Item_based_system_complete.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "column_names=['user_id','item_id', 'rating', 'timestamp']\n",
    "movie_columns=['item_id', 'movietitle']\n",
    "df=pd.read_csv('ratings.csv', sep=',', names=column_names)\n",
    "movie_titles=pd.read_csv('movies.csv', sep=',', names=movie_columns, encoding='latin-1')\n",
    "df=pd.merge(df,movie_titles, on='item_id', how='left', sort='False')\n",
    "moviemat=df.pivot_table(index='user_id', columns='item_id', values='rating')\n",
    "diff=set(range(1,3953))-set(moviemat.columns)\n",
    "columns=set(moviemat.columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>user_id</th>\n",
       "      <th>item_id</th>\n",
       "      <th>rating</th>\n",
       "      <th>timestamp</th>\n",
       "      <th>movietitle</th>\n",
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       "   user_id  item_id  rating  timestamp        movietitle\n",
       "0        1        1       5  978824268  Toy Story (1995)\n",
       "1        6        1       4  978237008  Toy Story (1995)\n",
       "2        8        1       4  978233496  Toy Story (1995)\n",
       "3        9        1       5  978225952  Toy Story (1995)\n",
       "4       10        1       5  978226474  Toy Story (1995)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "item_id  1     2     3     4     5     6     7     8     9     10    ...   \\\n",
       "user_id                                                              ...    \n",
       "1         5.0   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN  ...    \n",
       "2         NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN  ...    \n",
       "3         NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN  ...    \n",
       "4         NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN  ...    \n",
       "5         NaN   NaN   NaN   NaN   NaN   2.0   NaN   NaN   NaN   NaN  ...    \n",
       "\n",
       "item_id  3943  3944  3945  3946  3947  3948  3949  3950  3951  3952  \n",
       "user_id                                                              \n",
       "1         NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN  \n",
       "2         NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN  \n",
       "3         NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN  \n",
       "4         NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN  \n",
       "5         NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN  \n",
       "\n",
       "[5 rows x 3706 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "moviemat.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#code for inplace splitting of train set\n",
    "t_items=columns\n",
    "t_users=np.arange(1,6041)\n",
    "test_set=pd.DataFrame(index=t_items, columns=t_users)\n",
    "train_set=pd.DataFrame(index=t_items, columns=t_users)\n",
    "for user in t_users:\n",
    "    rated_movies=moviemat.loc[user][moviemat.loc[user].notnull()==True]\n",
    "    movie_count=rated_movies.count()\n",
    "    test_set_count=int(0.2*movie_count)\n",
    "    movie_for_tset=rated_movies.sample(n=test_set_count, replace=False)\n",
    "    test_set[user][movie_for_tset.index]=movie_for_tset\n",
    "    movie_for_train_set=rated_movies[~rated_movies.index.isin(movie_for_tset.index)]\n",
    "    train_set[user][movie_for_train_set.index]=movie_for_train_set\n",
    "    \n",
    "#splitting of train set and test set done"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_set.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
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       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>10</th>\n",
       "      <th>...</th>\n",
       "      <th>3943</th>\n",
       "      <th>3944</th>\n",
       "      <th>3945</th>\n",
       "      <th>3946</th>\n",
       "      <th>3947</th>\n",
       "      <th>3948</th>\n",
       "      <th>3949</th>\n",
       "      <th>3950</th>\n",
       "      <th>3951</th>\n",
       "      <th>3952</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 3706 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "  1    2    3    4    5    6    7    8    9    10   ...  3943 3944 3945 3946  \\\n",
