basic_model_evaluation.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import random\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "from surprise import SVD, SVDpp, NMF\n",
    "from surprise import Dataset\n",
    "from surprise import Reader\n",
    "from surprise import evaluate, print_perf\n",
    "from surprise import KNNBasic\n",
    "from surprise import AlgoBase, BaselineOnly\n",
    "from get_top_n import get_top_n\n",
    "from surprise.model_selection import GridSearchCV, train_test_split, cross_validate\n",
    "from surprise.accuracy import rmse, mae"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Set up training & test data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>reviewerID</th>\n",
       "      <th>productID</th>\n",
       "      <th>rating</th>\n",
       "      <th>date</th>\n",
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       "      <th>47007</th>\n",
       "      <td>A1Z7Y2GMAP9SRY</td>\n",
       "      <td>B0004MTMD0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>2013-03-15</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "           reviewerID   productID  rating        date\n",
       "46921  A3OXHLG6DIBRW8  B0004MTMD0     5.0  2012-10-24\n",
       "46941  A1K31E7YNVQRIT  B0004MTMD0     5.0  2014-02-04\n",
       "46946  A1XVQ3KHS22E3F  B0004MTMD0     4.0  2012-08-24\n",
       "46985  A14B4MJ7KZE63B  B0004MTMD0     4.0  2014-05-17\n",
       "47007  A1Z7Y2GMAP9SRY  B0004MTMD0     4.0  2013-03-15"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Load data\n",
    "dt = pd.read_csv('sample_data.csv',index_col=0)\n",
    "dt.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Construct missing ratings we need to predict\n",
    "select_data = dt.pivot_table('rating',index=['reviewerID','productID'],dropna=False)\n",
    "select_data = select_data.loc[select_data['rating'].isnull()]\n",
    "select_data.reset_index(inplace=True)\n",
    "missing_values = select_data[['reviewerID','productID']].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "reader = Reader(rating_scale=(1,5))\n",
    "sdt = Dataset.load_from_df(dt[['reviewerID','productID','rating']],reader)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "trainset, testset = train_test_split(sdt,test_size=0.2,random_state=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>reviewerID</th>\n",
       "      <th>productID</th>\n",
       "      <th>rating</th>\n",
       "    </tr>\n",
       "  </thead>\n",
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       "      <td>5.0</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>A36K2N527TXXJN</td>\n",
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       "      <td>2.0</td>\n",
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       "      <td>3.0</td>\n",
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       "  </tbody>\n",
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      "text/plain": [
       "       reviewerID   productID  rating\n",
       "0  A14MSHFCXPARFS  B005XVZKGA     5.0\n",
       "1  A1Z7Y2GMAP9SRY  B000VK3ZGA     2.0\n",
       "2  A3HAA7H8PBVM78  B00B9AAI9S     5.0\n",
       "3  A36K2N527TXXJN  B0041NYV8E     2.0\n",
       "4  A2QSBOAAGW1I1H  B000VK3ZGA     3.0"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_df = pd.DataFrame(testset)\n",
    "test_df.columns = ['reviewerID','productID','rating']\n",
    "test_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "merged = dt.merge(test_df, indicator=True, how='outer')\n",
    "trainset = Dataset.load_from_df(merged[merged['_merge'] == 'left_only'][['reviewerID','productID','rating']],reader)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Train Models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Baseline Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Baseline model: User's bias & item's bias\n",
    "class BaselineModel(AlgoBase):\n",
    "\n",
    "    def __init__(self):\n",
    "        AlgoBase.__init__(self)\n",
    "\n",
    "    def compute_bias(self):\n",
    "        bu = np.zeros(self.trainset.n_users)\n",
    "        bi = np.zeros(self.trainset.n_items)\n",
    "        global_mean = self.trainset.global_mean\n",
    "        \n",
