ISYE_6740.ipynb

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        "<a href=\"https://colab.research.google.com/github/jtsou/Amazon-Recommendation-Engine/blob/main/ISYE_6740.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IG_v-_u5qRUn"
      },
      "source": [
        "# Final Project - Build recommendation engine using Amazon electronic products dataset\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "j7539rMENc60"
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      "source": [
        "#import os\n",
        "#import json\n",
        "#import gzip\n",
        "import pandas as pd\n",
        "#from urllib.request import urlopen\n",
        "#import seaborn\n",
        "from matplotlib import pyplot as plt\n",
        "import random\n",
        "import numpy as np\n",
        "#from tqdm import tqdm_notebook as tqdm\n",
        "#from collections import defaultdict\n",
        "# import wget"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vIsfZkR_mM8_"
      },
      "source": [
        "## 1. Import data and build user/items dataframe - *Jennifer Tsou*"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "1.a Original COMPLETE Dataset (commented out as we do not use this for the purpose of the report)"
      ],
      "metadata": {
        "id": "O7x4QRNartjc"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "VW1rdCx5N2oM"
      },
      "outputs": [],
      "source": [
        "# !wget http://deepyeti.ucsd.edu/jianmo/amazon/categoryFilesSmall/Electronics.csv"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "M0jTq7bmOnU3"
      },
      "outputs": [],
      "source": [
        "# electronics_rating_full = pd.read_csv('Electronics.csv', header= None)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "j4MjG08nRDkA"
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      "source": [
        "# electronics_rating_full.columns = ['item','user','rating','timestamp']\n",
        "# electronics_rating_full.head()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "1.b Filtered Dataset (we use this for our project)"
      ],
      "metadata": {
        "id": "pZ9yNeLfr78y"
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    {
      "cell_type": "markdown",
      "source": [
        "data loading from github"
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              "         item            user  rating   timestamp\n",
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      ],
      "source": [
        "electronics_rating = pd.read_csv('https://raw.githubusercontent.com/jtsou/Amazon-Recommendation-Engine/main/Electronics_filtered.csv')\n",
        "electronics_rating.head()"
      ]
    },
    {
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      "source": [
        "# Data formatting and exploration"
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      "source": [
        "electronics_rating['timestamp'] = pd.to_datetime(electronics_rating['timestamp'],unit='s')"
      ]
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          "text": [
            "<class 'pandas.core.frame.DataFrame'>\n",
            "RangeIndex: 64087 entries, 0 to 64086\n",
            "Data columns (total 4 columns):\n",
            " #   Column     Non-Null Count  Dtype         \n",
            "---  ------     --------------  -----         \n",
            " 0   item       64087 non-null  object        \n",
            " 1   user       64087 non-null  object        \n",
            " 2   rating     64087 non-null  float64       \n",
            " 3   timestamp  64087 non-null  datetime64[ns]\n",
            "dtypes: datetime64[ns](1), float64(1), object(2)\n",
            "memory usage: 2.0+ MB\n"
          ]
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      "source": [
        "electronics_rating.info()"
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          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:1: FutureWarning: Treating datetime data as categorical rather than numeric in `.describe` is deprecated and will be removed in a future version of pandas. Specify `datetime_is_numeric=True` to silence this warning and adopt the future behavior now.\n",
            "  \"\"\"Entry point for launching an IPython kernel.\n"
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              "count                   64087\n",
              "unique                   3352\n",
              "top       2015-12-09 00:00:00\n",
              "freq                       99\n",
              "first     2003-01-18 00:00:00\n",
              "last      2018-09-26 00:00:00\n",
              "Name: timestamp, dtype: object"
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        "electronics_rating.timestamp.describe()"
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              "count              64087\n",
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              "top       A12DQZKRKTNF5E\n",
