PLSI_small_dataset.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PLSI IMPLEMENTATION ON SPARK "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. Libraries and file importation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import time\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import findspark\n",
    "findspark.init(\"/Users/amirbenmahjoub/Desktop/spark-2.2.0-bin-hadoop2.7\")\n",
    "import pyspark\n",
    "from numpy import random "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# importing the short csv file of ratings and save it in the right format. \n",
    "pd.read_csv(\"ratings.csv\").to_csv(\"ratings_short.csv\",sep=',',index=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Opening a Spark context\n",
    "sc = pyspark.SparkContext()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Shutting down the Spark contect (optional)\n",
    "#sc.stop()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "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>userId</th>\n",
       "      <th>movieId</th>\n",
       "      <th>rating</th>\n",
       "      <th>timestamp</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>31</td>\n",
       "      <td>2.5</td>\n",
       "      <td>1260759144</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1029</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1260759179</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>1061</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1260759182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>1129</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1260759185</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>1172</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1260759205</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   userId  movieId  rating   timestamp\n",
       "0       1       31     2.5  1260759144\n",
       "1       1     1029     3.0  1260759179\n",
       "2       1     1061     3.0  1260759182\n",
       "3       1     1129     2.0  1260759185\n",
       "4       1     1172     4.0  1260759205"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Some basic information on the database\n",
    "ratings_short = pd.read_csv(\"ratings_short.csv\")\n",
    "ratings_short.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of different ratings :  100004\n"
     ]
    }
   ],
   "source": [
    "print(\"number of different ratings : \", ratings_short.shape[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of different users :  671\n"
     ]
    }
   ],
   "source": [
    "print(\"number of different users : \", ratings_short.drop_duplicates(subset=['userId']).shape[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['1,31,2.5,1260759144',\n",
       " '1,1029,3.0,1260759179',\n",
       " '1,1061,3.0,1260759182',\n",
       " '1,1129,2.0,1260759185',\n",
       " '1,1172,4.0,1260759205',\n",
       " '1,1263,2.0,1260759151',\n",
       " '1,1287,2.0,1260759187',\n",
       " '1,1293,2.0,1260759148',\n",
       " '1,1339,3.5,1260759125',\n",
       " '1,1343,2.0,1260759131']"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#importing the document - creating the RDD object. \n",
    "document = sc.textFile(\"/Users/amirbenmahjoub/Desktop/3A Polytechnique/Database Management Systems/Data Management II-20180228/Project/PLSI/ratings_short.csv\")\n",
    "\n",
    "# Removing the header\n",
    "header = document.first()\n",
    "document = document.filter(lambda x: x != header)\n",
    "\n",
    "# Collecting the RDD to check the output\n",
    "document.collect()[0:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. The algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.1. Methodology : Running the 1st iteration of the algorithm step-by-step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# A parser for extracting the interresting information from the dataset.\n",
    "\n",
    "def parseLine(line):\n",
    "    line = line.split(',')\n",
    "    # We want to keep only the two first rows since we consider that a click-log is a 1-rating\n",
    "    line = line[0]+','+line[1]\n",
    "    return(line)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Defining the number of clusters. \n",