    "        for i in self.trainset.all_items():\n",
    "            dev_i = 0\n",
    "            for (u, r) in self.trainset.ir[i]:\n",
    "                dev_i += r - global_mean\n",
    "            bi[i] = dev_i/(len(self.trainset.ir[i]))\n",
    "        \n",
    "        for u in self.trainset.all_users():\n",
    "            dev_u = 0\n",
    "            for (i, r) in self.trainset.ur[u]:\n",
    "                dev_u += r - global_mean\n",
    "            bu[u] = dev_u/(len(self.trainset.ur[u]))\n",
    "        return bu, bi\n",
    "    \n",
    "    def fit(self, trainset):\n",
    "        AlgoBase.fit(self, trainset)\n",
    "        self.bu, self.bi = self.compute_bias()\n",
    "\n",
    "    def estimate(self, u, i):\n",
    "        est = self.trainset.global_mean\n",
    "        if self.trainset.knows_user(u):\n",
    "            est += self.bu[u]\n",
    "        if self.trainset.knows_item(i):\n",
    "            est += self.bi[i]\n",
    "        return est\n",
    "\n",
    "algo1 = BaselineModel()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Evaluating RMSE, MAE of algorithm BaselineModel on 5 split(s).\n",
      "\n",
      "                  Fold 1  Fold 2  Fold 3  Fold 4  Fold 5  Mean    Std     \n",
      "RMSE (testset)    1.0693  1.0473  1.0492  1.0318  1.0639  1.0523  0.0133  \n",
      "MAE (testset)     0.8207  0.8027  0.8011  0.7924  0.8068  0.8047  0.0093  \n",
      "Fit time          0.01    0.01    0.01    0.01    0.01    0.01    0.00    \n",
      "Test time         0.01    0.02    0.01    0.01    0.01    0.01    0.00    \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'fit_time': (0.0069425106048583984,\n",
       "  0.005530595779418945,\n",
       "  0.008042573928833008,\n",
       "  0.007688283920288086,\n",
       "  0.007315158843994141),\n",
       " 'test_mae': array([ 0.82067814,  0.80268038,  0.80105823,  0.79238046,  0.80678307]),\n",
       " 'test_rmse': array([ 1.06930759,  1.04734314,  1.04916014,  1.03179912,  1.06387034]),\n",
       " 'test_time': (0.00797891616821289,\n",
       "  0.019609451293945312,\n",
       "  0.013073444366455078,\n",
       "  0.012985706329345703,\n",
       "  0.009579658508300781)}"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Train using baseline model and test on testset\n",
    "cross_validate(algo1,trainset,measures=['RMSE','MAE'],verbose=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model-based Collaborative Filtering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Evaluating RMSE, MAE of algorithm SVD on 5 split(s).\n",
      "\n",
      "                  Fold 1  Fold 2  Fold 3  Fold 4  Fold 5  Mean    Std     \n",
      "RMSE (testset)    1.0003  0.9717  0.9827  0.9872  0.9620  0.9808  0.0131  \n",
      "MAE (testset)     0.8005  0.7639  0.7739  0.7739  0.7638  0.7752  0.0134  \n",
      "Fit time          0.52    0.52    0.53    0.52    0.31    0.48    0.09    \n",
      "Test time         0.03    0.02    0.02    0.02    0.01    0.02    0.01    \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'fit_time': (0.520179271697998,\n",
       "  0.5192575454711914,\n",
       "  0.5313317775726318,\n",
       "  0.5166738033294678,\n",
       "  0.30877065658569336),\n",
       " 'test_mae': array([ 0.80049529,  0.76387528,  0.77394335,  0.77390441,  0.76382835]),\n",
       " 'test_rmse': array([ 1.00028442,  0.97170039,  0.98272254,  0.98715191,  0.96199569]),\n",
       " 'test_time': (0.026485681533813477,\n",
       "  0.018795490264892578,\n",
       "  0.01836228370666504,\n",
       "  0.01898789405822754,\n",
       "  0.008472204208374023)}"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#SVD\n",
    "algo2 = SVD()\n",
    "cross_validate(algo2,trainset,measures=['RMSE','MAE'], verbose= True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Grid-searching hyper-parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Setting different values for the hyperparameters\n",
    "param_grid = {'n_factors':[90,100,110,120], 'lr_all': [0.003,0.004,0.005],\n",
    "              'reg_all': [0.06,0.07,0.08]}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "grid_search = GridSearchCV(SVD, param_grid, measures=['RMSE','MAE'],cv=3)\n",