       "1    5  NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN ...   NaN  NaN  NaN  NaN   \n",
       "2  NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN ...   NaN  NaN  NaN  NaN   \n",
       "3  NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN ...   NaN  NaN  NaN  NaN   \n",
       "4  NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN ...   NaN  NaN  NaN  NaN   \n",
       "5  NaN  NaN  NaN  NaN  NaN    2  NaN  NaN  NaN  NaN ...   NaN  NaN  NaN  NaN   \n",
       "\n",
       "  3947 3948 3949 3950 3951 3952  \n",
       "1  NaN  NaN  NaN  NaN  NaN  NaN  \n",
       "2  NaN  NaN  NaN  NaN  NaN  NaN  \n",
       "3  NaN  NaN  NaN  NaN  NaN  NaN  \n",
       "4  NaN  NaN  NaN  NaN  NaN  NaN  \n",
       "5  NaN  NaN  NaN  NaN  NaN  NaN  \n",
       "\n",
       "[5 rows x 3706 columns]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_set=train_set.transpose()\n",
    "test_set=test_set.transpose()\n",
    "train_set.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import pairwise_distances\n",
    "from sklearn import metrics\n",
    "mean_X=train_set.copy()\n",
    "mean_per_user=train_set.mean(axis=1)\n",
    "mean_X=mean_X.sub(mean_per_user,axis='index')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#adjusted_cosine_similarity\n",
    "#transpose\n",
    "X1=(mean_X.fillna(value=0,inplace=False))#mean_x_filled with 0s\n",
    "X2=X1.transpose()\n",
    "adjusted_cosine_sim=1-pairwise_distances(X2,metric='cosine')\n",
    "X4=(pd.DataFrame(data=adjusted_cosine_sim,index=columns,columns=columns)).copy()\n",
    "mean_X_trans=mean_X.transpose()\n",
    "#adjusted _cosine_similarity calculation done"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#cosine_similarity\n",
    "X_train_trans=train_set.transpose()\n",
    "X_train_trans=X_train_trans.fillna(value=0, inplace=False)\n",
    "cosine_sim=1-pairwise_distances(X_train_trans,metric='cosine')\n",
    "X3=(pd.DataFrame(data=cosine_sim,index=columns,columns=columns)).copy()\n",
    "#cosine_similarity_ends"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#pearson_correlation\n",
    "# pearson_sim=1-pairwise_distances(X2,metric='correlation')\n",
    "# X5=pd.DataFrame(pearson_sim)\n",
    "#pearson_correlation_ends"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.        ,  0.22163537,  0.12060874, ...,  0.04153478,\n",
       "        0.00391398,  0.02759603])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "###########################begin complete prediction calculation using numpy arrays\n",
    "\n",
    "#use X4.values for adjusted cosine similarity\n",
    "#use X3.values for cosine similarity\n",
    "#use X5.values for pearson correalation\n",
    "\n",
    "sorted_item_similarity=(X4.values).copy()\n",
    "\n",
    "#creating dictionary to map array indices of items to actual item indices in dataframe\n",
    "dict_indices={}\n",
    "X4_indices=X4.index\n",
    "np_array_indices=range(0,len(X4_indices))\n",
    "dict_indices=dict(zip(np_array_indices,X4_indices))    \n",
    "sorted_item_similarity[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([   0, 2898,  574, ..., 2938, 3549, 3240], dtype=int64)"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sorted_item_similarity=(-sorted_item_similarity).argsort(axis=1)\n",
    "#AXIS='columns'\n",
    "#(-sign)to do sorting in descending order\n",
    "#sorting each row in descending order and storing the index of sorted elements\n",
    "sorted_item_similarity[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([   1, 3114,  588, ..., 3154, 3792, 3473], dtype=int64)"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#replacing the np indices by actual indices from dictionary (dict_indices)\n",
    "for i in np_array_indices:\n",
    "    sorted_item_similarity[i]=[dict_indices[x] for x in sorted_item_similarity[i]]\n",
    "sorted_item_similarity[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#..........................prediction calculation starts using k nearest neighbours\n",
    "train_set=train_set.fillna(value=0)\n",
    "test_set_np=(test_set.values).copy()\n",
    "test_set_np=test_set_np.astype('float64')\n",
    "#create numpy arrays for train_set and predictions for faster calculations\n",
    "train_set_np=(train_set.values).copy()\n",