    "# nb of 'clusters' is a broadcast variable.\n",
    "nb_z = sc.broadcast(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# for a click-log couple (u,s), create a z tuples : [(u,s,z) for z in [1:nb_z]]\n",
    "\n",
    "def cartesianProd(us):\n",
    "    to_return = []\n",
    "    for z in range(nb_z.value):\n",
    "        to_return += [us+','+str(z)]\n",
    "    return(to_return)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('1,31,0', 0.306719161308564),\n",
       " ('1,31,1', 0.0669864792985333),\n",
       " ('1,31,2', 0.36536465897384085),\n",
       " ('1,1029,0', 0.9166589410183121),\n",
       " ('1,1029,1', 0.7192665553088856),\n",
       " ('1,1029,2', 0.9349789921296401),\n",
       " ('1,1061,0', 0.5455355258055459),\n",
       " ('1,1061,1', 0.917739012270406),\n",
       " ('1,1061,2', 0.599856633699085),\n",
       " ('1,1129,0', 0.17815209782815966),\n",
       " ('1,1129,1', 0.8363905222160266),\n",
       " ('1,1129,2', 0.8313195807469185)]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# creation of the tuples (u,s,z ; q*) with (u,s,z) as key.\n",
    "# We initialize q* randomly as the Google paper suggests. \n",
    "\n",
    "q0 = document.map(parseLine).flatMap(cartesianProd).map(lambda usz : (usz, random.rand()))\n",
    "q0.collect()[0:12]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(s,z, N(s,z)): \n",
      " [('31,0', 19.69358360164842)] \n",
      "\n",
      "(z, N(z)): \n",
      " [('0', 50168.96028468311)] \n",
      "\n",
      "(s,z, N(s,z)/N(z)): \n",
      " [('31,0', 0.0003925451811219016)] \n",
      "\n"
     ]
    }
   ],
   "source": [
    "##### ********* M-step (computation of the N(s,z)/N(z) = p(s|z) function) ********\n",
    "\n",
    "# return (s,z, N(s,z)) with (s,z) as keys and by summing all the users. \n",
    "Nsz = q0.map(lambda q : (q[0].split(',')[1]+','+q[0].split(',')[2],q[1])).reduceByKey(lambda x,y : x+y)\n",
    "print('(s,z, N(s,z)): \\n', Nsz.collect()[:1],'\\n')\n",
    "\n",
    "# return (z, N(z)=∑N(s,z)) with z as key and by summing N(s,z) on all the movies. \n",
    "Nz = Nsz.map(lambda N : (N[0].split(',')[1], N[1])).reduceByKey(lambda x,y : x+y)\n",
    "print('(z, N(z)): \\n', Nz.collect()[:1],'\\n')\n",
    "\n",
    "# return (s,z, N(s,z)/N(z)) with (s,z) as keys\n",
    "\n",
    "# (s,z, N(s,z)) --> ('z', ('s', N(s,z))) (z as key)\n",
    "Nsz = Nsz.map(lambda x : (x[0].split(',')[1], (x[0].split(',')[0],x[1]))) #('0', ('31', 0.6602937910124607))\n",
    "# ('z', ('s', N(s,z))) JOIN ('z', N(z)) --> ('z', ('s', N(s,z), N(z))) (z as key)\n",
    "tmpN = Nsz.join(Nz) #('0', (('31', 0.6602937910124607), 501.224237413403))\n",
    "#('z', ('s', N(s,z), N(z))) --> ('s,z', (N(s,z)/N(z))) (s,z as keys)\n",
    "Nsz_normalized = tmpN.map(lambda x : (x[1][0][0]+','+x[0], x[1][0][1]/x[1][1]))\n",
    "print('(s,z, N(s,z)/N(z)): \\n', Nsz_normalized.collect()[:1],'\\n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(u,z, p~(z|u)): \n",
      " [('1,1', 10.177155055236593)] \n",
      "\n",
      "(u, ∑p~(z|u)): \n",
      " [('1', 31.900072304077035)] \n",
      "\n",
      "(u,z, p(z|u)): \n",
      " [('4,0', 0.3335209269009333)] \n",
      "\n"
     ]
    }
   ],
   "source": [
    "##### ********* M-step (computation of the p(z|u) function) ********\n",
    "\n",
    "# p~(z|u) is the un-normalized value of p(z|u), i.e. ∑p~(z|u) ≠ 1 - Same spirit as the part above. \n",
    "\n",
    "# return (u,z, p~(z|u)) with (u,z) as keys \n",
    "Puz = q0.map(lambda q : (q[0].split(',')[0]+','+q[0].split(',')[2],q[1])).reduceByKey(lambda x,y : x+y)\n",
    "print('(u,z, p~(z|u)): \\n', Puz.collect()[:1],'\\n')\n",
    "\n",
    "# return (u, ∑p~(z|u)) with u as key. \n",
    "Pu = Puz.map(lambda p : (p[0].split(',')[0], p[1])).reduceByKey(lambda x,y : x+y)\n",
    "print('(u, ∑p~(z|u)): \\n', Pu.collect()[:1],'\\n')\n",
    "\n",
    "# return (u, z, p(z|u)=p~(z|u)/∑p~(z|u)) with (u,z) as keys. \n",
    "Puz = Puz.map(lambda x : (x[0].split(',')[0], (x[0].split(',')[1],x[1]))) #('1', ('1', 9.849132242962598))\n",
    "tmpP = Puz.join(Pu) #('4', (('0', 104.52747209196086), 314.82837141455155))\n",