    "grid_search.fit(trainset)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'mae': 0.77357077495765203, 'rmse': 0.97603688284646928}"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grid_search.best_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'mae': {'lr_all': 0.005, 'n_factors': 100, 'reg_all': 0.06},\n",
       " 'rmse': {'lr_all': 0.005, 'n_factors': 100, 'reg_all': 0.06}}"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grid_search.best_params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#Effect of Hyperparameters on Accuracy (RMSE) of the Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Hyperparameter :- Latent Factors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [],
   "source": [
    "param_grid_factor = {'n_factors':[80,90,100,110,120,130]}\n",
    "grid_search_factor = GridSearchCV(SVD, param_grid_factor, measures=['RMSE','MAE'],cv=3)\n",
    "grid_search_factor.fit(trainset)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'mean_fit_time': array([ 0.4042391 ,  0.41179323,  0.47682969,  0.4924407 ,  0.50511503,\n",
       "         0.46406269]),\n",
       " 'mean_test_mae': array([ 0.78022743,  0.77914948,  0.78091705,  0.77645614,  0.78283748,\n",
       "         0.7834829 ]),\n",
       " 'mean_test_rmse': array([ 0.98383856,  0.98177342,  0.98544486,  0.98168339,  0.98862245,\n",
       "         0.9905214 ]),\n",
       " 'mean_test_time': array([ 0.02897938,  0.03007452,  0.02823671,  0.02838691,  0.02830275,\n",
       "         0.01602403]),\n",
       " 'param_n_factors': [80, 90, 100, 110, 120, 130],\n",
       " 'params': [{'n_factors': 80},\n",
       "  {'n_factors': 90},\n",
       "  {'n_factors': 100},\n",
       "  {'n_factors': 110},\n",
       "  {'n_factors': 120},\n",
       "  {'n_factors': 130}],\n",
       " 'rank_test_mae': array([3, 2, 4, 1, 5, 6]),\n",
       " 'rank_test_rmse': array([3, 2, 4, 1, 5, 6]),\n",
       " 'split0_test_mae': array([ 0.77990536,  0.78211892,  0.78219136,  0.77526789,  0.78601612,\n",
       "         0.78496845]),\n",
       " 'split0_test_rmse': array([ 0.97488591,  0.97559685,  0.98017888,  0.97193675,  0.98199601,\n",
       "         0.98669713]),\n",
       " 'split1_test_mae': array([ 0.77218887,  0.76861317,  0.77111593,  0.76684323,  0.77769616,\n",
       "         0.77171654]),\n",
       " 'split1_test_rmse': array([ 0.98455313,  0.97978987,  0.9799637 ,  0.98170185,  0.99102257,\n",
       "         0.98360807]),\n",
       " 'split2_test_mae': array([ 0.78858807,  0.78671634,  0.78944385,  0.78725731,  0.78480016,\n",
       "         0.79376371]),\n",
       " 'split2_test_rmse': array([ 0.99207664,  0.98993355,  0.99619199,  0.99141155,  0.99284876,\n",
       "         1.00125899]),\n",
       " 'std_fit_time': array([ 0.03569944,  0.00854806,  0.03487153,  0.03709732,  0.00988522,\n",
       "         0.04614213]),\n",
       " 'std_test_mae': array([ 0.00669882,  0.00768307,  0.0075364 ,  0.00837626,  0.0036692 ,\n",
       "         0.00906181]),\n",
       " 'std_test_rmse': array([ 0.00703625,  0.00601864,  0.00759988,  0.00795057,  0.00474454,\n",
       "         0.00769664]),\n",
       " 'std_test_time': array([ 0.00022179,  0.00550247,  0.00404995,  0.00372221,  0.00282062,\n",
       "         0.00229036])}"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grid_factor_results = grid_search_factor.cv_results\n",
    "grid_factor_results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Effect of Latent Factors on Accuracy of the model')"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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XwJtvwne/m+v+8Ae48063l7MFt/76ORbcoEF1v+/MWpHGkrhvSJpW3D4DNq25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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3d1445f630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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HJC7cZmbLnwMVgHIEXbdlgdVmVh+o4u4Tw22+CVwA5JnERa1cYjk6NOxAh4Yd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\nZwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3d1467b208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,6))\n",
    "plt.subplot(2,1,1)\n",