    "train_set_np=train_set_np.astype('float64')\n",
    "predictions=test_set_np.copy()\n",
    "#create a dictionary to map actual items to numpy indices by reversing dict_indices\n",
    "rev_indices={v:k for k,v in dict_indices.items()}\n",
    "#create a dictionary to map actual users to numpy indices\n",
    "rev_user_indices=dict(zip(list(test_set.index),range(0,len(test_set.index))))\n",
    "#creating a dictionary which maps each items to its active users in test set(users who rated that item)\n",
    "items=list(test_set.columns)\n",
    "indices={}\n",
    "for target_item in items:\n",
    "    active_users=test_set[target_item][test_set[target_item].isnull()==False].index\n",
    "    indices.update({target_item:active_users})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Code to generate predictions on a test_set for a given k\n",
    "k=50\n",
    "for target_item in items:\n",
    "    rev_tar_item=rev_indices[target_item]#np index of target item \n",
    "    for users in indices[target_item]:\n",
    "        k_sim=sorted_item_similarity[rev_tar_item][1:k]\n",
    "        #note k_sim contains actual indices of k similar items\n",
    "        weighted_sum=0\n",
    "        similarity_sum=0\n",
    "        rev_user_idx=rev_user_indices[users]#np index of user\n",
    "        \n",
    "        \n",
    "        for j in k_sim:\n",
    "            rev_j=rev_indices[j]#np index of each similar item j\n",
    "            #change adjusted_cosine_sim to cosine_sim for evaluating using cosine_similarity\n",
    "            #change adjusted_cosine_sim to pearson_sim for evaluating using pearson correalation\n",
    "            weighted_sum+=adjusted_cosine_sim[rev_tar_item][rev_j]*train_set_np[rev_user_idx][rev_j] \n",
    "            similarity_sum+=abs(adjusted_cosine_sim[rev_tar_item][rev_j])\n",
    "            \n",
    "            \n",
    "        if similarity_sum!=0:\n",
    "            predictions[rev_user_idx,rev_tar_item]=(weighted_sum/similarity_sum)\n",
    "        else:\n",
    "            predictions[rev_user_idx,rev_tar_item]=0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Roshan\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:7: RuntimeWarning: invalid value encountered in greater\n",
      "  import sys\n",
      "C:\\Users\\Roshan\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:8: RuntimeWarning: invalid value encountered in less\n",
      "  \n"
     ]
    }
   ],
   "source": [
    "#code to create a set of predictions for evaluation metrics \n",
    "pred_dataframe=pd.DataFrame(data=predictions,index=test_set.index,columns=test_set.columns)\n",
    "pred_dataframe=pred_dataframe.astype('float64')\n",
    "pred_dataframe=pred_dataframe.add(mean_per_user,axis='index')\n",
    "absolute_predictions=(pred_dataframe.values).copy()\n",
    "absolute_predictions=absolute_predictions.astype('float64')\n",
    "absolute_predictions[absolute_predictions>5]=5\n",
    "absolute_predictions[absolute_predictions<1]=1\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4.,  4.,  5., ...,  4.,  4.,  5.])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_true"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MAE: 2.21560968803\n",
      "MSE: 6.0671178916\n",
      "RMSE: 2.46315202365\n",
      "precision=  0.9565217391304348\n",
      "recall=  0.0005820670435403787\n",
      "f1 score=  0.0011634261136279503\n"
     ]
    }
   ],
   "source": [
    "#######################################Calculation of Error metrics##############\n",
    "# extract all non-nan values from test set and predictions\n",
    "y_pred=absolute_predictions[~np.isnan(absolute_predictions)]\n",
    "y_true=test_set_np[~np.isnan(test_set_np)]\n",
    "from sklearn import metrics\n",
    "print('MAE:', metrics.mean_absolute_error(y_true,y_pred))\n",
    "print('MSE:', metrics.mean_squared_error(y_true,y_pred))\n",
    "print('RMSE:', np.sqrt(metrics.mean_squared_error(y_true,y_pred)))\n",
    "################################Precision and Recall\n",
    "tp=y_pred[(y_pred>=4) &(y_true>=4)].shape[0]\n",
    "fp=y_pred[(y_pred>=4) & (y_true<4)].shape[0]\n",
    "tn=y_pred[(y_pred<4) & (y_true>=4)].shape[0]\n",
    "precision=tp/(tp+fp)\n",
    "recall=tp/(tp+tn)\n",