    "Puz = tmpP.map(lambda x : (x[0]+','+x[1][0][0], x[1][0][1]/x[1][1]))\n",
    "print('(u,z, p(z|u)): \\n', Puz.collect()[:1],'\\n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(u,s;z, p(s|z)*p(u|z)): \n",
      " [('9,534,0', 8.589712747956928e-05)] \n",
      "\n",
      "(u,s, ∑p(s|z)*p(u|z)): \n",
      " [('232,534', 0.0002640562387517774)] \n",
      "\n",
      "(u,s;z, q*(u,s;z)): \n",
      " [('15,608,0', 0.33179066417839137)] \n",
      "\n"
     ]
    }
   ],
   "source": [
    "##### ********* E-step (computation of the q*(u,s;z) function) ********\n",
    "\n",
    "# 1st pre-step: join q0(u,s;z) & p(z|u) on u & z - and forget old value of q*\n",
    "\n",
    "# (u,s,z ; q*) --> (u,z ; s)\n",
    "tmpQ0 = q0.map(lambda x : (x[0].split(',')[0]+','+x[0].split(',')[2] , x[0].split(',')[1])) #('4,0', 0.346651199923261)\n",
    "# (u,z ; s) JOIN (u,z ; p(z|u)) --> (u,z ; (s,p(z|u)))\n",
    "tmpQ0 = tmpQ0.join(Puz) #('9,0', ('1', 0.3019536803179005))\n",
    "\n",
    "# 2nd pre-step: join q0(u,s;z) & N(s,z)/N(z) on s & z\n",
    "\n",
    "#(u,z ; (s,p(z|u))) --> (s,z;(u,p(z|u)))\n",
    "tmpQ0 = tmpQ0.map(lambda x : (x[1][0]+','+x[0].split(',')[1] ,\\\n",
    "                             (x[0].split(',')[0],x[1][1]))) #('1,0', ('9', 0.3019536803179005))\n",
    "#(s,z;(u,p(z|u))) JOIN (s,z; p(s|z) ) --> (s,z;(u,p(z|u),p(s|z)))\n",
    "tmpQ0 = tmpQ0.join(Nsz_normalized) #('534,0', (('9', 0.3019536803179005), 7.06974580116717e-05))\n",
    "\n",
    "\n",
    "\n",
    "# 1st step for computing q*(u,s;z) --> return ((u,s;z), p(s|z)*p(u|z)) =  ((u,s;z), q*~) with : \n",
    "# q*~ = p(s|z)*p(u|z),  the unormalized version of q* - i.e. ∑q*~ ≠ 1\n",
    "tmpQ0 = tmpQ0.map(lambda x : (x[1][0][0]+','+x[0],\\\n",
    "                             x[1][0][1]*x[1][1]))\n",
    "print('(u,s;z, p(s|z)*p(u|z)): \\n', tmpQ0.collect()[:1],'\\n')\n",
    "\n",
    "# 2nd step for computing q*(u,s;z) --> return ((u,s), ∑p(s|z)*p(u|z))\n",
    "sumTmpQ0 = tmpQ0.map(lambda x : (x[0].split(',')[0]+','+x[0].split(',')[1],x[1])).reduceByKey(lambda x,y : x+y)\n",
    "print('(u,s, ∑p(s|z)*p(u|z)): \\n', sumTmpQ0.collect()[:1],'\\n')\n",
    "\n",
    "\n",
    "# 3rd step for computing q*(u,s;z) --> return ((u,s,z), p(s|z)*p(u|z)/{∑p(s|z)*p(u|z))}\n",
    "\n",
    "#((u,s;z), q*~) --> ((u,s); (z,q*~))\n",
    "tmpQ0 = tmpQ0.map(lambda x : (x[0].split(',')[0]+','+x[0].split(',')[1],\\\n",
    "                             (x[0].split(',')[2],x[1])))\n",
    "#((u,s); (z,q*~)) JOIN ((u,s), ∑q*~) --> ((u,s); ( (z,q*~) ,∑q*~))\n",
    "tmpQ0 = tmpQ0.join(sumTmpQ0)\n",
    "q1 = tmpQ0.map(lambda x : (x[0]+','+x[1][0][0], x[1][0][1]/x[1][1]))\n",
    "print('(u,s;z, q*(u,s;z)): \\n', q1.collect()[:1],'\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.2 Full algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2.1 Splitting into testing and training set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Number of clusters\n",
    "#We will discuss after the optimal number nb_z. \n",
    "nb_z = sc.broadcast(3)\n",
    "#Number of iterations of the EM algorithm - We will discuss the optimal number after. \n",
    "nb_iter = 30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Same functions as above. \n",
    "\n",
    "# A parser for extracting the interresting information from the dataset.\n",
    "\n",
    "def parseLine(line):\n",
    "    line = line.split(',')\n",
    "    line = line[0]+','+line[1]\n",
    "    return(line)\n",
    "\n",
    "# for a click-log couple (u,s), create a tuple (u,s,z) for z in Z\n",
    "\n",
    "def cartesianProd(us):\n",
    "    to_return = []\n",
    "    for z in range(nb_z.value):\n",
    "        to_return += [us+','+str(z)]\n",
    "    return(to_return)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total number of elements at the begining: 100004\n",
      "train: ['1,31', '1,1029', '1,1061']\n",
      "nb elements in train: 90000\n",
      "test: ['1,2193', '2,50', '2,265']\n",
      "nb elements in test: 9654\n"
     ]
    }
   ],
   "source": [
    "# Train/test splitting of the initial document. \n",
    "\n",
    "#RQ : \n",
    "#Here, we make sure  to avoid the case where there are \"u\" or \"s\" elements in the test that are not in the train. \n",
