user_artist_recommendation.ipynb

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   "source": [
    "# USER ARTIST RECOMMENDATION \n",
    "\n",
    "This notebook contains the following sections:\n",
    "\n",
    "1. Importing Necessary Libraries\n",
    "2. Loading the data\n",
    "3. Applying the different Algorithms on the dataset\n",
    "4. Visualization of the RMSE of algorithms\n",
    "5. saving the predictions & Trained algorithms\n"
   ]
  },
  {
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   "execution_count": 0,
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    "outputId": "5da1a2c0-f4da-4012-dade-8f8d8c1512ca"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Drive already mounted at /content/drive; to attempt to forcibly remount, call drive.mount(\"/content/drive\", force_remount=True).\n"
     ]
    }
   ],
   "source": [
    "from google.colab import drive\n",
    "drive.mount('/content/drive')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "cAWJk_DfDLLD"
   },
   "outputs": [],
   "source": [
    "root_path = 'drive/My Drive/datasets/'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "NrhKrNRDtDJR"
   },
   "source": [
    "## Importing the Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "4GRwkqe-C9ZZ"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 71
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    "colab_type": "code",
    "id": "c5nB93LmuF2U",
    "outputId": "164551ad-b437-4062-b89b-8bf454b0c4b1"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.6/dist-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n",
      "  import pandas.util.testing as tm\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set()"
   ]
  },
  {
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   "execution_count": 0,
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    {
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     "text": [
      "Requirement already satisfied: surprise in /usr/local/lib/python3.6/dist-packages (0.1)\n",
      "Requirement already satisfied: scikit-surprise in /usr/local/lib/python3.6/dist-packages (from surprise) (1.1.0)\n",
      "Requirement already satisfied: six>=1.10.0 in /usr/local/lib/python3.6/dist-packages (from scikit-surprise->surprise) (1.12.0)\n",
      "Requirement already satisfied: joblib>=0.11 in /usr/local/lib/python3.6/dist-packages (from scikit-surprise->surprise) (0.14.1)\n",
      "Requirement already satisfied: scipy>=1.0.0 in /usr/local/lib/python3.6/dist-packages (from scikit-surprise->surprise) (1.4.1)\n",
      "Requirement already satisfied: numpy>=1.11.2 in /usr/local/lib/python3.6/dist-packages (from scikit-surprise->surprise) (1.18.2)\n"
     ]
    }
   ],
   "source": [
    "!pip install surprise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
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    "id": "scObM5l6H-yD"
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   "source": [
    "# for the data loading & model building\n",
    "from surprise import Reader\n",
    "from surprise import Dataset\n",
    "from surprise.model_selection import cross_validate\n",
    "\n",
    "# built-in in surprise library\n",
    "from surprise import NormalPredictor\n",
    "from surprise import KNNBasic\n",
    "from surprise import KNNWithMeans\n",
    "from surprise import KNNWithZScore\n",
    "from surprise import KNNBaseline\n",
    "from surprise import SVD\n",
    "from surprise import BaselineOnly\n",
    "from surprise import CoClustering\n",
    "\n",
    "# for the metrics\n",
    "from surprise.accuracy import rmse\n",
    "from surprise import accuracy\n",
    "from surprise.model_selection import train_test_split\n",
    "\n",
    "from surprise import dump"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "XD5Qs2RJHFvv"
   },
   "outputs": [],
   "source": [
    "df=pd.read_csv(root_path+'processed_user_song_norm_rating.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
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    "df.head()"
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    "colab": {},
    "colab_type": "code",
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   "source": [
    "df_matrix=df.copy()"
   ]
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   "metadata": {
    "colab": {},
