Spark_MovieLens.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook, we will use Spark APIs to implement [Matrix Factorizationan and Alternating Least Squares](https://blog.insightdatascience.com/explicit-matrix-factorization-als-sgd-and-all-that-jazz-b00e4d9b21ea) (ALS) algorithm and predict the ratings for the movies in [MovieLens small dataset](https://grouplens.org/datasets/movielens/latest/). The approach used here can be applied to other rating datasets as well. **This notebook has to run in Spark environment.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "import time"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data Exploration"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's load the data and do a quick inspection."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "movies = spark.read.load(\"ml-latest-small/movies.csv\", format='csv', header = True)\n",
    "ratings = spark.read.load(\"ml-latest-small/ratings.csv\", format='csv', header = True)\n",
    "links = spark.read.load(\"ml-latest-small/links.csv\", format='csv', header = True)\n",
    "tags = spark.read.load(\"ml-latest-small/tags.csv\", format='csv', header = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-------+--------------------+--------------------+\n",
      "|movieId|               title|              genres|\n",
      "+-------+--------------------+--------------------+\n",
      "|      1|    Toy Story (1995)|Adventure|Animati...|\n",
      "|      2|      Jumanji (1995)|Adventure|Childre...|\n",
      "|      3|Grumpier Old Men ...|      Comedy|Romance|\n",
      "|      4|Waiting to Exhale...|Comedy|Drama|Romance|\n",
      "|      5|Father of the Bri...|              Comedy|\n",
      "+-------+--------------------+--------------------+\n",
      "only showing top 5 rows\n",
      "\n"
     ]
    }
   ],
   "source": [
    "movies.show(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+------+-------+------+----------+\n",
      "|userId|movieId|rating| timestamp|\n",
      "+------+-------+------+----------+\n",
      "|     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",
      "+------+-------+------+----------+\n",
      "only showing top 5 rows\n",
      "\n"
     ]
    }
   ],
   "source": [
    "ratings.show(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-------+-------+------+\n",
      "|movieId| imdbId|tmdbId|\n",
      "+-------+-------+------+\n",
      "|      1|0114709|   862|\n",
      "|      2|0113497|  8844|\n",
      "|      3|0113228| 15602|\n",
      "|      4|0114885| 31357|\n",
      "|      5|0113041| 11862|\n",
      "+-------+-------+------+\n",
      "only showing top 5 rows\n",
      "\n"
     ]
    }
   ],
   "source": [
    "links.show(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+------+-------+--------------------+----------+\n",
      "|userId|movieId|                 tag| timestamp|\n",
      "+------+-------+--------------------+----------+\n",
      "|    15|    339|sandra 'boring' b...|1138537770|\n",
      "|    15|   1955|             dentist|1193435061|\n",
      "|    15|   7478|            Cambodia|1170560997|\n",
      "|    15|  32892|             Russian|1170626366|\n",
      "|    15|  34162|         forgettable|1141391765|\n",
      "+------+-------+--------------------+----------+\n",
      "only showing top 5 rows\n",
      "\n"
     ]
    }
   ],
   "source": [
    "tags.show(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because the goal of this notebook is to predict ratings, I'll not explore \"movies\", \"links\" and \"tags\" much. But just out of curiosity, let's check how the movies distribute across various genres."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+--------------------+-----+\n",
      "|              genres|count|\n",
      "+--------------------+-----+\n",
      "|               Drama| 1170|\n",
      "|              Comedy|  809|\n",
      "|        Comedy|Drama|  425|\n",
      "|         Documentary|  365|\n",
      "|       Drama|Romance|  356|\n",
      "|      Comedy|Romance|  341|\n",
      "|Comedy|Drama|Romance|  264|\n",
      "|              Horror|  183|\n",
      "|      Drama|Thriller|  172|\n",
      "|         Crime|Drama|  135|\n",
      "|Crime|Drama|Thriller|  116|\n",
      "|     Horror|Thriller|  112|\n",
      "|           Drama|War|  107|\n",
      "|        Comedy|Crime|   77|\n",
      "|            Thriller|   74|\n",
      "|       Action|Comedy|   67|\n",
      "|     Children|Comedy|   64|\n",
      "|     Action|Thriller|   57|\n",
      "|       Comedy|Horror|   57|\n",
      "|        Action|Drama|   53|\n",
      "+--------------------+-----+\n",
      "only showing top 20 rows\n",
      "\n"
     ]
    }
   ],
   "source": [
    "movies.groupby(\"genres\").count().orderBy(\"count\", ascending=False).show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It's not surprising that Drama and Comedy are the most dominant types. Many movies are labeled as multiple genres. It would be better if we make each distinct genre a column and count the number of movies that are labeled as each of them. However, this is out of the scope of this work. Below are some numbers for the rating data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Distinct values of ratings:\n",
      "[u'0.5', u'1.0', u'1.5', u'2.0', u'2.5', u'3.0', u'3.5', u'4.0', u'4.5', u'5.0']\n"
     ]
    }
   ],
   "source": [
    "print 'Distinct values of ratings:'\n",
    "print sorted(ratings.select('rating').distinct().rdd.map(lambda r: r[0]).collect())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For the users that rated movies and the movies that were rated:\n",
      "Minimum number of ratings per user is 20\n",
      "Minimum number of ratings per movie is 1\n"
     ]
    }
   ],
   "source": [
    "tmp1 = ratings.groupBy(\"userID\").count().select('count').rdd.min()[0]\n",
    "tmp2 = ratings.groupBy(\"movieId\").count().select('count').rdd.min()[0]\n",