    "f1_score=2*precision*recall/(precision+recall)\n",
    "print('precision= ',precision)\n",
    "print('recall= ',recall)\n",
    "print('f1 score= ',f1_score)\n",
    "#..............END of calculation of error metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "##################             plotting error vs k      #################################\n",
    "from sklearn import metrics\n",
    "\n",
    "train_set=train_set.fillna(value=0)\n",
    "train_set.head()\n",
    "#creating np array of test_set\n",
    "test_set_np=(test_set.values).copy()\n",
    "test_set_np=test_set_np.astype('float64')\n",
    "predictions=test_set_np.copy()\n",
    "rev_indices={v:k for k,v in dict_indices.items()}\n",
    "rev_user_indices=dict(zip(list(test_set.index),range(0,len(test_set.index))))\n",
    "#creating a dictionary which maps each items to its active users in test set(users who rated that item)\n",
    "items=list(test_set.columns)\n",
    "indices={}\n",
    "for target_item in items:\n",
    "    active_users=test_set[target_item][test_set[target_item].isnull()==False].index\n",
    "    indices.update({target_item:active_users})\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "50\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Roshan\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:27: RuntimeWarning: invalid value encountered in greater\n",
      "C:\\Users\\Roshan\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:28: RuntimeWarning: invalid value encountered in less\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100\n",
      "200\n",
      "500\n",
      "750\n",
      "1000\n"
     ]
    }
   ],
   "source": [
    "error=[]\n",
    "k_values=[50,100,200,500,750,1000]\n",
    "for k in k_values:\n",
    "    print(k)\n",
    "    for target_item in items:\n",
    "        rev_tar_item=rev_indices[target_item]#np index of target item \n",
    "        for users in indices[target_item]:\n",
    "            k_sim=sorted_item_similarity[rev_tar_item][1:k]\n",
    "            #note k_sim contains actual indices of k similar items\n",
    "            weighted_sum=0\n",
    "            similarity_sum=0\n",
    "            rev_user_idx=rev_user_indices[users]#np index of user\n",
    "            for j in k_sim:\n",
    "                rev_j=rev_indices[j]#np index of each similar item j\n",
    "                weighted_sum+=adjusted_cosine_sim[rev_tar_item][rev_j]*train_set_np[rev_user_idx][rev_j] \n",
    "                similarity_sum+=abs(adjusted_cosine_sim[rev_tar_item][rev_j])\n",
    "            if similarity_sum!=0:\n",
    "                predictions[rev_user_idx,rev_tar_item]=(weighted_sum/similarity_sum)\n",
    "            else:\n",
    "                predictions[rev_user_idx,rev_tar_item]=0\n",
    "    #error calculation\n",
    "    pred_dataframe=pd.DataFrame(data=predictions,index=test_set.index,columns=test_set.columns)\n",
    "    pred_dataframe=pred_dataframe.astype('float64')\n",
    "    pred_dataframe=pred_dataframe.add(mean_per_user,axis='index')\n",
    "    absolute_predictions=(pred_dataframe.values).copy()\n",
    "    absolute_predictions=absolute_predictions.astype('float64')\n",
    "    absolute_predictions[absolute_predictions>5]=5\n",
    "    absolute_predictions[absolute_predictions<0]=0\n",
    "    # extract all non-nan values from test set and predictions\n",
    "    y_pred=absolute_predictions[~np.isnan(absolute_predictions)]\n",
    "    y_true=test_set_np[~np.isnan(test_set_np)]\n",
    "    error.append(metrics.mean_absolute_error(y_true,y_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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qisxJFhERyXDlhjUz62Zmp5vZPtFxJzObBLySkupEEjRsGH6+9BLcdhu0bx9C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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x294f8382390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.figure(figsize=(10,6))\n",
    "plt.plot(k_values,error,color='blue', linestyle='dashed', marker='o',\n",
    "         markerfacecolor='red', markersize=10)\n",
    "plt.title('Error Rate vs. K Value')\n",
    "plt.xlabel('K')\n",
    "plt.ylabel('Error Rate')\n",
    "plt.savefig(\"item_based_error_vs_k.jpeg\")\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}