    "#For example :  if in the test the user u0 has clicked on the film s0 but s0 is not in the train, \n",
    "#then p(s0|u0) can not be computed and we cannot check if the model well predict the value.\n",
    "\n",
    "# This function takes into input :\n",
    "# --> doc : the first two rows (the useful ones) of the initial document - doc = document.map(parseLine)\n",
    "# --> alpha : the probability that an element is selected in the test set. With the law of large number\n",
    "#it becomes ~ the proportion of the split.\n",
    "# --> seed : corresponding to the seed of the random function on Python\n",
    "\n",
    "#This function returns two RDDs as output : \n",
    "# --> output[0] = train set RDD\n",
    "# --> output[1] = test set RDD\n",
    "\n",
    "#**************************************************************************************************************\n",
    "\n",
    "\n",
    "def splitTrainTest(document, alpha=0.1, seed=42):\n",
    "    \n",
    "    #Splitting train/test\n",
    "    train_test = document.randomSplit([1-alpha, alpha], seed=seed)\n",
    "    train, test = train_test[0], train_test[1]\n",
    "    \n",
    "    # We need to check that film 's' in the test set is also in the train set \n",
    "    # This is mandatory for evaluating our model\n",
    "    \n",
    "    # Creating two RDD with s values of train/test sets.  \n",
    "    s_train = train.map(lambda x : x.split(',')[1])\n",
    "    s_test = test.map(lambda x : x.split(',')[1])\n",
    "    # Creating a comment reference for the film values that need to be broadcasted between all the computers \n",
    "    #in the cluster and that we will use to filter our testing set. \n",
    "    #common reference for the films\n",
    "    s_common = sc.broadcast(s_test.intersection(s_train).collect()) \n",
    "    \n",
    "    # Same for a users 'u'\n",
    "    u_train = train.map(lambda x : x.split(',')[0])\n",
    "    u_test = test.map(lambda x : x.split(',')[0])\n",
    "    #common reference for the users\n",
    "    u_common = sc.broadcast(u_test.intersection(u_train).collect())  \n",
    "    \n",
    "    # filtering the test set : If an element(s or u)from the test set is not in the train set, we delete it\n",
    "    test = test.map(lambda x : (x.split(',')[0], x.split(',')[1])) \\\n",
    "               .filter(lambda x : x[1] in s_common.value) \\\n",
    "               .filter(lambda x : x[0] in u_common.value) \\\n",
    "               .map(lambda x : (x[0]+','+x[1]))\n",
    "            \n",
    "    return([train,test])\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "doc = document.map(parseLine)\n",
    "train_test = splitTrainTest(doc, alpha=0.1)\n",
    "train = train_test[0]\n",
    "test = train_test[1]\n",
    "\n",
    "print(\"Total number of elements at the begining:\",doc.count())\n",
    "print(\"train:\",train.collect()[:3])\n",
    "print(\"nb elements in train:\",train.count())\n",
    "print(\"test:\",test.collect()[:3])\n",
    "print(\"nb elements in test:\",test.count())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2.2 Runing the EM iterations. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-8.034951417718874\n",
      "-8.02904846664227\n",
      "-8.028808910114238\n",
      "-8.028446014745514\n",
      "-8.027836676457698\n",
      "-8.026776294209572\n",
      "-8.024925660897285\n",
      "-8.02175501745174\n",
      "-8.016479262080429\n",
      "-8.007894975888048\n",
      "-7.994134254665722\n",
      "-7.972799951266452\n",
      "-7.941921144379914\n",
      "-7.902191911827641\n",
      "-7.859307852532423\n",
      "-7.821432969625984\n",
      "-7.79279436549364\n",
      "-7.772314461812054\n",
      "-7.757161549583767\n",
      "-7.745192708717117\n",
      "-7.735143222253832\n",
      "-7.726442037647042\n",
      "-7.718856755749021\n",
      "-7.712259104334182\n",
      "-7.706599917436935\n",
      "-7.701831982447259\n",
      "-7.697860683126727\n",
      "-7.694519885929915\n",
      "-7.691575290111013\n",
      "-7.6889717989614494\n"
     ]
    }
   ],
   "source": [
    "#### We use the same method/code as the 2.1 part. \n",