    "plt.plot(param_grid_factor['n_factors'],grid_factor_results['mean_test_rmse'],'r--')\n",
    "plt.xlabel('Latent Factors')\n",
    "plt.ylabel('RMSE')\n",
    "plt.title('Effect of Latent Factors on Accuracy of the model')\n",
    "plt.figure(figsize=(10,6))\n",
    "plt.subplot(2,1,2)\n",
    "plt.plot(param_grid_factor['n_factors'],grid_factor_results['mean_test_mae'],'g--')\n",
    "plt.xlabel('Latent Factors')\n",
    "plt.ylabel('MAE')\n",
    "plt.title('Effect of Latent Factors on Accuracy of the model')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'mean_fit_time': array([ 0.1161449 ,  0.22441824,  0.32670069,  0.43446859,  0.53849037,\n",
       "         0.55040161,  0.69216084]),\n",
       " 'mean_test_mae': array([ 0.80122851,  0.78487631,  0.77871453,  0.77851489,  0.77840865,\n",
       "         0.77969984,  0.78233854]),\n",
       " 'mean_test_rmse': array([ 1.00258199,  0.98796027,  0.98352713,  0.98342985,  0.98649362,\n",
       "         0.98752014,  0.9942491 ]),\n",
       " 'mean_test_time': array([ 0.02705097,  0.02607059,  0.02557532,  0.02564764,  0.02545222,\n",
       "         0.02502751,  0.02157958]),\n",
       " 'param_n_epochs': [5, 10, 15, 20, 25, 30, 35],\n",
       " 'params': [{'n_epochs': 5},\n",
       "  {'n_epochs': 10},\n",
       "  {'n_epochs': 15},\n",
       "  {'n_epochs': 20},\n",
       "  {'n_epochs': 25},\n",
       "  {'n_epochs': 30},\n",
       "  {'n_epochs': 35}],\n",
       " 'rank_test_mae': array([7, 6, 3, 2, 1, 4, 5]),\n",
       " 'rank_test_rmse': array([7, 5, 2, 1, 3, 4, 6]),\n",
       " 'split0_test_mae': array([ 0.80110007,  0.78644357,  0.77944053,  0.77681701,  0.77783443,\n",
       "         0.77856804,  0.78392313]),\n",
       " 'split0_test_rmse': array([ 1.00167902,  0.98855986,  0.98376177,  0.97965301,  0.98578549,\n",
       "         0.98423378,  0.994395  ]),\n",
       " 'split1_test_mae': array([ 0.79646256,  0.77627171,  0.76974982,  0.77107979,  0.77164254,\n",
       "         0.76970097,  0.77093507]),\n",
       " 'split1_test_rmse': array([ 0.99611507,  0.97632805,  0.97185202,  0.97297059,  0.97506826,\n",
       "         0.97552722,  0.98186325]),\n",
       " 'split2_test_mae': array([ 0.80612289,  0.79191365,  0.78695326,  0.78764787,  0.78574898,\n",
       "         0.79083049,  0.79215743]),\n",
       " 'split2_test_rmse': array([ 1.00995189,  0.9989929 ,  0.99496759,  0.99766596,  0.99862711,\n",
       "         1.00279941,  1.00648907]),\n",
       " 'std_fit_time': array([ 0.00075949,  0.00255168,  0.00199991,  0.00691735,  0.00259647,\n",
       "         0.12563495,  0.10952979]),\n",
       " 'std_test_mae': array([ 0.00394486,  0.00648125,  0.00704201,  0.00686961,  0.00577322,\n",
       "         0.00866314,  0.00873614]),\n",
       " 'std_test_rmse': array([ 0.00568483,  0.0092626 ,  0.00943835,  0.01042956,  0.00963089,\n",
       "         0.01137375,  0.01005398]),\n",
       " 'std_test_time': array([  2.52841826e-04,   3.35256256e-04,   8.46240056e-05,\n",
       "          1.44436801e-04,   1.84405773e-04,   2.68636281e-03,\n",
       "          5.35643852e-03])}"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "param_grid_n_epoch = {'n_epochs':[5,10,15,20,25,30,35]}\n",
    "grid_search_n_epoch = GridSearchCV(SVD, param_grid_n_epoch, measures=['RMSE','MAE'],cv=3)\n",
    "grid_search_n_epoch.fit(trainset)\n",
    "cv_results = grid_search_n_epoch.cv_results\n",
    "cv_results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Effect of no. of SGD iterations on Accuracy of the model')"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ssZGclJWVt1dXVgZt2sT8446Dfv2WXjf7A/Hoo+Np2uz8bFtmQ4bA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\niRMREREpQUriRERERErQ/wMSqb04/W+MkgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3d064bc438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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LLMhawK9e+lWiwxEREUkK5XZ1qpmlAvcBxwNLgelm9rK7fxWbxt2vipv+CuDA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\niIhIElISJyIiIpKElMSJiIiIJKH/D1nrJuMus1rVAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3d06295f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,6))\n",
