN5-sAaWWdmu",
        "outputId": "1a8425b2-4b34-46a5-9ac2-4a2852bac3b9"
      },
      "source": [
        "drive.mount('/content/drive')"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Drive already mounted at /content/drive; to attempt to forcibly remount, call drive.mount(\"/content/drive\", force_remount=True).\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tG1lBDTVW95Y",
        "outputId": "c7e0ee31-0cef-4f04-de49-6f7da65c1b42"
      },
      "source": [
        "os.listdir('drive/MyDrive/fastcampus/recommend/movielens')"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "['ratings.csv', 'tags.csv', 'movies.csv', 'README.txt', 'links.csv']"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "h_JBQbguYEyf"
      },
      "source": [
        "# 데이터 불러오기"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SjBUmuqbW0kj"
      },
      "source": [
        "path = '/content/drive/MyDrive/fastcampus/recommend/movielens'\n",
        "\n",
        "tags_df = pd.read_csv(os.path.join(path, 'tags.csv'), encoding='utf-8')\n",
        "ratings_df = pd.read_csv(os.path.join(path, 'ratings.csv'), encoding='utf-8')"
      ],
      "execution_count": 34,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 195
        },
        "id": "HYSDvzxlX7pC",
        "outputId": "1dcb5ae5-5bb2-4282-c802-5c255c74ab7a"
      },
      "source": [
        "ratings_df.head()"
      ],
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "execute_result",
          "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>userId</th>\n",
              "      <th>movieId</th>\n",
              "      <th>rating</th>\n",
              "      <th>timestamp</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>4.0</td>\n",
              "      <td>964982703</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>3</td>\n",
              "      <td>4.0</td>\n",
              "      <td>964981247</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1</td>\n",
              "      <td>6</td>\n",
              "      <td>4.0</td>\n",
              "      <td>964982224</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1</td>\n",
              "      <td>47</td>\n",
              "      <td>5.0</td>\n",
              "      <td>964983815</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1</td>\n",
              "      <td>50</td>\n",
              "      <td>5.0</td>\n",
              "      <td>964982931</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   userId  movieId  rating  timestamp\n",
              "0       1        1     4.0  964982703\n",
              "1       1        3     4.0  964981247\n",
              "2       1        6     4.0  964982224\n",
              "3       1       47     5.0  964983815\n",
              "4       1       50     5.0  964982931"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 35
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ncTPZnDqYQAd"
      },
      "source": [
        "train_df, test_df = train_test_split(ratings_df, test_size = 0.2, random_state =1234)"
      ],
      "execution_count": 37,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-snRkPNIaZjF",
        "outputId": "ef0e6131-f0e7-4cb5-e246-df3ffe89e2cc"
      },
      "source": [
        "print(train_df.shape)\n",
        "print(test_df.shape)"
      ],
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(80668, 4)\n",
            "(20168, 4)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 195
        },
        "id": "CKQzlf5Habkr",
        "outputId": "88a666ea-0b76-4e62-89fa-a928832044d2"
      },
      "source": [
        "train_df.head()"
      ],
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "execute_result",
          "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>userId</th>\n",
              "      <th>movieId</th>\n",
              "      <th>rating</th>\n",
              "      <th>timestamp</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>95713</th>\n",
              "      <td>600</td>\n",
              "      <td>5943</td>\n",
              "      <td>3.0</td>\n",
              "      <td>1237714356</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>61560</th>\n",
              "      <td>407</td>\n",
              "      <td>2571</td>\n",
              "      <td>5.0</td>\n",
              "      <td>1424349171</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>77204</th>\n",
              "      <td>482</td>\n",
              "      <td>8958</td>\n",
              "      <td>4.0</td>\n",
              "      <td>1105397126</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>93367</th>\n",
              "      <td>599</td>\n",
              "      <td>2322</td>\n",
              "      <td>2.5</td>\n",
              "      <td>1498515283</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>90892</th>\n",