    "\n",
    "##### Initialisation of q*. \n",
    "\n",
    "# creation of the tuples (u,s,z ; q*)\n",
    "q = train.flatMap(cartesianProd).map(lambda usz : (usz,random.rand()))\n",
    "\n",
    "# Here we fix the number of partition at the begining. We will in fact use coalesce function along with the initial \n",
    "# number of partitions in order to control the nb of partitions of our RDD's after a join operation all along \n",
    "# the algorithm. This is crucial to speed up the execution and avoid OutOfMemoryError due to a high nb of partitions.\n",
    "num_part = q.getNumPartitions()\n",
    "# We will store here the different values of the log-likelihood function. This list will be usefull to acess \n",
    "# the convergence of the log-likelihood and then the optimal number of iteration to use. \n",
    "loglik = []\n",
    "\n",
    "# We run the EM algorithm on nb_iter iterations. We will explain how we find the optimal number nb_iter after. \n",
    "for k in range(nb_iter) :\n",
    "    \n",
    "    ################### The detailed comments are already written in 2.1 part. #####################\n",
    "    \n",
    "    # *************************** M-step **************************\n",
    "    # ********* computation of the N(s,z), N(z) & N(s,z)/N(z) = p(s|z)  functions *********\n",
    "    \n",
    "    Nsz = q.map(lambda Q : (Q[0].split(',')[1]+','+Q[0].split(',')[2],Q[1])).reduceByKey(lambda x,y : x+y)\n",
    "    Nz = Nsz.map(lambda N : (N[0].split(',')[1], N[1])).reduceByKey(lambda x,y : x+y)\n",
    "    Nsz = Nsz.map(lambda x : (x[0].split(',')[1], (x[0].split(',')[0],x[1])))\n",
    "    \n",
    "    # We use here coalesce to control the high nb of partitions generated by the join operation, as discussed at the\n",
    "    # begining of the algorithm. \n",
    "    tmpN = Nsz.join(Nz).coalesce(num_part)\n",
    "    Nsz_normalized = tmpN.map(lambda x : (x[1][0][0]+','+x[0], x[1][0][1]/x[1][1]))\n",
    "    \n",
    "    \n",
    "    # ********* computation of the p(z|u) function *********\n",
    "  \n",
    "\n",
    "    Puz = q.map(lambda Q : (Q[0].split(',')[0]+','+Q[0].split(',')[2],Q[1])).reduceByKey(lambda x,y : x+y)\n",
    "    Pu = Puz.map(lambda p : (p[0].split(',')[0], p[1])).reduceByKey(lambda x,y : x+y)\n",
    "    Puz = Puz.map(lambda x : (x[0].split(',')[0], (x[0].split(',')[1],x[1])))\n",
    "    \n",
    "    # Same here for the coalesce. \n",
    "    tmpP = Puz.join(Pu).coalesce(num_part)\n",
    "    Puz = tmpP.map(lambda x : (x[0]+','+x[1][0][0], x[1][0][1]/x[1][1]))\n",
    "\n",
    "    \n",
    "    # *************************** E-step **************************\n",
    "    # ********* computation of the q*(u,s;z) function *********\n",
    "\n",
    "   \n",
    "    tmpQ = q.map(lambda x : (x[0].split(',')[0]+','+x[0].split(',')[2] , x[0].split(',')[1]))\n",
    "    # Same here for the coalesce. \n",
    "    tmpQ = tmpQ.join(Puz).coalesce(num_part) \n",
    "    tmpQ = tmpQ.map(lambda x : (x[1][0]+','+x[0].split(',')[1] ,\\\n",
    "                                 (x[0].split(',')[0],x[1][1])))\n",
    "    # Same here for the coalesce. \n",
    "    tmpQ = tmpQ.join(Nsz_normalized).coalesce(num_part)\n",
    "\n",
    "    tmpQ = tmpQ.map(lambda x : (x[1][0][0]+','+x[0],\\\n",
    "                                 x[1][0][1]*x[1][1]))\n",
    "\n",
    "    sumTmpQ = tmpQ.map(lambda x : (x[0].split(',')[0]+','+x[0].split(',')[1],x[1])).reduceByKey(lambda x,y : x+y)\n",
    "    \n",
    "    # We compute here the log-likelihood.\n",
    "    log = sumTmpQ.map(lambda x : np.log(x[1]))\n",
    "    N = sumTmpQ.count()\n",
    "    logLik = log.reduce(lambda x,y:x+y)\n",
    "    print((1/N)*logLik)\n",
    "    loglik.append(1/N*logLik)\n",
    "\n",
    "    # We continue our E-step\n",
    "    tmpQ = tmpQ.map(lambda x : (x[0].split(',')[0]+','+x[0].split(',')[1],\\\n",
    "                                 (x[0].split(',')[2],x[1])))\n",
    "    # Same here for the coalesce. \n",
    "    tmpQ = tmpQ.join(sumTmpQ).coalesce(num_part) \n",
    "    q = tmpQ.map(lambda x : (x[0]+','+x[1][0][0], x[1][0][1]/x[1][1]))\n",
    "    \n",