    "colab_type": "code",
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   "source": [
    "df_matrix['rating']=df_matrix.norm_plays.apply(lambda x:math.ceil(x*5))"
   ]
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    "df_matrix.head()"
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  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 136
    },
    "colab_type": "code",
    "id": "bSomtK0CHNr4",
    "outputId": "95119bf3-923c-4511-da07-9bf66f95e74d"
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    {
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       "3     23888\n",
       "0     23011\n",
       "5     14720\n",
       "4     11203\n",
       "Name: rating, dtype: int64"
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     "metadata": {
      "tags": []
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   ],
   "source": [
    "df_matrix.rating.value_counts()"
   ]
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  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "L-KKPhcaub8B"
   },
   "source": [
    "## Loading the dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "1w8i0DwWIMKY"
   },
   "outputs": [],
   "source": [
    "reader = Reader(rating_scale=(0, 5))\n",
    "data = Dataset.load_from_df(df_matrix[['user_id', 'artist_mbid', 'rating']], reader)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "XYDlKOy3ujvv"
   },
   "source": [
    "## Applying different algorithms on the dataset\n",
    "\n",
    "Surprise is a Python scikit building and analyzing recommender systems that deal with explicit rating data.\n",
    "\n",
    "1. **NormalPredictor**\n",
    "Algorithm predicting a random rating based on the distribution of the training set, which is assumed to be normal.\n",
    "2. **BaselineOnly**\n",
    "Algorithm predicting the baseline estimate for given user and item.\n",
    "3. **KNNBasic**\n",
    "A basic collaborative filtering algorithm.\n",
    "4.**KNNWithMeans**\n",
    "A basic collaborative filtering algorithm, taking into account the mean ratings of each user.\n",
    "5. **KNNWithZScore**\tA basic collaborative filtering algorithm, taking into account\n",
    "6. **KNNBaseline**\n",
    "A basic collaborative filtering algorithm taking into account a baseline rating.\n",
    "7. **SVD**\n",
    "The famous SVD algorithm, as popularized by Simon Funk during the Netflix Prize.When baselines are not used, this is equivalent to Probabilistic Matrix Factorization.\n",
    "8. **CoClustering**\n",
    "A collaborative filtering algorithm based on co-clustering.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "U2p5DTCZIU5B"
   },
   "outputs": [],
   "source": [
    "benchmark = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 102
    },
    "colab_type": "code",
    "id": "-oNirLYzIdks",
    "outputId": "abceab3a-9795-47b3-8adb-5f998dca550c"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test_rmse    0.999404\n",
      "fit_time      20.8388\n",
      "test_time     1.41231\n",
      "Algorithm         SVD\n",
      "dtype: object\n"
     ]
    }
   ],
   "source": [
    "algorithm=SVD()\n",
    "results = cross_validate(algorithm, data, measures=['RMSE'], cv=3, verbose=False,n_jobs=-1)\n",
    "# Get results & append algorithm name\n",
    "tmp = pd.DataFrame.from_dict(results).mean(axis=0)\n",
    "tmp = tmp.append(pd.Series([str(algorithm).split(' ')[0].split('.')[-1]], index=['Algorithm']))\n",
    "benchmark.append(tmp)\n",
    "print(tmp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 102
    },
    "colab_type": "code",
    "id": "pOEzZZz-N0e1",
    "outputId": "60b80055-43d9-4117-82da-0a3a49317b48"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[test_rmse    0.999404\n",
       " fit_time      20.8388\n",
       " test_time     1.41231\n",
       " Algorithm         SVD\n",
       " dtype: object]"
      ]
     },
     "execution_count": 17,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "benchmark"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 102
    },
    "colab_type": "code",
    "id": "Bv3a1ODGOw4r",
    "outputId": "a48925f9-0521-4cef-f6cb-d7f4dc0ca352"
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test_rmse         1.04965\n",
      "fit_time          5.97117\n",
      "test_time         1.03193\n",