              "      <td>590</td>\n",
              "      <td>2959</td>\n",
              "      <td>3.5</td>\n",
              "      <td>1258416553</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "       userId  movieId  rating   timestamp\n",
              "95713     600     5943     3.0  1237714356\n",
              "61560     407     2571     5.0  1424349171\n",
              "77204     482     8958     4.0  1105397126\n",
              "93367     599     2322     2.5  1498515283\n",
              "90892     590     2959     3.5  1258416553"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 39
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "C6F3emmMadIw"
      },
      "source": [
        "# 이번에는 트레이닝 셋 8만 개중 1000개만 가져와서 해보겠다.\n",
        "\n",
        "train_df = train_df[:1000]"
      ],
      "execution_count": 40,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 402
        },
        "id": "zrq8CytCan2z",
        "outputId": "f06fadc0-76c4-44fa-c175-b78288f35199"
      },
      "source": [
        "train_df"
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "execute_result",
          "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>userId</th>\n",
              "      <th>movieId</th>\n",
              "      <th>rating</th>\n",
              "      <th>timestamp</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>95713</th>\n",
              "      <td>600</td>\n",
              "      <td>5943</td>\n",
              "      <td>3.0</td>\n",
              "      <td>1237714356</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>61560</th>\n",
              "      <td>407</td>\n",
              "      <td>2571</td>\n",
              "      <td>5.0</td>\n",
              "      <td>1424349171</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>77204</th>\n",
              "      <td>482</td>\n",
              "      <td>8958</td>\n",
              "      <td>4.0</td>\n",
              "      <td>1105397126</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>93367</th>\n",
              "      <td>599</td>\n",
              "      <td>2322</td>\n",
              "      <td>2.5</td>\n",
              "      <td>1498515283</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>90892</th>\n",
              "      <td>590</td>\n",
              "      <td>2959</td>\n",
              "      <td>3.5</td>\n",
              "      <td>1258416553</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8026</th>\n",
              "      <td>56</td>\n",
              "      <td>454</td>\n",
              "      <td>3.0</td>\n",
              "      <td>835799253</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>83682</th>\n",
              "      <td>534</td>\n",
              "      <td>2716</td>\n",
              "      <td>4.5</td>\n",
              "      <td>1459787997</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>52176</th>\n",
              "      <td>339</td>\n",
              "      <td>8874</td>\n",
              "      <td>3.0</td>\n",
              "      <td>1460185453</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>32181</th>\n",
              "      <td>220</td>\n",
              "      <td>5502</td>\n",
              "      <td>1.0</td>\n",
              "      <td>1230061876</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>33351</th>\n",
              "      <td>226</td>\n",
              "      <td>4214</td>\n",
              "      <td>4.0</td>\n",
              "      <td>1096422021</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>1000 rows × 4 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "       userId  movieId  rating   timestamp\n",
              "95713     600     5943     3.0  1237714356\n",
              "61560     407     2571     5.0  1424349171\n",
              "77204     482     8958     4.0  1105397126\n",
              "93367     599     2322     2.5  1498515283\n",
              "90892     590     2959     3.5  1258416553\n",
              "...       ...      ...     ...         ...\n",
              "8026       56      454     3.0   835799253\n",
              "83682     534     2716     4.5  1459787997\n",
              "52176     339     8874     3.0  1460185453\n",
              "32181     220     5502     1.0  1230061876\n",
              "33351     226     4214     4.0  1096422021\n",
              "\n",
              "[1000 rows x 4 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 41
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "E8jZGpG1arNf"
      },
      "source": [
        "# Sparse Matrix 만들기"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WLqSJMrJaovb"
      },
      "source": [
        "sparse_matrix = train_df.groupby('movieId').apply(lambda x : pd.Series(x['rating'].values, index = x['userId'])).unstack()\n",
        "# 이번에는 sparse matrix에 빈공간을 0으로 채워주자\n",