    "    # we need to persist q at this point because otherwise the final collect may crash/take time because. \n",
    "    #In fact, otherwise, spark must go back to all operations performed on all iterations. \n",
    "    q.persist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Saving the loglik list. \n",
    "#np.savetxt(\"loglik_3_clusters_30_iterations.csv\", loglik, delimiter=\",\", fmt='%s', header=header)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
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J473dfQOAu28ws/o9dUFEpJLS8go+Wr+L+Xk7mL82Sh4rthTi4VBH/65tObJ/F7557CCO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\nFkooIiKSFkooIiKSFv8fgJf9vfGgg/YAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106254860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting the loglik. \n",
    "fig = plt.figure()\n",
    "fig.suptitle('log-likelihood = f(nb of iterations)', fontsize=14, fontweight='bold')\n",
    "ax = fig.add_subplot(111)\n",
    "fig.subplots_adjust(top=0.85)\n",
    "ax.set_xlabel('number of iterations')\n",
    "ax.set_ylabel('log-likelihood')\n",
    "ax.plot(loglik)\n",
    "plt.savefig('loglik_3_clusters_30_iterations.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "loglikelihood = pd.read_csv(\"loglikelihood.csv\", sep=';')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0vRl6z66nawIPo1Z7d0INhP+DFrcOo9hq5e+CAg4VFHDIEIfSPLWkpELdDi4u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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109df5588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "two_cluster, = plt.plot(loglikelihood['Iteration'], loglikelihood['2_cluster'], 'g', label='2_cluster')\n",
    "three_cluster, = plt.plot(loglikelihood['Iteration'], loglikelihood['3_cluster'], 'k', label='3_cluster')\n",
    "four_cluster,=plt.plot(loglikelihood['Iteration'], loglikelihood['4_cluster'], 'b', label='4_cluster')\n",
    "five_cluster,=plt.plot(loglikelihood['Iteration'], loglikelihood['5_cluster'], 'y', label='5_cluster')\n",
    "six_cluster,=plt.plot(loglikelihood['Iteration'], loglikelihood['6_cluster'], 'r',label='6_cluster')\n",
    "ten_cluster,=plt.plot(loglikelihood['Iteration'], loglikelihood['10_cluster'], 'c',label='10_cluster')\n",
    "fifteen_cluster,=plt.plot(loglikelihood['Iteration'], loglikelihood['15_cluster'], 'magenta',label='15_cluster')\n",
    "twenty_cluster,=plt.plot(loglikelihood['Iteration'], loglikelihood['20_cluster'], 'orange',label='20_cluster')\n",
    "plt.legend([two_cluster,three_cluster,four_cluster,five_cluster,six_cluster, ten_cluster, fifteen_cluster, twenty_cluster], ['2_cluster', '3_cluster','4_cluster','5_cluster','6_cluster','10_cluster','15_cluster','20_cluster'])\n",
    "plt.title(\"loglikelihood = f(nb of iterations)\")\n",
    "plt.xlabel(\"iterations\")\n",
    "plt.ylabel(\"loglikelihood\")\n",
    "plt.savefig('multiple.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2.3 Computing the final result and introducing the threshold method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PythonRDD[2141] at RDD at PythonRDD.scala:48"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Our goal here is to compute an RDD gathering the final result which means the tuples: ((u,s); p(s|u)) with (u,s)\n",
    "# as keys and for all the possible couples (u,s) of our training set (even the couples that was not a clik-log\n",
    "# in the training set. \n",
    "\n",
    "\n",
    "#(u, z, p(z|u)) -> (z, (u,p(z|u)))\n",
    "Puz_bis = Puz.map(lambda x : (x[0].split(',')[1], \\\n",
    "                 \n",
    "                 (x[0].split(',')[0],x[1])))\n",
    "\n",
    "#(s,z, p(s|z)) -> (z, (s,p(s|z)))\n",
    "Nsz_normalized_bis =  Nsz_normalized.map(lambda x : (x[0].split(',')[1], \\\n",
    "                 (x[0].split(',')[0],x[1])))\n",
    "\n",
    "# Generating all the possible couples (u,s)\n",
    "# JOIN --> (z, (u, p(z|u),s, p(s|z)))\n",
    "final = Puz_bis.join(Nsz_normalized_bis)\n",
    "# (z, (u, p(z|u),s, p(s|z))) --> ((u,s), p(z|u) * p(s|z))\n",
    "final = final.map(lambda  x: (x[1][0][0] +','+x[1][1][0], \\\n",
    "                           (x[1][0][1]*x[1][1][1])))\n",
    "#((u,s), p(z|u) * p(s|z)) --> ((u,s); p(s|u))\n",