      "Algorithm    CoClustering\n",
      "dtype: object\n"
     ]
    }
   ],
   "source": [
    "algorithm=CoClustering()\n",
    "results = cross_validate(algorithm, data, measures=['RMSE'], cv=3, verbose=False,n_jobs=-1)\n",
    "# Get results & append algorithm name\n",
    "tmp = pd.DataFrame.from_dict(results).mean(axis=0)\n",
    "tmp = tmp.append(pd.Series([str(algorithm).split(' ')[0].split('.')[-1]], index=['Algorithm']))\n",
    "benchmark.append(tmp)\n",
    "print(tmp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 102
    },
    "colab_type": "code",
    "id": "tqZiqb3LO48X",
    "outputId": "a916ec3d-271e-4565-d980-0a4917339420"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test_rmse         0.98313\n",
      "fit_time         0.238169\n",
      "test_time        0.847652\n",
      "Algorithm    BaselineOnly\n",
      "dtype: object\n"
     ]
    }
   ],
   "source": [
    "algorithm=BaselineOnly()\n",
    "results = cross_validate(algorithm, data, measures=['RMSE'], cv=3, verbose=False,n_jobs=-1)\n",
    "# Get results & append algorithm name\n",
    "tmp = pd.DataFrame.from_dict(results).mean(axis=0)\n",
    "tmp = tmp.append(pd.Series([str(algorithm).split(' ')[0].split('.')[-1]], index=['Algorithm']))\n",
    "benchmark.append(tmp)\n",
    "print(tmp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 102
    },
    "colab_type": "code",
    "id": "ijo6IraOPBU9",
    "outputId": "41718e7f-fc00-48ef-aa1e-cc4ebc555de5"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test_rmse            1.38196\n",
      "fit_time            0.275818\n",
      "test_time            1.07479\n",
      "Algorithm    NormalPredictor\n",
      "dtype: object\n"
     ]
    }
   ],
   "source": [
    "algorithm=NormalPredictor()\n",
    "results = cross_validate(algorithm, data, measures=['RMSE'], cv=3, verbose=False,n_jobs=-1)\n",
    "# Get results & append algorithm name\n",
    "tmp = pd.DataFrame.from_dict(results).mean(axis=0)\n",
    "tmp = tmp.append(pd.Series([str(algorithm).split(' ')[0].split('.')[-1]], index=['Algorithm']))\n",
    "benchmark.append(tmp)\n",
    "print(tmp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 102
    },
    "colab_type": "code",
    "id": "sOj8_DpBPt9M",
    "outputId": "57df75af-6c2f-41e1-f682-ebf8c94cfad8"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test_rmse        1.03562\n",
      "fit_time         8.32349\n",
      "test_time        25.0677\n",
      "Algorithm    KNNBaseline\n",
      "dtype: object\n"
     ]
    }
   ],
   "source": [
    "#KNNBaseline(), KNNBasic(), KNNWithMeans(), KNNWithZScore()\n",
    "algorithm=KNNBaseline()\n",
    "results = cross_validate(algorithm, data, measures=['RMSE'], cv=3, verbose=False,n_jobs=-1)\n",
    "# Get results & append algorithm name\n",
    "tmp = pd.DataFrame.from_dict(results).mean(axis=0)\n",
    "tmp = tmp.append(pd.Series([str(algorithm).split(' ')[0].split('.')[-1]], index=['Algorithm']))\n",
    "benchmark.append(tmp)\n",
    "print(tmp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 102
    },
    "colab_type": "code",
    "id": "HuqmAPczQWFa",
    "outputId": "c63d594b-d214-4a5e-bad7-831872685748"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test_rmse     1.05706\n",
      "fit_time      6.88764\n",
      "test_time     20.2464\n",
      "Algorithm    KNNBasic\n",
      "dtype: object\n"
     ]
    }
   ],
   "source": [
    "algorithm=KNNBasic()\n",
    "results = cross_validate(algorithm, data, measures=['RMSE'], cv=3, verbose=False,n_jobs=-1)\n",
    "# Get results & append algorithm name\n",
    "tmp = pd.DataFrame.from_dict(results).mean(axis=0)\n",
    "tmp = tmp.append(pd.Series([str(algorithm).split(' ')[0].split('.')[-1]], index=['Algorithm']))\n",
    "benchmark.append(tmp)\n",
    "print(tmp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 102
    },
    "colab_type": "code",
    "id": "hfwbofoBQrcu",
    "outputId": "8d565439-beb3-4fb6-b18f-053e492792a4"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test_rmse          1.0416\n",
      "fit_time          6.46295\n",
      "test_time         20.9325\n",
      "Algorithm    KNNWithMeans\n",
      "dtype: object\n"
     ]
    }
   ],
   "source": [
    "algorithm=KNNWithMeans()\n",
    "results = cross_validate(algorithm, data, measures=['RMSE'], cv=3, verbose=False,n_jobs=-1)\n",