        "\n",
        "sparse_matrix = sparse_matrix.fillna(0)"
      ],
      "execution_count": 42,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jcNS8QvlbLXo",
        "outputId": "460e45e1-7312-4ceb-8e33-2c16d2184e6a"
      },
      "source": [
        "type(sparse_matrix) # 데이터프레임인뎅 matrix factorization을 위해 numpy로 구현해야됨"
      ],
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "pandas.core.frame.DataFrame"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 44
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 274
        },
        "id": "OEZlvHzFbPlI",
        "outputId": "b8a476bb-250d-485b-a762-1a2e94ce5e8f"
      },
      "source": [
        "sparse_matrix.head()"
      ],
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "execute_result",
          "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>userId</th>\n",
              "      <th>1</th>\n",
              "      <th>2</th>\n",
              "      <th>4</th>\n",
              "      <th>5</th>\n",
              "      <th>6</th>\n",
              "      <th>7</th>\n",
              "      <th>10</th>\n",
              "      <th>15</th>\n",
              "      <th>16</th>\n",
              "      <th>17</th>\n",
              "      <th>18</th>\n",
              "      <th>19</th>\n",
              "      <th>20</th>\n",
              "      <th>21</th>\n",
              "      <th>22</th>\n",
              "      <th>23</th>\n",
              "      <th>24</th>\n",
              "      <th>28</th>\n",
              "      <th>29</th>\n",
              "      <th>31</th>\n",
              "      <th>32</th>\n",
              "      <th>33</th>\n",
              "      <th>34</th>\n",
              "      <th>36</th>\n",
              "      <th>38</th>\n",
              "      <th>40</th>\n",
              "      <th>41</th>\n",
              "      <th>42</th>\n",
              "      <th>45</th>\n",
              "      <th>46</th>\n",
              "      <th>47</th>\n",
              "      <th>49</th>\n",
              "      <th>50</th>\n",
              "      <th>51</th>\n",
              "      <th>52</th>\n",
              "      <th>56</th>\n",
              "      <th>57</th>\n",
              "      <th>58</th>\n",
              "      <th>59</th>\n",
              "      <th>61</th>\n",
              "      <th>...</th>\n",
              "      <th>551</th>\n",
              "      <th>552</th>\n",
              "      <th>553</th>\n",
              "      <th>555</th>\n",
              "      <th>557</th>\n",
              "      <th>560</th>\n",
              "      <th>561</th>\n",
              "      <th>563</th>\n",
              "      <th>564</th>\n",
              "      <th>567</th>\n",
              "      <th>568</th>\n",
              "      <th>569</th>\n",
              "      <th>570</th>\n",
              "      <th>571</th>\n",
              "      <th>572</th>\n",
              "      <th>573</th>\n",
              "      <th>577</th>\n",
              "      <th>578</th>\n",
              "      <th>579</th>\n",
              "      <th>580</th>\n",
              "      <th>582</th>\n",
              "      <th>583</th>\n",
              "      <th>584</th>\n",
              "      <th>586</th>\n",
              "      <th>587</th>\n",
              "      <th>590</th>\n",
              "      <th>593</th>\n",
              "      <th>596</th>\n",
              "      <th>597</th>\n",
              "      <th>599</th>\n",
              "      <th>600</th>\n",
              "      <th>601</th>\n",
              "      <th>602</th>\n",
              "      <th>603</th>\n",
              "      <th>604</th>\n",
              "      <th>605</th>\n",
              "      <th>606</th>\n",
              "      <th>607</th>\n",
              "      <th>608</th>\n",
              "      <th>610</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>movieId</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",
              "      <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",
              "      <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",
              "      <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>0.0</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",
              "      <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",
              "      <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",
              "      <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",
              "      <td>0.0</td>\n",
              "      <td>5.0</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",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>...</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",
              "      <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",