    "plt.subplot(2,1,1)\n",
    "plt.plot(param_grid_n_epoch['n_epochs'],cv_results['mean_test_rmse'],'r--')\n",
    "plt.xlabel('Stochastic Gradient Descent method iterations')\n",
    "plt.ylabel('RMSE')\n",
    "plt.title('Effect of no. of SGD iterations on Accuracy of the model')\n",
    "plt.figure(figsize=(10,6))\n",
    "plt.subplot(2,1,1)\n",
    "plt.plot(param_grid_n_epoch['n_epochs'],cv_results['mean_test_mae'],'g--')\n",
    "plt.xlabel('Stochastic Gradient Descent method iterations')\n",
    "plt.ylabel('MAE')\n",
    "plt.title('Effect of no. of SGD iterations on Accuracy of the model')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "param_grid_lr = {'lr_all': [0.001,0.002,0.003,0.004,0.005]}\n",
    "grid_search_lr = GridSearch(SVD, param_grid_lr, measures=['RMSE','MAE'])\n",
    "grid_search_lr.evaluate(dt)\n",
    "results_df = pd.DataFrame.from_dict(grid_search_lr.cv_results)\n",
    "rm=[]\n",
    "rm=results_df['RMSE']\n",
    "mae_svd=[]\n",
    "for d in grid_search_lr.cv_results['scores']:\n",
    "    mae_svd.append(d['MAE'])\n",
    "n_ep=[]\n",
    "n_ep=results_df['lr_all']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.figure(figsize=(10,6))\n",
    "plt.subplot(2,1,1)\n",
    "plt.plot(n_ep,rm,'r--')\n",
    "plt.xlabel('Learning Rate')\n",
    "plt.ylabel('RMSE')\n",
    "plt.title('Effect of Learning Rate on Accuracy of the model')\n",
    "plt.figure(figsize=(10,6))\n",
    "plt.subplot(2,1,1)\n",
    "plt.plot(n_ep,mae_svd,'g--')\n",
    "plt.xlabel('Learning Rate')\n",
    "plt.ylabel('MAE')\n",
    "plt.title('Effect of Learning Rate on Accuracy of the model')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## KNN Collaborative Filtering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "## define algorithm config\n",
    "algo_name = KNNBasic ##  KNNWithMeans,KNNBaseline\n",
    "sim_option={'name': 'cosine', ## cosine, msd, pearson, personbaseline\n",
    "                 'user_based': 'False', ## False for item-based\n",
    "                 'min_surpport':0 }##  if |Iuv|<min_support then sim(u,v)=0\n",
    "max_k = 10 ## The (max) number of neighbors to take into account for aggregation\n",
    "min_k = 7 ##  If there are not enough neighbors, the prediction is set the the global mean of all ratings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "knn_default = algo_name(k = max_k, min_k = min_k, sim_options=sim_option)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing the cosine similarity matrix...\n",
      "Computing the cosine similarity matrix...\n",
      "Computing the cosine similarity matrix...\n",
      "Computing the cosine similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "Done computing similarity matrix.\n",
      "Done computing similarity matrix.\n",
      "Done computing similarity matrix.\n",
      "Computing the cosine similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "Evaluating RMSE, MAE of algorithm KNNBasic on 5 split(s).\n",
      "\n",
      "                  Fold 1  Fold 2  Fold 3  Fold 4  Fold 5  Mean    Std     \n",
      "RMSE (testset)    1.0417  1.0558  1.0268  1.0305  1.0443  1.0398  0.0104  \n",
      "MAE (testset)     0.8257  0.8442  0.8057  0.8222  0.8298  0.8255  0.0124  \n",
      "Fit time          0.83    0.79    0.82    0.76    0.41    0.72    0.16    \n",
      "Test time         0.25    0.24    0.24    0.29    0.12    0.23    0.06    \n"
     ]
    }
   ],
   "source": [
    "#Train model\n",
    "perf = cross_validate(knn_default, trainset, measures=['RMSE','MAE'], verbose= 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Changing hyper-paramater of KNN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "algo_name = KNNBasic\n",
    "#Define the different hyper-paramter range\n",
    "grid_param = {'k':[5,10,20],\n",
    "             'min_k':[5,6,7,8],\n",
    "             'sim_options':{'name':['msd','cosine','pearson'],\n",
    "                           'min_surpport':[0,3,5],\n",
    "                           'user_based':[False]}\n",
    "             }"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "grid_search = GridSearchCV(algo_name, grid_param, measures=['RMSE', 'MAE'],cv=3);\n",
    "grid_search.fit(trainset);\n",
