user_based.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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": 4,
   "metadata": {},
   "outputs": [
    {
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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": 4,
     "metadata": {},
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    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
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       "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",
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       "5         NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN  \n",
       "\n",
       "[5 rows x 3706 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "moviemat.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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": 7,
   "metadata": {},
   "outputs": [
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     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_set.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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": 8,
     "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": 9,
   "metadata": {},
   "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": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "#adjusted_cosine_similarity\n",
    "#transpose\n",
    "X1=(mean_X.fillna(value=0,inplace=False))#mean_x_filled with 0s\n",
    "X2=X1#no transpose for user based(transpose done in item based)\n",
    "adjusted_cosine_sim=1-pairwise_distances(X2,metric='cosine')\n",
    "X4=(pd.DataFrame(data=adjusted_cosine_sim,index=train_set.index,columns=train_set.index)).copy()\n",
    "#adjusted _cosine_similarity calculation done"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(6040, 6040)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "adjusted_cosine_sim.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#cosine_similarity\n",
    "mean_X_trans=mean_X.transpose()\n",
    "X_train_trans=train_set#no transpose for user based(transpose done in item based)\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=train_set.index,columns=train_set.index)).copy()\n",
    "#cosine_similarity_ends"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "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": 132,
   "metadata": {},
   "outputs": [],
   "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",
    "\n",
    "#creating dictionary to map array indices of items to actual item indices in dataframe\n",
    "dict_indices={}\n",
    "train_set_indices=train_set.columns\n",
    "np_array_indices=range(0,len(train_set_indices))\n",
    "dict_indices=dict(zip(np_array_indices,train_set_indices))  \n",
    "\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(test_set.index,range(0,len(test_set.index))))\n",
    "#creating dictionary to map array indices of users to actual user indices in dataframe\n",
    "user_indices={v:k for k,v in rev_user_indices.items()}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.        ,  0.04756055, -0.05244479, ...,  0.        ,\n",
       "        0.03092461, -0.00271576])"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sorted_item_similarity=(X4.values).copy()\n",
    "sorted_item_similarity[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([   0, 1336,  378, ..., 2416,   74, 3786], dtype=int64)"
      ]
     },
     "execution_count": 147,
     "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": 148,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([   1, 1337,  379, ..., 2417,   75, 3787], dtype=int64)"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#replacing the np indices by actual indices from dictionary (dict_indices)\n",
    "columns_range=range(0,test_set.index.shape[0])\n",
    "for i in columns_range:\n",
    "    sorted_item_similarity[i]=[user_indices[x] for x in sorted_item_similarity[i]]\n",
    "sorted_item_similarity[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [],
   "source": [
    "#..........................prediction calculation starts using k nearest neighbours\n",
    "\n",
    "\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",
    "#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": 151,
   "metadata": {},
   "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",
    "        rev_user_idx=rev_user_indices[users]#np index of user\n",
    "        #print(rev_user_idx)\n",
    "        k_sim=sorted_item_similarity[rev_user_idx][1:k]\n",
    "        #note k_sim contains actual indices of k similar users\n",
    "        weighted_sum=0\n",
    "        similarity_sum=0\n",
    "        for j in k_sim:\n",
    "            rev_j=rev_user_indices[j]#np index of each similar user j\n",
    "            \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",
    "            \n",
    "            weighted_sum+=adjusted_cosine_sim[rev_user_idx][rev_j]*train_set_np[rev_j][rev_tar_item] \n",
    "            similarity_sum+=abs(adjusted_cosine_sim[rev_user_idx][rev_j])\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": 152,
   "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": 153,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MAE: 0.96798750167\n",
      "MSE: 1.59461888131\n",
      "RMSE: 1.26278219868\n",
      "precision=  0.6660395652740192\n",
      "recall=  0.812986875342248\n",
      "f1 score=  0.7322133129693268\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": 157,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "##################             plotting error vs k      #################################\n",
    "from sklearn import metrics\n",
    "\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",
    "#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": 158,
   "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:33: RuntimeWarning: invalid value encountered in greater\n",
      "C:\\Users\\Roshan\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:34: 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",
    "            rev_user_idx=rev_user_indices[users]#np index of user\n",
    "            #print(rev_user_idx)\n",
    "            k_sim=sorted_item_similarity[rev_user_idx][1:k]\n",
    "            #note k_sim contains actual indices of k similar users\n",
    "            weighted_sum=0\n",
    "            similarity_sum=0\n",
    "            for j in k_sim:\n",
    "                rev_j=rev_user_indices[j]#np index of each similar user j\n",
    "\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",
    "\n",
    "                weighted_sum+=adjusted_cosine_sim[rev_user_idx][rev_j]*train_set_np[rev_j][rev_tar_item] \n",
    "                similarity_sum+=abs(adjusted_cosine_sim[rev_user_idx][rev_j])\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\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": 159,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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TgY7uvs7MdifsaNDe3TWPTSQJCgrgxGhvkJEj4ayzwjIf99wDu+0Wb20iIhKf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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2640d29fc88>"
      ]
     },
     "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(\"user_based_error_vs_k.jpeg\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "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
}