    "# Get results & append algorithm name\n",
    "tmp = pd.DataFrame.from_dict(results).mean(axis=0)\n",
    "tmp = tmp.append(pd.Series([str(algorithm).split(' ')[0].split('.')[-1]], index=['Algorithm']))\n",
    "benchmark.append(tmp)\n",
    "print(tmp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 102
    },
    "colab_type": "code",
    "id": "LiQWV93SQ-n1",
    "outputId": "cc7f586d-50af-46c8-a38f-4c735d296e7f"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test_rmse          1.04342\n",
      "fit_time            6.5001\n",
      "test_time           24.731\n",
      "Algorithm    KNNWithZScore\n",
      "dtype: object\n"
     ]
    }
   ],
   "source": [
    "algorithm=KNNWithZScore()\n",
    "results = cross_validate(algorithm, data, measures=['RMSE'], cv=3, verbose=False,n_jobs=-1)\n",
    "# Get results & append algorithm name\n",
    "tmp = pd.DataFrame.from_dict(results).mean(axis=0)\n",
    "tmp = tmp.append(pd.Series([str(algorithm).split(' ')[0].split('.')[-1]], index=['Algorithm']))\n",
    "benchmark.append(tmp)\n",
    "print(tmp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 578
    },
    "colab_type": "code",
    "id": "PrG5PPRaRYXA",
    "outputId": "cd370730-03b3-4881-aec0-d3243fe6ef2e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[test_rmse    0.999404\n",
       " fit_time      20.8388\n",
       " test_time     1.41231\n",
       " Algorithm         SVD\n",
       " dtype: object, test_rmse         1.04965\n",
       " fit_time          5.97117\n",
       " test_time         1.03193\n",
       " Algorithm    CoClustering\n",
       " dtype: object, test_rmse         0.98313\n",
       " fit_time         0.238169\n",
       " test_time        0.847652\n",
       " Algorithm    BaselineOnly\n",
       " dtype: object, test_rmse            1.38196\n",
       " fit_time            0.275818\n",
       " test_time            1.07479\n",
       " Algorithm    NormalPredictor\n",
       " dtype: object, test_rmse        1.03562\n",
       " fit_time         8.32349\n",
       " test_time        25.0677\n",
       " Algorithm    KNNBaseline\n",
       " dtype: object, test_rmse     1.05706\n",
       " fit_time      6.88764\n",
       " test_time     20.2464\n",
       " Algorithm    KNNBasic\n",
       " dtype: object, test_rmse          1.0416\n",
       " fit_time          6.46295\n",
       " test_time         20.9325\n",
       " Algorithm    KNNWithMeans\n",
       " dtype: object, test_rmse          1.04342\n",
       " fit_time            6.5001\n",
       " test_time           24.731\n",
       " Algorithm    KNNWithZScore\n",
       " dtype: object]"
      ]
     },
     "execution_count": 29,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "benchmark"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "YwL4o4R7wIpP"
   },
   "source": [
    "## Viewing the RMSE of cross-validated algorithms in a tabular form along with bar plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "MMZ6sbvqUi_V"
   },
   "outputs": [],
   "source": [
    "results = pd.DataFrame(benchmark).set_index('Algorithm').sort_values('test_rmse')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 328
    },
    "colab_type": "code",
    "id": "31Za5f3kVSqO",
    "outputId": "70a03fed-91b6-4f6c-9ea6-98d8da0edcd7"
   },
   "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>test_rmse</th>\n",
       "      <th>fit_time</th>\n",
       "      <th>test_time</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Algorithm</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>BaselineOnly</th>\n",
       "      <td>0.983130</td>\n",
       "      <td>0.238169</td>\n",
       "      <td>0.847652</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SVD</th>\n",
       "      <td>0.999404</td>\n",
       "      <td>20.838790</td>\n",
       "      <td>1.412307</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>KNNBaseline</th>\n",
       "      <td>1.035618</td>\n",
       "      <td>8.323485</td>\n",
       "      <td>25.067735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>KNNWithMeans</th>\n",
       "      <td>1.041597</td>\n",
       "      <td>6.462947</td>\n",
       "      <td>20.932547</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>KNNWithZScore</th>\n",
       "      <td>1.043424</td>\n",