              "freq                  59\n",
              "Name: user, dtype: object"
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              "   rating  frequency\n",
              "0     1.0       2053\n",
              "1     2.0       1672\n",
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      ],
      "source": [
        "# Find out the rating distribution\n",
        "electronics_rating.groupby('rating').size().reset_index(name='frequency')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 316
        },
        "id": "5yilJuVsSZDb",
        "outputId": "41bcc110-c3ea-43d0-f540-140225978e28"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x7fd07cb8b9d0>]],\n",
              "      dtype=object)"
            ]
          },
          "metadata": {},
          "execution_count": 14
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "electronics_rating.hist(column=\"rating\",grid=False,bins=5)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ndXMI3HQSeog"
      },
      "source": [
        "# Create user_id and item_id columns - Ming Lu"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "E54XNzHcSeDh"
      },
      "outputs": [],
      "source": [
        "# Create indices df for user and item lists\n",
        "user_list = pd.DataFrame(electronics_rating.user.unique(),columns=[\"user\"]).reset_index().rename(columns={\"index\":\"user_index\"})\n",
        "item_list = pd.DataFrame(electronics_rating.item.unique(),columns=[\"item\"]).reset_index().rename(columns={\"index\":\"item_index\"})"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "y7xqZYwLSqRx"
      },
      "outputs": [],
      "source": [
        "# Add user_id and item_id columns to the df\n",
        "electronics_rating = electronics_rating.merge(user_list,on='user')\n",
        "electronics_rating = electronics_rating.merge(item_list,on='item')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "y5TwNzUnSrXL",
        "outputId": "73f09786-4d54-43e7-fe42-ff3930bbb287"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "         item            user  rating  timestamp  user_index  item_index\n",
              "0  B00001P4ZH  A2VFN33XFSDW9C     4.0 2017-08-11           0           0\n",
              "1  B00001P4ZH  A19MJFMEE3035J     2.0 2017-03-18           1           0\n",
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              "3  B00001P4ZH   ABMF4UC4Z00NT     2.0 2016-09-12           3           0\n",
              "4  B00001P4ZH  A2WJOOZA5T2KQ5     1.0 2016-05-07           4           0"
            ],
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              "          document.querySelector('#df-75f0cc5e-5848-4916-95fb-649564687996 button.colab-df-convert');\n",
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              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
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              "          const element = document.querySelector('#df-75f0cc5e-5848-4916-95fb-649564687996');\n",
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              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ],
      "source": [
        "electronics_rating.head()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7ijLP4bHSw45"
      },
      "source": [
        "# Split train and test data - Ming Lu"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "cHxjuHtzS3_p"
      },
      "outputs": [],
      "source": [
        "from sklearn.model_selection import train_test_split\n",
        "\n",
        "train, test = train_test_split(electronics_rating, test_size=0.2, random_state=42, stratify=electronics_rating.user)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zNOgGAjiS4DY",
        "outputId": "b53b084d-540d-4575-f59e-f890a3567516"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(4963, 4963)"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ],
      "source": [
        "# Validate both datasets contains the same users\n",
        "train.user.unique().shape[0],test.user.unique().shape[0]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "liinbHBjlqi-"
      },
      "source": [
        "## 2. Build similarity function to calculate distance between users - *Jennifer Tsou*"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "5ttvLwISiKNS"
      },
      "outputs": [],
      "source": [
        "# KNN model with cosine\n",
        "from sklearn.neighbors import NearestNeighbors\n",
        "n_users = electronics_rating.user.unique().shape[0]\n",
        "n_items = electronics_rating.item.unique().shape[0]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "S2UtYCejTEiK"
      },
      "outputs": [],
      "source": [
        "# create user-item matrix for training dataset\n",
        "# Ming - I updated the for loop to generate the matrix using the user_id and item_id\n",
        "data_matrix_train = np.zeros((n_users, n_items))\n",
        "for line in train.itertuples():\n",