              "      <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",
              "      <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",
              "      <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>3.0</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>3</th>\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",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>3.0</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",
              "      <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",
              "      <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",
              "      <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",
              "      <td>0.0</td>\n",
              "      <td>...</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",
              "      <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",
              "      <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",
              "      <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",
              "      <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",
              "      <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>0.0</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",
              "      <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",
              "      <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",
              "      <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",
              "      <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",
              "      <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>...</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",
              "      <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",
              "      <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",
              "      <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",
              "      <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",
              "      <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>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>4.0</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",
              "      <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",
              "      <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",
              "      <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",
              "      <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",
              "      <td>0.0</td>\n",
              "      <td>...</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",
              "      <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",
              "      <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",
              "      <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",
              "      <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",
              "      <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>9</th>\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",
              "      <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",
              "      <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",
              "      <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",
              "      <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",
              "      <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>...</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",
              "      <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",
              "      <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",
              "      <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",
              "      <td>0.0</td>\n",
              "      <td>1.5</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",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>5 rows × 347 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "userId   1    2    4    5    6    7    10   ...  603  604  605  606  607  608  610\n",
              "movieId                                     ...                                   \n",
              "1        0.0  0.0  0.0  0.0  0.0  0.0  0.0  ...  0.0  3.0  0.0  0.0  0.0  0.0  0.0\n",
              "3        0.0  0.0  0.0  0.0  0.0  0.0  0.0  ...  0.0  0.0  0.0  0.0  0.0  0.0  0.0\n",
              "5        0.0  0.0  0.0  0.0  0.0  0.0  0.0  ...  0.0  0.0  0.0  0.0  0.0  0.0  0.0\n",
              "6        0.0  0.0  0.0  0.0  4.0  0.0  0.0  ...  0.0  0.0  0.0  0.0  0.0  0.0  0.0\n",
              "9        0.0  0.0  0.0  0.0  0.0  0.0  0.0  ...  0.0  0.0  0.0  0.0  0.0  0.0  0.0\n",
              "\n",
              "[5 rows x 347 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 45