       "      <td>6.500100</td>\n",
       "      <td>24.730976</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CoClustering</th>\n",
       "      <td>1.049652</td>\n",
       "      <td>5.971171</td>\n",
       "      <td>1.031934</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>KNNBasic</th>\n",
       "      <td>1.057062</td>\n",
       "      <td>6.887641</td>\n",
       "      <td>20.246378</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NormalPredictor</th>\n",
       "      <td>1.381961</td>\n",
       "      <td>0.275818</td>\n",
       "      <td>1.074793</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 test_rmse   fit_time  test_time\n",
       "Algorithm                                       \n",
       "BaselineOnly      0.983130   0.238169   0.847652\n",
       "SVD               0.999404  20.838790   1.412307\n",
       "KNNBaseline       1.035618   8.323485  25.067735\n",
       "KNNWithMeans      1.041597   6.462947  20.932547\n",
       "KNNWithZScore     1.043424   6.500100  24.730976\n",
       "CoClustering      1.049652   5.971171   1.031934\n",
       "KNNBasic          1.057062   6.887641  20.246378\n",
       "NormalPredictor   1.381961   0.275818   1.074793"
      ]
     },
     "execution_count": 31,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 381
    },
    "colab_type": "code",
    "id": "n3Hz6xXlVZiG",
    "outputId": "40b7aa50-deb1-4f82-f259-d2adbec41555"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fe254eb3860>"
      ]
     },
     "execution_count": 37,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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KseCJiFSKBU9EpFIseCIilWLBExGpFAueiEilWPBERCrFgiciUikWPBGRStUyZKeMjAwE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\neCIilWLBExGpFAueiEilWPBERCr1/wCxb6XiI/CpygAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "results.test_rmse.plot(kind='bar')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "trjisV2Q2Zpj"
   },
   "source": [
    "#### 1.Applying on the train & test dataset\n",
    "#### 2.saving the predictions and trained model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "W_64lLv7Voht",
    "outputId": "cdb1e71b-88a4-4b3d-a3df-2e95d4664758"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE: 0.9983\n"
     ]
    }
   ],
   "source": [
    "name='SVD'\n",
    "trainset, testset = train_test_split(data, test_size=0.25)\n",
    "algo = SVD()\n",
    "predictions = algo.fit(trainset).test(testset)\n",
    "accuracy.rmse(predictions)\n",
    "\n",
    "dump.dump('./predictions_'+name, predictions, algo)\n",
    "predictions, algo = dump.load('./predictions_'+name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "--nP2MDCWtA6",
    "outputId": "89c2830f-978e-42f1-a123-7ce3467ffbb4"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimating biases using als...\n",
      "RMSE: 0.9823\n"
     ]
    }
   ],
   "source": [
    "name='BaselineOnly'\n",
    "algo=BaselineOnly()\n",
    "predictions = algo.fit(trainset).test(testset)\n",
    "accuracy.rmse(predictions)\n",
    "\n",
    "dump.dump('./predictions_'+name, predictions, algo)\n",
    "predictions, algo = dump.load('./predictions_'+name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 85
    },
    "colab_type": "code",
    "id": "52sXD14BX4l3",
    "outputId": "18679e78-c73c-4524-d110-2a596f9490f8"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimating biases using als...\n",
      "Computing the msd similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "RMSE: 1.0298\n"
     ]
    }
   ],
   "source": [
    "name='KNNBaseline'\n",
    "algo=KNNBaseline()\n",
    "predictions = algo.fit(trainset).test(testset)\n",
    "accuracy.rmse(predictions)\n",
    "\n",
    "dump.dump('./predictions_'+name, predictions, algo)\n",
    "predictions, algo = dump.load('./predictions_'+name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 68
    },
    "colab_type": "code",
    "id": "43YbcoyooDTr",
    "outputId": "fa10d0b3-7543-47c2-946b-ae42fe8ab643"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing the msd similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "RMSE: 1.0354\n"
     ]
    }
   ],
   "source": [
    "name='KNNWithMeans'\n",
    "algo=KNNWithMeans()\n",
    "predictions = algo.fit(trainset).test(testset)\n",
    "accuracy.rmse(predictions)\n",