        "    data_matrix_train[line[5], line[6]] = line[3]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "26yMBa7xTHNk"
      },
      "outputs": [],
      "source": [
        "# create user-item matrix for testing dataset\n",
        "data_matrix_test = np.zeros((n_users, n_items))\n",
        "for line in test.itertuples():\n",
        "    data_matrix_test[line[5], line[6]] = line[3]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "XfEvO6EITL-R"
      },
      "outputs": [],
      "source": [
        "# calculate similarity\n",
        "from sklearn.metrics.pairwise import pairwise_distances \n",
        "user_similarity = pairwise_distances(data_matrix_train, metric='cosine')\n",
        "item_similarity = pairwise_distances(data_matrix_train.T, metric='cosine')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GOpt9D5wmZ1W"
      },
      "source": [
        "## 3. Build function to make predictions based on similarity - *Jennifer Tsou*"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "lpO--fDVg5wz"
      },
      "outputs": [],
      "source": [
        "# build function to make predictions based on similarity\n",
        "def predict(ratings, similarity, type='user'):\n",
        "    if type == 'user':\n",
        "        mean_user_rating = ratings.mean(axis=1)\n",
        "        #We use np.newaxis so that mean_user_rating has same format as ratings\n",
        "        ratings_diff = (ratings - mean_user_rating[:, np.newaxis])\n",
        "        pred = mean_user_rating[:, np.newaxis] + similarity.dot(ratings_diff) / np.array([np.abs(similarity).sum(axis=1)]).T\n",
        "    elif type == 'item':\n",
        "        pred = ratings.dot(similarity) / np.array([np.abs(similarity).sum(axis=1)])\n",
        "    return pred\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "hyzvTLgD3ok0"
      },
      "outputs": [],
      "source": [
        "# make prediction on training data\n",
        "user_prediction = predict(data_matrix_train, user_similarity, type='user')\n",
        "item_prediction = predict(data_matrix_train, item_similarity, type='item')\n",
        "# make prediction on testing data\n",
        "#user_prediction = predict(data_matrix_test, user_similarity, type='user')\n",
        "#item_prediction = predict(data_matrix_test, item_similarity, type='item')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "O8ueMYAtwsLT"
      },
      "outputs": [],
      "source": [
        "# Computing total mean squared error\n",
        "def mse(data_matrix,prediction):\n",
        "    xs, ys = data_matrix.nonzero()\n",
        "    error = 0\n",
        "    for x, y in zip(xs, ys):\n",
        "        error += pow(data_matrix[x, y] - prediction[x, y], 2)\n",
        "    return np.sqrt(error)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Qijt58OewsyV",
        "outputId": "4454a523-40c7-4185-df2f-8df70078b7b1"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "MSE_user:  510.8944645208593\n",
            "MSE_item:  516.8892642813942\n"
          ]
        }
      ],
      "source": [
        "MSE_user = mse(data_matrix_test, user_prediction)\n",
        "MSE_item = mse(data_matrix_test, item_prediction)\n",
        "print('MSE_user: ', MSE_user)\n",
        "print('MSE_item: ', MSE_item)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gZiNS0Rhm05Y"
      },
      "source": [
        "## 4. Build utility functions for training the models - MSE, SGD, etc. - *Ming Lu*"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "WOJ_I-jUTqDq"
      },
      "outputs": [],
      "source": [
        "# Full user rating-item matrix\n",
        "def full_matrix(b,user_bias,item_bias,P,Q):\n",
        "    return b + user_bias[:,np.newaxis] + item_bias[np.newaxis:,] + P.dot(Q.T)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "hMtlmbXYTrUL"
      },
      "outputs": [],
      "source": [
        "# Ratings for user i and item j\n",
        "def get_rating(b,user_bias,item_bias,P,Q,i,j):\n",
        "    prediction = b + user_bias[i] + item_bias[j] + P[i, :].dot(Q[j, :].T)\n",
        "    return prediction"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "dsC99FraTtzZ"
      },
      "outputs": [],
      "source": [
        "# Stochastic gradient descent to get optimized P and Q matrix\n",
        "def sgd(b,user_bias,item_bias,P,Q,samples,alpha,beta):\n",
        "    # alpha – Learning rate for stochastic gradient descent\n",
        "    # beta – Regularization parameter for bias\n",
        "    \n",
        "    for i, j, r in samples:\n",
        "        prediction = get_rating(b,user_bias,item_bias,P,Q,i,j)\n",
        "        e = (r - prediction)\n",
        "\n",
        "        # Update the bias terms and P & Q matrices\n",
        "        user_bias[i] += alpha * (e - beta * user_bias[i])\n",
        "        item_bias[j] += alpha * (e - beta * item_bias[j])\n",
        "\n",
        "        P[i, :] += alpha * (e * Q[j, :] - beta * P[i,:])\n",