    "cv_results = grid_search.cv_results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'mae': 0.83906233507951156, 'rmse': 1.0616663064943952}"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grid_search.best_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'mae': {'k': 10,\n",
       "  'min_k': 8,\n",
       "  'sim_options': {'min_surpport': 0, 'name': 'msd', 'user_based': False}},\n",
       " 'rmse': {'k': 10,\n",
       "  'min_k': 8,\n",
       "  'sim_options': {'min_surpport': 0, 'name': 'msd', 'user_based': False}}}"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grid_search.best_params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "### get the result of different hyper-parameter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['mean_fit_time', 'mean_test_mae', 'mean_test_rmse',\n",
       "       'mean_test_time', 'param_k', 'param_min_k', 'param_sim_options',\n",
       "       'params', 'rank_test_mae', 'rank_test_rmse', 'split0_test_mae',\n",
       "       'split0_test_rmse', 'split1_test_mae', 'split1_test_rmse',\n",
       "       'split2_test_mae', 'split2_test_rmse', 'std_fit_time',\n",
       "       'std_test_mae', 'std_test_rmse', 'std_test_time'], dtype=object)"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results_df.columns.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean_test_mae</th>\n",
       "      <th>mean_test_rmse</th>\n",
       "      <th>param_k</th>\n",
       "      <th>param_min_k</th>\n",
       "      <th>sim_matric</th>\n",
       "      <th>min_support</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.850990</td>\n",
       "      <td>1.082520</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>msd</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.850990</td>\n",
       "      <td>1.082520</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>msd</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.850990</td>\n",
       "      <td>1.082520</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>msd</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.862696</td>\n",
       "      <td>1.101631</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>cosine</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.862696</td>\n",
       "      <td>1.101631</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>cosine</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   mean_test_mae  mean_test_rmse  param_k  param_min_k sim_matric  min_support\n",
       "0       0.850990        1.082520        5            5        msd            0\n",
       "1       0.850990        1.082520        5            5        msd            3\n",
       "2       0.850990        1.082520        5            5        msd            5\n",
       "3       0.862696        1.101631        5            5     cosine            0\n",
       "4       0.862696        1.101631        5            5     cosine            3"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#\n",
    "results_df = pd.DataFrame.from_dict(grid_search.cv_results)\n",
    "plotdata = results_df.loc[:,['mean_test_mae','mean_test_rmse','param_k','param_min_k']]\n",
    "name_list = []\n",
    "min_surppot_list = []\n",
    "for param in results_df.params:\n",
    "#     print(param)\n",
    "    name_list.append(param['sim_options']['name'])\n",
    "    min_surppot_list.append(param['sim_options']['min_surpport'])\n",
    "    \n",
    "name_list = pd.Series(name_list)\n",
    "min_surppot_list = pd.Series(min_surppot_list)\n",
    "\n",
    "plotdata['sim_matric'] = name_list\n",
    "plotdata['min_support'] = min_surppot_list\n",
    "plotdata.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean_test_mae</th>\n",
       "      <th>mean_test_rmse</th>\n",
       "      <th>param_k</th>\n",
       "      <th>param_min_k</th>\n",
       "      <th>sim_matric</th>\n",
       "      <th>min_support</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>0.864359</td>\n",
       "      <td>1.083793</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>cosine</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>57</th>\n",
       "      <td>0.847923</td>\n",
       "      <td>1.074051</td>\n",