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "W7Y_XoHAbdFm"
      },
      "source": [
        "sparse_matrix = sparse_matrix.to_numpy()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UuGNJGyQbhZp",
        "outputId": "d1c6dc1f-865e-49d5-f95c-dea491a76b2d"
      },
      "source": [
        "sparse_matrix"
      ],
      "execution_count": 49,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0., 0., 0., ..., 0., 0., 0.],\n",
              "       [0., 0., 0., ..., 0., 0., 0.],\n",
              "       [0., 0., 0., ..., 0., 0., 0.],\n",
              "       ...,\n",
              "       [0., 0., 0., ..., 0., 0., 0.],\n",
              "       [0., 0., 0., ..., 0., 0., 0.],\n",
              "       [0., 0., 0., ..., 0., 0., 0.]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 49
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0yuE3_rBbxv9"
      },
      "source": [
        "# Implement Matrix Factorization"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2reeHt-UboKb"
      },
      "source": [
        "class MF():\n",
        "    \n",
        "    def __init__(self, R, K, alpha, beta, iterations):\n",
        "        \"\"\"\n",
        "        Perform matrix factorization to predict empty\n",
        "        entries in a matrix.\n",
        "        \n",
        "        Arguments\n",
        "        - R (ndarray)   : user-item rating matrix\n",
        "        - K (int)       : number of latent dimensions\n",
        "        - alpha (float) : learning rate\n",
        "        - beta (float)  : regularization parameter\n",
        "        \"\"\"\n",
        "        \n",
        "        self.R = R\n",
        "        self.num_users, self.num_items = R.shape\n",
        "        self.K = K\n",
        "        self.alpha = alpha\n",
        "        self.beta = beta\n",
        "        # epochs \n",
        "        self.iterations = iterations\n",
        "\n",
        "    def train(self):\n",
        "        # Initialize user and item latent feature matrice\n",
        "        self.P = np.random.normal(scale=1./self.K, size=(self.num_users, self.K))\n",
        "        self.Q = np.random.normal(scale=1./self.K, size=(self.num_items, self.K))\n",
        "        \n",
        "        # Initialize the biases\n",
        "        self.b_u = np.zeros(self.num_users)\n",
        "        self.b_i = np.zeros(self.num_items)\n",
        "        self.b = np.mean(self.R[np.where(self.R != 0)])\n",
        "        \n",
        "        # Create a list of training samples\n",
        "        self.samples = [\n",
        "            (i, j, self.R[i, j])\n",
        "            for i in range(self.num_users)\n",
        "            for j in range(self.num_items)\n",
        "            if self.R[i, j] > 0\n",
        "        ]\n",
        "        \n",
        "        # Perform stochastic gradient descent for number of iterations\n",
        "        training_process = []\n",
        "        for i in range(self.iterations):\n",
        "            np.random.shuffle(self.samples)\n",
        "            self.sgd()\n",
        "            mse = self.mse()\n",
        "            training_process.append((i, mse))\n",
        "            # if (i+1) % 10 == 0:\n",
        "            print(\"Iteration: %d ; error = %.4f\" % (i+1, mse))\n",
        "        \n",
        "        return training_process\n",
        "\n",
        "    def mse(self):\n",
        "        \"\"\"\n",
        "        A function to compute the total mean square error\n",
        "        \"\"\"\n",
        "        xs, ys = self.R.nonzero()\n",
        "        predicted = self.full_matrix()\n",
        "        error = 0\n",
        "        for x, y in zip(xs, ys):\n",
        "            error += pow(self.R[x, y] - predicted[x, y], 2)\n",
        "        return np.sqrt(error)\n",
        "\n",
        "    def sgd(self):\n",
        "        \"\"\"\n",
        "        Perform stochastic graident descent\n",
        "        \"\"\"\n",
        "        for i, j, r in self.samples:\n",
        "            # Computer prediction and error\n",
        "            prediction = self.get_rating(i, j)\n",
        "            e = (r - prediction)\n",
        "            \n",
        "            # Update biases\n",
        "            self.b_u[i] += self.alpha * (e - self.beta * self.b_u[i])\n",
        "            self.b_i[j] += self.alpha * (e - self.beta * self.b_i[j])\n",
        "            \n",
        "            # Create copy of row of P since we need to update it but use older values for update on Q\n",
        "            P_i = self.P[i, :][:]\n",
        "            \n",
        "            # Update user and item latent feature matrices\n",
        "            self.P[i, :] += self.alpha * (e * self.Q[j, :] - self.beta * self.P[i,:])\n",