        "        Q[j, :] += alpha * (e * P[i, :] - beta * Q[j,:])\n",
        "    return user_bias, item_bias, P, Q"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7KNkZk34psG_"
      },
      "source": [
        "## 5. Build training function - *Jonhua Qin*"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "T89vGWprTxSD"
      },
      "outputs": [],
      "source": [
        "def train_model(data_matrix, K, alpha, beta, iterations=100):\n",
        "    # data_matrix – The user-item rating matrix \n",
        "    # K – Number of latent features\n",
        "    # iterations – Number of iterations to perform stochastic gradient descent\n",
        "    \n",
        "    # Define number of user and items\n",
        "    n_users = data_matrix.shape[0]\n",
        "    n_items = data_matrix.shape[1]\n",
        "    \n",
        "    # Initializing user-feature (P) and item-feature (Q) matrix \n",
        "    P = np.random.normal(scale=1./K, size=(n_users, K))\n",
        "    Q = np.random.normal(scale=1./K, size=(n_items, K))\n",
        "\n",
        "    # Initialize bias terms\n",
        "    user_bias = np.zeros(n_users)\n",
        "    item_bias = np.zeros(n_items)\n",
        "    b = np.mean(data_matrix[np.where(data_matrix != 0)])\n",
        "    \n",
        "    # Define list of training samples\n",
        "    samples = [\n",
        "    (i, j, data_matrix[i, j])\n",
        "    for i in range(n_users)\n",
        "    for j in range(n_items)\n",
        "    if data_matrix[i, j] > 0\n",
        "    ]\n",
        "    \n",
        "    # Stochastic gradient descent for given number of iterations\n",
        "    training_process = []\n",
        "    for i in range(iterations):\n",
        "        np.random.shuffle(samples)\n",
        "        user_bias, item_bias, P, Q = sgd(b,user_bias,item_bias,P,Q,samples,alpha,beta)\n",
        "        prediction = full_matrix(b,user_bias,item_bias,P,Q)\n",
        "        error = mse(data_matrix,prediction)\n",
        "        training_process.append((i, error))\n",
        "        if (i+1) % 20 == 0:\n",
        "            print(\"Iteration: %d ; error = %.4f\" % (i+1, error))\n",
        "\n",
        "    return training_process,b,user_bias,item_bias,P,Q"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jeEBi4-Hp0y3"
      },
      "source": [
        "## 6. Make predictions using the model - *Jonhua Qin*"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0D4jp-UiTy8x",
        "outputId": "9fc3d0a6-18e1-4f7c-d7c1-7715f00c82ea"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteration: 20 ; error = 199.4380\n",
            "Iteration: 40 ; error = 192.3041\n",
            "Iteration: 60 ; error = 187.6527\n",
            "Iteration: 80 ; error = 184.2580\n",
            "Iteration: 100 ; error = 181.4742\n"
          ]
        }
      ],
      "source": [
        "# predict the missing ratings with alpha = 0.001, beta=0.01, K=20\n",
        "training_process,b,user_bias,item_bias,P,Q = train_model(data_matrix_train, K=20, alpha=0.001, beta=0.01, iterations=100)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vuxHbFJXT0Ce",
        "outputId": "7b03bca2-7d24-4fae-c5d4-742dc985ef49"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteration: 20 ; error = 199.6648\n",
            "Iteration: 40 ; error = 192.7936\n",
            "Iteration: 60 ; error = 188.4594\n",
            "Iteration: 80 ; error = 185.4842\n",
            "Iteration: 100 ; error = 183.2813\n"
          ]
        }
      ],
      "source": [
        "# predict the missing ratings with alpha = 0.001, beta=0.01, K=50\n",
        "training_process_2,b_2,user_bias_2,item_bias_2,P_2,Q_2 = train_model(data_matrix_train, K=50, alpha=0.001, beta=0.01, iterations=100)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Vdk9URD8T1SR",
        "outputId": "e2b46a4f-13b7-428e-bff4-6b7abda30841"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteration: 20 ; error = 163.4672\n",
            "Iteration: 40 ; error = 98.3780\n",
            "Iteration: 60 ; error = 57.0105\n",
            "Iteration: 80 ; error = 37.9154\n",
            "Iteration: 100 ; error = 28.3092\n"
          ]
        }
      ],
      "source": [
        "# predict the missing ratings with alpha = 0.01, beta=0.01, K=20\n",
        "training_process_3,b_3,user_bias_3,item_bias_3,P_3,Q_3 = train_model(data_matrix_train, K=20, alpha=0.01, beta=0.01, iterations=100)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "j_ba43JeT2Qa",
        "outputId": "2c7fdaab-104e-4d8f-afe8-e0405b88eb7c"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteration: 20 ; error = 199.6858\n",
            "Iteration: 40 ; error = 192.8633\n",
            "Iteration: 60 ; error = 188.6084\n",
            "Iteration: 80 ; error = 185.7383\n",
            "Iteration: 100 ; error = 183.6894\n"
          ]
        }
      ],
      "source": [
        "# predict the missing ratings with alpha = 0.001, beta=0.1, K=20\n",