    "final = final.reduceByKey(lambda x,y : x+y)\n",
    "result = final \n",
    "result.persist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('102,2599', 0.0011295927448667434),\n",
       " ('102,1341', 9.93421484056972e-05),\n",
       " ('102,349', 0.00030380414136750366),\n",
       " ('102,7841', 6.087661914754206e-09),\n",
       " ('102,4537', 9.934214856880203e-05),\n",
       " ('102,6215', 9.934214856874904e-05),\n",
       " ('102,7065', 2.9023510908802532e-05),\n",
       " ('102,4855', 0.00036737130935736705),\n",
       " ('102,8529', 9.180674022934234e-05),\n",
       " ('102,5705', 9.212840325138163e-07),\n",
       " ('102,1237', 0.0004139330234356138),\n",
       " ('102,236', 0.0002764223014668826),\n",
       " ('102,4718', 4.509544550325192e-07),\n",
       " ('102,66665', 5.081517482820518e-05),\n",
       " ('102,7135', 0.00013245609015885204),\n",
       " ('102,105954', 2.1703513801105362e-08),\n",
       " ('102,56885', 2.6392089704632866e-12),\n",
       " ('102,39659', 1.1210099693374801e-10),\n",
       " ('102,8239', 8.086146085623974e-05),\n",
       " ('102,2884', 3.311404336116794e-05)]"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result.take(20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Here we define a threshold t: if the probability p(s|u) > t, then we predict a click-log (u,s).\n",
    "\n",
    "# shape - rdd = [('u,s',p(s|u))]\n",
    "\n",
    "\n",
    "\n",
    "def prediction(rdd, threshold):\n",
    "    return(rdd.map(lambda x : (x[0],x[1]>=threshold.value)))\n",
    "\n",
    "# We will define the best value for the threshold after. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Computing the clik-log prediction for all the couples (u,s) and for a specific threshold.\n",
    "#pred_1 = prediction(result,sc.broadcast(.1)) - Division by zero.\n",
    "#pred_2 = prediction(result,sc.broadcast(.01))\n",
    "pred_3 = prediction(result,sc.broadcast(.001))\n",
    "pred_4 = prediction(result,sc.broadcast(.0001))\n",
    "pred_5 = prediction(result,sc.broadcast(.00001))\n",
    "pred_6 = prediction(result,sc.broadcast(.000001))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. Algorithm performance : Precision, recall & F1-score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# This function computes the precision and recall of the algorithm /!\\/!\\ ON THE TEST SET /!\\/!\\\n",
    "# This function takes as input the prediction rdd above [('u,s', clik log-boolean)] , a \n",
    "# train rdde set with the shape : ['u,s'] and a test rdd set with the shape : ['u,s']\n",
    "# The ouput is the tupple : (precision,recall, F1 score)\n",
    "\n",
    "# The idea of the algorithm is described in part 5 of the Latex file. \n",
    "# We remove from pred the movies on the training set(films already seen by users) in order to no impact the calculaition\n",
    "# of False Negatives et False Positives. \n",
    "\n",
    "\n",
    "def precisionRecallTest(pred, train, test) :\n",
    "    # pred is of the form [('u,s', boolean)]\n",
    "    # train is of the form : ['u,s']\n",
    "    # test is of the form : ['u,s']\n",
    "    \n",
    "    \n",
    "    # Remove from pred the films already seen by users. To do so we use substractByKey() so we need \n",
    "    # to append something to the train rdd\n",
    "    to_remove = train.map(lambda x : (x,1))\n",
    "    predict = pred.subtractByKey(to_remove)\n",
    "    \n",
    "    \n",
    "    # positive predictions (we predict that user u has seen film s)\n",
    "    pos = predict.filter(lambda x : x[1])\\\n",
    "                 .map(lambda x : x[0])\n",
    "    # Number of positive predictions\n",
    "    nb_pos = pos.count()\n",
    "    # Number of true positivies\n",
    "    nb_TP = pos.intersection(test).count() \n",
    "    # Number of false positives\n",
    "    nb_FP = nb_pos - nb_TP \n",
    "    \n",
    "    #negatives predictions (we predict that user u has never seen film s)\n",
    "    # Same spirit. \n",
    "    neg = predict.filter(lambda x : not(x[1]))\\\n",
    "                 .map(lambda x : x[0])\n",
    "    nb_neg = neg.count()\n",
    "    nb_FN = neg.intersection(test).count() # Our negative predictions are actually in the train set\n",