       "      <td>10</td>\n",
       "      <td>7</td>\n",
       "      <td>cosine</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>93</th>\n",
       "      <td>0.849282</td>\n",
       "      <td>1.072954</td>\n",
       "      <td>20</td>\n",
       "      <td>7</td>\n",
       "      <td>cosine</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    mean_test_mae  mean_test_rmse  param_k  param_min_k sim_matric  \\\n",
       "21       0.864359        1.083793        5            7     cosine   \n",
       "57       0.847923        1.074051       10            7     cosine   \n",
       "93       0.849282        1.072954       20            7     cosine   \n",
       "\n",
       "    min_support  \n",
       "21            0  \n",
       "57            0  \n",
       "93            0  "
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plotdata_max_k = plotdata[plotdata.param_min_k == 7]\n",
    "plotdata_max_k = plotdata_max_k[plotdata_max_k.min_support == 0]\n",
    "plotdata_max_k = plotdata_max_k[plotdata_max_k.sim_matric == 'cosine']\n",
    "plotdata_max_k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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OJSI1hApCNXR++/N55YJX2O276TaxG4+ufjTqSCJSA6ggVFM5h+eQn5vPCc1O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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3d145ccb00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(2, 1, 1) \n",
    "plt.plot(plotdata_max_k.param_k, plotdata_max_k.mean_test_mae, 'r')\n",
    "plt.subplot(2, 1, 2)\n",
    "plt.plot(plotdata_max_k.param_k, plotdata_max_k.mean_test_rmse, 'g')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean_test_mae</th>\n",
       "      <th>mean_test_rmse</th>\n",
       "      <th>param_k</th>\n",
       "      <th>param_min_k</th>\n",
       "      <th>sim_matric</th>\n",
       "      <th>min_support</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>0.853892</td>\n",
       "      <td>1.083260</td>\n",
       "      <td>10</td>\n",
       "      <td>5</td>\n",
       "      <td>cosine</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>0.849898</td>\n",
       "      <td>1.076657</td>\n",
       "      <td>10</td>\n",
       "      <td>6</td>\n",
       "      <td>cosine</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>57</th>\n",
       "      <td>0.847923</td>\n",
       "      <td>1.074051</td>\n",
       "      <td>10</td>\n",
       "      <td>7</td>\n",
       "      <td>cosine</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>66</th>\n",
       "      <td>0.845878</td>\n",
       "      <td>1.071098</td>\n",
       "      <td>10</td>\n",
       "      <td>8</td>\n",
       "      <td>cosine</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    mean_test_mae  mean_test_rmse  param_k  param_min_k sim_matric  \\\n",
       "39       0.853892        1.083260       10            5     cosine   \n",
       "48       0.849898        1.076657       10            6     cosine   \n",
       "57       0.847923        1.074051       10            7     cosine   \n",
       "66       0.845878        1.071098       10            8     cosine   \n",
       "\n",
       "    min_support  \n",
       "39            0  \n",
       "48            0  \n",
       "57            0  \n",
       "66            0  "
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plotdata_mink = plotdata[plotdata.sim_matric =='cosine']\n",
    "plotdata_mink = plotdata_mink[plotdata_mink.min_support == 0]\n",
    "plotdata_mink = plotdata_mink[plotdata_mink.param_k == 10]\n",
    "plotdata_mink"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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a66iAkhpRmNkgYBRQGRjr7g8VKW8FPAfUi9W5293fKVK+ALjf3R82s5OA8XFf0Ra4z91H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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3d07f7cda0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(2, 1, 1) \n",
    "plt.plot(plotdata_mink.param_min_k, plotdata_mink.mean_test_mae, 'r')\n",
    "plt.subplot(2, 1, 2)\n",
    "plt.plot(plotdata_mink.param_min_k, plotdata_mink.mean_test_rmse, 'g')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean_test_mae</th>\n",