        "            self.Q[j, :] += self.alpha * (e * P_i - self.beta * self.Q[j,:])\n",
        "\n",
        "    def get_rating(self, i, j):\n",
        "        \"\"\"\n",
        "        Get the predicted rating of user i and item j\n",
        "        \"\"\"\n",
        "        prediction = self.b + self.b_u[i] + self.b_i[j] + self.P[i, :].dot(self.Q[j, :].T)\n",
        "        return prediction\n",
        "    \n",
        "    def full_matrix(self):\n",
        "        \"\"\"\n",
        "        Computer the full matrix using the resultant biases, P and Q\n",
        "        \"\"\"\n",
        "        return self.b + self.b_u[:,np.newaxis] + self.b_i[np.newaxis:,] + self.P.dot(self.Q.T)"
      ],
      "execution_count": 50,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4cKhCpmUiBoV"
      },
      "source": [
        "## Train MF"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Ga8L1W3FiA0I",
        "outputId": "bf21a342-06ab-44c3-87eb-92b413c1c0ce"
      },
      "source": [
        "sparse_matrix.shape"
      ],
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(799, 347)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 52
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "B33AwbAViFNC"
      },
      "source": [
        "mf = MF(sparse_matrix, K=50, alpha=0.1, beta=0.01,iterations=20)"
      ],
      "execution_count": 54,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Ml--kupSiT4F",
        "outputId": "926bd478-68e9-4de0-e1c6-d987a93f150b"
      },
      "source": [
        "training_process = mf.train()"
      ],
      "execution_count": 58,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Iteration: 1 ; error = 25.1691\n",
            "Iteration: 2 ; error = 21.4122\n",
            "Iteration: 3 ; error = 18.7209\n",
            "Iteration: 4 ; error = 16.5556\n",
            "Iteration: 5 ; error = 14.7192\n",
            "Iteration: 6 ; error = 13.0626\n",
            "Iteration: 7 ; error = 11.5756\n",
            "Iteration: 8 ; error = 10.2315\n",
            "Iteration: 9 ; error = 8.9916\n",
            "Iteration: 10 ; error = 7.8999\n",
            "Iteration: 11 ; error = 6.9385\n",
            "Iteration: 12 ; error = 6.0865\n",
            "Iteration: 13 ; error = 5.3413\n",
            "Iteration: 14 ; error = 4.6895\n",
            "Iteration: 15 ; error = 4.1272\n",
            "Iteration: 16 ; error = 3.6495\n",
            "Iteration: 17 ; error = 3.2386\n",
            "Iteration: 18 ; error = 2.8883\n",
            "Iteration: 19 ; error = 2.5902\n",
            "Iteration: 20 ; error = 2.3356\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cS09A-HBiZpH"
      },
      "source": [
        "# 이번에는 8만개 전부를 다 사용해보자\n",
        "train_df_large, test_df = train_test_split(ratings_df, test_size = 0.2, random_state =1234)"
      ],
      "execution_count": 61,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "sKPn5G4_jDZn",
        "outputId": "d7dec9ea-2fb7-48b5-fd56-aa956fc5ef84"
      },
      "source": [
        "print(train_df_large.shape)"
      ],
      "execution_count": 62,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(80668, 4)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GrxWG9fjjF7e"
      },
      "source": [
        "sparse_matrix_large = train_df_large.groupby('movieId').apply(lambda x : pd.Series(x['rating'].values, index = x['userId'])).unstack()\n",
        "\n",
        "sparse_matrix_large = sparse_matrix_large.fillna(0)"
      ],
      "execution_count": 64,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "y8xlgQaGjaFq",
        "outputId": "f13240e8-bf40-4e87-fcfe-3f5ac861c28d"
      },
      "source": [
        "print(type(sparse_matrix_large))\n",
        "print(sparse_matrix.shape)"
      ],
      "execution_count": 66,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "<class 'pandas.core.frame.DataFrame'>\n",
            "(799, 347)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "i0-KdyjXjgzz"
      },
      "source": [
        "sparse_matrix_large = sparse_matrix_large.to_numpy()"
      ],
      "execution_count": 67,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CPGamFtqjs9t",
        "outputId": "278b2190-8f6f-46a5-bec2-7367180352e5"
      },
      "source": [
        "sparse_matrix_large.shape"
      ],
      "execution_count": 68,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(8938, 610)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 68
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KRl5510vjv50",
        "outputId": "e56a5ab8-ecb7-4595-c430-44f1c7a81894"
      },
      "source": [
        "# 다시 Train\n",
        "mf = MF(sparse_matrix_large, K=300, alpha=0.1, beta=0.01,iterations=20)\n",
        "training_process = mf.train()\n",
        "\n",
        "# 보면 에러값이 NaN으로 떠버림\n",
        "# 이유가 뭘까 ...\n",
        "# 너무 sparse해서 학습이 안되는 것이 아닐까??"