    "    nb_TN = nb_neg - nb_FN\n",
    "    \n",
    "    \n",
    "    # compute precision and recall\n",
    "    precision = nb_TP / (nb_FP + nb_TP)\n",
    "    recall = nb_TP / (nb_FN + nb_TP)\n",
    "    F1_score = 2 * (precision * recall)/(precision + recall)\n",
    "    \n",
    "    return((precision,recall, F1_score))\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
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PwbpkPYWHWHh4OHZ2djz98Q2uppTCIeU8G2u9y8vjj1Hh1GNU+dcvBAU2w2RK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\nO2TYAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e2a2ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plotting some results of the optimization \n",
    "\n",
    "\n",
    "precision_20 = [0.06179838984011793,\n",
    "0.05281031785400847,\n",
    "0.0455299037438448,\n",
    "0.03793495565158062,\n",
    "0.028900911161731206,\n",
    "0.026981093540292933,\n",
    "0.008732843759643534,\n",
    "0.00525162140306895]\n",
    "recall_20 = [ 0.1129065672260203,\n",
    "0.14336026517505698,\n",
    "0.19059457219805262,\n",
    "0.2591671845866998,\n",
    "0.35746840687797804,\n",
    "0.3831572405220634,\n",
    "0.7943857468406877,\n",
    "0.892686969131966]\n",
    "\n",
    "\n",
    "precision_15 = [0.05842021758839529,\n",
    "0.05034165926726634,\n",
    "0.044070854107684215,\n",
    "0.03674524621762609,\n",
    "0.028982459092247507,\n",
    "0.027347324193158776,\n",
    "0.00865213213647514,\n",
    "0.0047596254250340106]\n",
    "recall_15 = [0.10679511083488709,\n",
    "0.13507354464470686,\n",
    "0.18220426766107314,\n",
    "0.24880878392376218,\n",
    "0.3568469028382018,\n",
    "0.3869898487673503,\n",
    "0.8180029003521856,\n",
    "0.9136109384711001]\n",
    "\n",
    "\n",
    "precision_10 = [0.07359376243137879,0.062439174307227376,0.051000428317934283,0.041507268553940324,\n",
    "                0.030738738419883734,0.028419815790471138,0.007666534158668863,0.004036308767714573]\n",
    "recall_10 = [0.09581520613217319,0.12626890408120986,0.1726745390511705,0.24725502382432152,\n",
    "0.3598508390304537,0.3883364408535322,0.8250466128029832,0.9285270354257302]\n",
    "\n",
    "\n",
    "precision_5 = [0.0600788481316421,\n",
    "0.0546227893440788,\n",
    "0.04691621865295355,\n",
    "0.0415425553040232,\n",
    "0.03053153791637137,\n",
    "0.028176641580058136,\n",
    "0.007693692747447314,\n",
    "0.0033626281671464]\n",
    "recall_5 = [0.07261238864719287,\n",
    "0.10109799047027139,\n",
    "0.14553552931427388,\n",
    "0.21669774186865548,\n",
    "0.33467992541951525,\n",
    "0.3664802154547338,\n",
    "0.8498031903874042,\n",
    "0.9681997099647814]\n",
    "\n",
    "precision_3 = [0.08041374708041375,\n",
    "0.06389520117631332,\n",
    "0.05404612405375271,\n",
    "0.04088666286479383,\n",
    "0.02942365617482362,\n",
    "0.02666321727809861,\n",
    "0.00661169160069094,\n",
    "0.0027037463980262304]\n",
    "recall_3 = [0.024963745597679717,\n",
    "0.04951315516884193,\n",
    "0.09540087010565569,\n",
    "0.17081002693184172,\n",
    "0.30153304329811476,\n",
    "0.3309509011808577,\n",
    "0.8488709343277397,\n",
    "0.9732753262896209]\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "#plt.plot(precision_20, recall_20)\n",
    "\n",
    "\n",
    "three_cluster, = plt.plot(precision_3, recall_3, 'k', label='3_cluster')\n",
    "five_cluster,=plt.plot(precision_5, recall_5, 'y', label='5_cluster')\n",
    "ten_cluster,=plt.plot(precision_10, recall_10, 'c',label='10_cluster')\n",
    "fifteen_cluster,=plt.plot(precision_15, recall_15, 'magenta',label='15_cluster')\n",
    "twenty_cluster,=plt.plot(precision_20, recall_20, 'orange',label='20_cluster')\n",
    "plt.legend([three_cluster,five_cluster, ten_cluster, fifteen_cluster, twenty_cluster], [ '3_cluster','5_cluster','10_cluster','15_cluster','20_cluster'])\n",
    "plt.title(\"recall= f(precision)\")\n",
    "plt.xlabel(\"precision\")\n",
    "plt.ylabel(\"recall\")\n",
    "plt.savefig('precision_recall.png')\n",
    "\n",
    "plt.show()"
   ]
  }
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