       "      <th>mean_test_rmse</th>\n",
       "      <th>param_k</th>\n",
       "      <th>param_min_k</th>\n",
       "      <th>sim_matric</th>\n",
       "      <th>min_support</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>54</th>\n",
       "      <td>0.840341</td>\n",
       "      <td>1.063863</td>\n",
       "      <td>10</td>\n",
       "      <td>7</td>\n",
       "      <td>msd</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>57</th>\n",
       "      <td>0.847923</td>\n",
       "      <td>1.074051</td>\n",
       "      <td>10</td>\n",
       "      <td>7</td>\n",
       "      <td>cosine</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>60</th>\n",
       "      <td>0.858387</td>\n",
       "      <td>1.080303</td>\n",
       "      <td>10</td>\n",
       "      <td>7</td>\n",
       "      <td>pearson</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    mean_test_mae  mean_test_rmse  param_k  param_min_k sim_matric  \\\n",
       "54       0.840341        1.063863       10            7        msd   \n",
       "57       0.847923        1.074051       10            7     cosine   \n",
       "60       0.858387        1.080303       10            7    pearson   \n",
       "\n",
       "    min_support  \n",
       "54            0  \n",
       "57            0  \n",
       "60            0  "
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plotdata_sim = plotdata[plotdata.param_min_k == 7]\n",
    "plotdata_sim = plotdata_sim[plotdata_sim.min_support == 0]\n",
    "plotdata_sim = plotdata_sim[plotdata_sim.param_k == 10]\n",
    "plotdata_sim"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Metrics - Coverage"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [],
   "source": [
    "trainset, testset = train_test_split(sdt,test_size=0.2,random_state=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Function to calculate coverage ratio\n",
    "def coverage_ratio(predictions, n):\n",
    "    top_n = get_top_n(predictions, n)\n",
    "    product_list = []\n",
    "    recommended_list = []\n",
    "    for uid, iid, true_r, est, _ in predictions:\n",
    "        product_list.append(iid)\n",
    "    for uid, user_ratings in top_n.items():\n",
    "        recommended_list.append(user_ratings[0][0])\n",
    "    coverage = float(len(set(recommended_list))) / float(len(set(product_list)))\n",
    "    return coverage"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Function to predict missing values based on an algorithm\n",
    "def mv_prediction(algo,missing_values):\n",
    "    predictions = [algo.predict(uid, iid)\n",
    "                       for (uid, iid) in missing_values]\n",
    "    return predictions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Baseline Coverage Ratio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.05"
      ]
     },
     "execution_count": 166,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "algo1.fit(trainset)\n",
    "mv_blprediction = mv_prediction(algo1,missing_values)\n",
    "coverage_ratio(mv_blprediction,7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "SVD Coverage Ratio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<surprise.prediction_algorithms.matrix_factorization.SVD at 0x7f3d16611a90>"
      ]
     },
     "execution_count": 161,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "algo2.fit(trainset)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.19"
      ]
     },
     "execution_count": 162,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mv_svdprediction = mv_prediction(algo2,missing_values)\n",
    "coverage_ratio(mv_svdprediction,7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "KNN Coverage ratio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing the cosine similarity matrix...\n",
      "Done computing similarity matrix.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.21"
      ]
     },
     "execution_count": 164,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "knn_default.fit(trainset)\n",
    "mv_knnprediction = mv_prediction(knn_default,missing_values)\n",
    "coverage_ratio(mv_knnprediction,7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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