      ],
      "execution_count": 70,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:82: RuntimeWarning: overflow encountered in multiply\n",
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:81: RuntimeWarning: overflow encountered in multiply\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Iteration: 1 ; error = nan\n",
            "Iteration: 2 ; error = nan\n",
            "Iteration: 3 ; error = nan\n",
            "Iteration: 4 ; error = nan\n",
            "Iteration: 5 ; error = nan\n",
            "Iteration: 6 ; error = nan\n",
            "Iteration: 7 ; error = nan\n",
            "Iteration: 8 ; error = nan\n",
            "Iteration: 9 ; error = nan\n",
            "Iteration: 10 ; error = nan\n",
            "Iteration: 11 ; error = nan\n",
            "Iteration: 12 ; error = nan\n",
            "Iteration: 13 ; error = nan\n",
            "Iteration: 14 ; error = nan\n",
            "Iteration: 15 ; error = nan\n",
            "Iteration: 16 ; error = nan\n",
            "Iteration: 17 ; error = nan\n",
            "Iteration: 18 ; error = nan\n",
            "Iteration: 19 ; error = nan\n",
            "Iteration: 20 ; error = nan\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "i_fxzoCVj0mO",
        "outputId": "c2bbe817-501d-4c60-ae1c-2f00df11072e"
      },
      "source": [
        "# 아까 그 작은 train set의 k를 300으로 조정해보자\n",
        "\n",
        "mf = MF(sparse_matrix, K=300, alpha=0.1, beta=0.01,iterations=20)\n",
        "training_process = mf.train()"
      ],
      "execution_count": 71,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Iteration: 1 ; error = 25.2446\n",
            "Iteration: 2 ; error = 21.6010\n",
            "Iteration: 3 ; error = 19.0632\n",
            "Iteration: 4 ; error = 17.1451\n",
            "Iteration: 5 ; error = 15.5344\n",
            "Iteration: 6 ; error = 14.2320\n",
            "Iteration: 7 ; error = 13.0584\n",
            "Iteration: 8 ; error = 12.0171\n",
            "Iteration: 9 ; error = 11.0658\n",
            "Iteration: 10 ; error = 10.1795\n",
            "Iteration: 11 ; error = 9.3455\n",
            "Iteration: 12 ; error = 8.5453\n",
            "Iteration: 13 ; error = 7.7855\n",
            "Iteration: 14 ; error = 7.0665\n",
            "Iteration: 15 ; error = 6.3906\n",
            "Iteration: 16 ; error = 5.7818\n",
            "Iteration: 17 ; error = 5.2347\n",
            "Iteration: 18 ; error = 4.7526\n",
            "Iteration: 19 ; error = 4.3208\n",
            "Iteration: 20 ; error = 3.9337\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Rn6G4wWDkc4b",
        "outputId": "4c2835a5-c086-4670-9577-f565a0dd163f"
      },
      "source": [
        "mf.full_matrix()"
      ],
      "execution_count": 72,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[4.8824881 , 4.90612605, 4.55584619, ..., 3.97892669, 3.77095567,\n",
              "        4.1278937 ],\n",
              "       [4.19300213, 4.21577027, 3.86489783, ..., 3.28800953, 3.0793722 ,\n",
              "        3.42914141],\n",
              "       [3.71701884, 3.73943503, 3.38787564, ..., 2.81118423, 2.60748621,\n",
              "        2.94567105],\n",
              "       ...,\n",
              "       [4.10942132, 4.13276552, 3.78103918, ..., 3.20422   , 2.99734616,\n",
              "        3.34553365],\n",
              "       [4.40456962, 4.42789152, 4.07681012, ..., 3.49971546, 3.28829363,\n",
              "        3.64357773],\n",
              "       [3.8747832 , 3.89845911, 3.54724741, ..., 2.97022301, 2.76195351,\n",
              "        3.11242619]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 72
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "nupHajBNkhLo",
        "outputId": "b4fc9f02-207c-4294-8598-a7eeedb93ad5"
      },
      "source": [
        "# Training Process를 그래프로 확인해보자\n",
        "\n",
        "x = [x for x, y in training_process]\n",
        "y = [y for x, y in training_process]\n",
        "plt.figure(figsize=(16,4))\n",
        "plt.plot(x,y)\n",
        "plt.xticks(x, x)\n",
        "plt.xlabel('Iterations')\n",
        "plt.ylabel('Mean Squared Error')\n",
        "plt.grid(axis = 'y')"
      ],
      "execution_count": 73,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 1152x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_RCOugB8k63D"
      },
      "source": [
        "  "
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}