    "\n",
    "dump.dump('./predictions_'+name, predictions, algo)\n",
    "predictions, algo = dump.load('./predictions_'+name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 68
    },
    "colab_type": "code",
    "id": "S-QyODDqoUVE",
    "outputId": "23d3d2c7-b407-4f21-a665-24e4215a72b9"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing the msd similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "RMSE: 1.0383\n"
     ]
    }
   ],
   "source": [
    "name='KNNWithZScore'\n",
    "algo=KNNWithZScore()\n",
    "predictions = algo.fit(trainset).test(testset)\n",
    "accuracy.rmse(predictions)\n",
    "\n",
    "dump.dump('./predictions_'+name, predictions, algo)\n",
    "predictions, algo = dump.load('./predictions_'+name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "3mFmP86Yob9U",
    "outputId": "24c123bd-159c-404a-b59c-9a5382778fde"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE: 1.0517\n"
     ]
    }
   ],
   "source": [
    "name='CoClustering'\n",
    "algo=CoClustering()\n",
    "predictions = algo.fit(trainset).test(testset)\n",
    "accuracy.rmse(predictions)\n",
    "\n",
    "dump.dump('./predictions_'+name, predictions, algo)\n",
    "predictions, algo = dump.load('./predictions_'+name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 68
    },
    "colab_type": "code",
    "id": "RrWj51Aur_eo",
    "outputId": "cb6b8c44-3e9f-4598-9ccf-b703cba5b2a1"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing the msd similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "RMSE: 1.0523\n"
     ]
    }
   ],
   "source": [
    "name='KNNBasic'\n",
    "algo=KNNBasic()\n",
    "predictions = algo.fit(trainset).test(testset)\n",
    "accuracy.rmse(predictions)\n",
    "\n",
    "dump.dump('./predictions_'+name, predictions, algo)\n",
    "predictions, algo = dump.load('./predictions_'+name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "Bdqbj3pysIHW",
    "outputId": "9e96aec6-a917-4a82-eb5b-68a94cc2cf16"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE: 1.3870\n"
     ]
    }
   ],
   "source": [
    "name='NormalPredictor'\n",
    "algo=NormalPredictor()\n",
    "predictions = algo.fit(trainset).test(testset)\n",
    "accuracy.rmse(predictions)\n",
    "\n",
    "dump.dump('./predictions_'+name, predictions, algo)\n",
    "predictions, algo = dump.load('./predictions_'+name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 204
    },
    "colab_type": "code",
    "id": "tnSbP6j6vWDj",
    "outputId": "652c5802-3c91-442b-8b64-2f63c9a0c65f"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['.config',\n",
       " 'predictions_CoClustering',\n",
       " 'drive',\n",
       " 'predictions_KNNBasic',\n",
       " 'predictions_KNNWithZScore',\n",
       " 'predictions_NormalPredictor',\n",
       " 'predictions_KNNBaseline',\n",
       " 'predictions_BaselineOnly',\n",
       " 'predictions_KNNWithMeans',\n",
       " 'predictions_SVD',\n",
       " 'sample_data']"
      ]
     },
     "execution_count": 64,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import os\n",
    "os.listdir()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "AG4DtNY4wRnI",
    "outputId": "92a5e396-6b69-4353-efa3-958f3c0517e2"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'./drive/My Drive/datasets/predictions_SVD'"
      ]
     },
     "execution_count": 71,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import shutil\n",
    "shutil.move('./predictions_SVD', './drive/My Drive/datasets/predictions_SVD')\n",
    "shutil.move('./predictions_BaselineOnly', './drive/My Drive/datasets/predictions_BaselineOnly')\n",
    "shutil.move('./predictions_KNNBasic', './drive/My Drive/datasets/predictions_KNNBasic')\n",
    "shutil.move('./predictions_KNNWithMeans', './drive/My Drive/datasets/predictions_KNNWithMeans')\n",
    "shutil.move('./predictions_CoClustering', './drive/My Drive/datasets/predictions_CoClustering')\n",
    "shutil.move('./predictions_KNNWithZScore', './drive/My Drive/datasets/predictions_KNNWithZScore')\n",
    "shutil.move('./predictions_KNNBaseline', './drive/My Drive/datasets/predictions_KNNBaseline')\n",
    "shutil.move('./predictions_NormalPredictor', './drive/My Drive/datasets/predictions_NormalPredictor')"
   ]
  }
 ],
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