        "training_process_4,b_4,user_bias_4,item_bias_4,P_4,Q_4 = train_model(data_matrix_train, K=20, alpha=0.001, beta=0.1, iterations=100)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "EUp-0tzqT305",
        "outputId": "b8e26a2e-b2ca-4c91-8ceb-7c7d10ab7276"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteration: 20 ; error = 181.4399\n",
            "Iteration: 40 ; error = 163.8237\n",
            "Iteration: 60 ; error = 132.6573\n",
            "Iteration: 80 ; error = 100.4325\n",
            "Iteration: 100 ; error = 75.6433\n"
          ]
        }
      ],
      "source": [
        "# predict the missing ratings with alpha = 0.005, beta=0.01, K=20\n",
        "training_process_5,b_5,user_bias_5,item_bias_5,P_5,Q_5 = train_model(data_matrix_train, K=20, alpha=0.005, beta=0.01, iterations=100)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AvdhP5_3T6LY"
      },
      "source": [
        "Convert the best model into prediction matrix"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Round the predictions to integer ratings\n",
        "prediction_1 = np.around(full_matrix(b,user_bias,item_bias,P,Q),0)\n",
        "MSE_1 = mse(data_matrix_test, prediction_1)\n",
        "print(MSE_1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "N0hL8pZ4FReL",
        "outputId": "43030998-21bf-409e-9707-90d7480c73db"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "103.40212763768452\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Round the predictions to integer ratings\n",
        "prediction_2 = np.around(full_matrix(b_2,user_bias_2,item_bias_2,P_2,Q_2),0)\n",
        "MSE_2 = mse(data_matrix_test, prediction_2)\n",
        "print(MSE_2)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "01d9ejFxFSDz",
        "outputId": "662d367d-ee48-48e3-a714-19ac50c94986"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "103.30053242844394\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Round the predictions to integer ratings\n",
        "prediction_3 = np.around(full_matrix(b_3,user_bias_3,item_bias_3,P_3,Q_3),0)\n",
        "MSE_3 = mse(data_matrix_test, prediction_3)\n",
        "print(MSE_3)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ycBCEP3lFSLA",
        "outputId": "78805da9-6ce8-4ebe-bc3e-eb9b79009155"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "112.26753760548951\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Round the predictions to integer ratings\n",
        "prediction_4 = np.around(full_matrix(b_4,user_bias_4,item_bias_4,P_4,Q_4),0)\n",
        "MSE_4 = mse(data_matrix_test, prediction_4)\n",
        "print(MSE_4)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GpoKKu_vFSRA",
        "outputId": "2cc5ce4f-3d9d-484d-aa55-40f23eee4d88"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "103.39245620450265\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Round the predictions to integer ratings\n",
        "prediction_5 = np.around(full_matrix(b_5,user_bias_5,item_bias_5,P_5,Q_5),0)\n",
        "MSE_5 = mse(data_matrix_test, prediction_5)\n",
        "print(MSE_5)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DzZezI8JFSfG",
        "outputId": "9ffc8ed2-0756-4757-96df-0b2580115a25"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "106.91585476438937\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "training_process = np.array(training_process)\n",
        "training_process_2 = np.array(training_process_2)\n",
        "training_process_3 = np.array(training_process_3)\n",
        "training_process_4 = np.array(training_process_4)\n",
        "training_process_5 = np.array(training_process_5)"
      ],
      "metadata": {
        "id": "xCb7OniGFbYR"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NktQA1V4UFI6"
      },
      "source": [
        "Validate the prediction results with the test dataset - **to be completed**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ut2m_JwAqKKV"
      },
      "source": [
        "## 7. Visualize Results - *Ming Lu*"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "Tz6DfogaUMpp",
        "outputId": "bd977a4a-916b-4244-f222-892f782a0275"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "plt.plot(training_process[:,0],training_process[:,1],label=\"model 1\")\n",
        "plt.plot(training_process_2[:,0],training_process_2[:,1],label=\"model 2\")\n",
        "plt.plot(training_process_3[:,0],training_process_3[:,1],label=\"model 3\")\n",
        "plt.plot(training_process_4[:,0],training_process_4[:,1],label=\"model 4\")\n",
        "plt.plot(training_process_5[:,0],training_process_5[:,1],label=\"model 5\")\n",
        "plt.title(\"MSE Cost vs. Iteration\")\n",
        "plt.xlabel(\"Iterations\")\n",
        "plt.ylabel(\"MSE\")\n",
        "plt.legend()\n",
        "plt.show()"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [],
      "name": "ISYE 6740.ipynb",
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}