    "print 'For the users that rated movies and the movies that were rated:'\n",
    "print 'Minimum number of ratings per user is {}'.format(tmp1)\n",
    "print 'Minimum number of ratings per movie is {}'.format(tmp2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3063 out of 9066 movies are rated by only one user\n"
     ]
    }
   ],
   "source": [
    "tmp1 = ratings.groupBy(\"movieId\").count().withColumnRenamed(\"count\", \"rating count\")\\\n",
    ".groupBy(\"rating count\").count().orderBy('rating count').first()[1]\n",
    "# Or use pandas: tmp1 = sum(ratings.groupBy(\"movieId\").count().toPandas()['count'] == 1)\n",
    "tmp2 = ratings.select('movieId').distinct().count()\n",
    "print '{} out of {} movies are rated by only one user'.format(tmp1, tmp2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of users: 671\n"
     ]
    }
   ],
   "source": [
    "print \"Number of users:\", ratings.select('userId').union(tags.select('userId')).distinct().count()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of users who rated movies: 671\n"
     ]
    }
   ],
   "source": [
    "print \"Number of users who rated movies:\", ratings.select('userId').distinct().count()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of movies: 9125\n"
     ]
    }
   ],
   "source": [
    "print \"Number of movies:\", ratings.select('movieId').union(tags.select('movieId')).distinct().count()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of rated movies: 9066\n"
     ]
    }
   ],
   "source": [
    "print \"Number of rated movies:\", ratings.select('movieId').distinct().count()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Process Data for Training\n",
    "We will use a dataframe-based API from [pyspark.ml](https://spark.apache.org/docs/latest/ml-collaborative-filtering.html) to predict the ratings. First, we need to convert the rating dataframe to the right form for the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ratings = ratings.select(\"userId\", \"movieId\", \"rating\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "root\n",
      " |-- userId: string (nullable = true)\n",
      " |-- movieId: string (nullable = true)\n",
      " |-- rating: string (nullable = true)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# inspect the schema of the data frame\n",
    "ratings.printSchema()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The userId and movieId have to be integers, and the rating has to be float numbers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Below is a correct and efficient way to change the column types, but it somehow produced \n",
    "# errors on my laptop later when working on the dataframe due to some java issues...\n",
    "# So I used the withColumn() method instead\n",
    "\n",
    "\"\"\"\n",
    "from pyspark.sql.types import *\n",
    "\n",
    "schema = StructType([\n",
    "    StructField(\"userId\", IntegerType(), True),\n",
    "    StructField(\"movieId\", IntegerType(), True),\n",
    "    StructField(\"rating\", FloatType(), True)])\n",
    "\n",
    "df = spark.createDataFrame(ratings.rdd, schema)\n",
    "\"\"\"\n",
    "\n",
    "df = ratings.withColumn('userId', ratings['userId'].cast('int')).\\\n",
    "withColumn('movieId', ratings['movieId'].cast('int')).withColumn('rating', ratings['rating'].cast('float'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "root\n",
      " |-- userId: integer (nullable = true)\n",
      " |-- movieId: integer (nullable = true)\n",
      " |-- rating: float (nullable = true)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# inspect the schema again\n",
    "df.printSchema()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I will split the data into training/validation/testing sets using a 60/20/20 split."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train, validation, test = df.randomSplit([0.6,0.2,0.2], seed = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The number of ratings in each set: 60004, 20027, 19973\n"
     ]
    }
   ],
   "source": [
    "print \"The number of ratings in each set: {}, {}, {}\".format(train.count(), validation.count(), test.count())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Benchmark\n",
    "\n",
    "Here I define a benchmark model which simply uses the mean rating of each movie (in the training set) as the prediction. We can later compare our model performance with this benchmark."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-------+------------------+\n",
      "|movieId|        prediction|\n",
      "+-------+------------------+\n",
      "|   1580|3.6327433628318584|\n",
      "|   3175|          3.515625|\n",
      "|   1088| 3.264705882352941|\n",
      "|   1645|             3.325|\n",
      "|   2366| 3.611111111111111|\n",
      "+-------+------------------+\n",
      "only showing top 5 rows\n",
      "\n"
     ]
    }
   ],
   "source": [
    "mean_rating = train.groupby('movieId').mean().select('movieId','avg(rating)')\n",
    "mean_rating = mean_rating.withColumnRenamed('avg(rating)','prediction')\n",
    "mean_rating.show(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use SQL to combine the above predictions and the testing set dataframe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+------+-------+------+------------------+\n",
      "|userId|movieId|rating|        prediction|\n",
      "+------+-------+------+------------------+\n",
      "|     1|     31|   2.5| 3.185185185185185|\n",
      "|     1|   1129|   2.0|3.1666666666666665|\n",
      "|     1|   1263|   2.0|3.8636363636363638|\n",
      "|     2|     39|   5.0|3.5616438356164384|\n",
      "|     2|     47|   4.0| 4.025547445255475|\n",
      "+------+-------+------+------------------+\n",
      "only showing top 5 rows\n",
      "\n"
     ]
    }
   ],
   "source": [
    "test.createOrReplaceTempView(\"test\")\n",
    "mean_rating.createOrReplaceTempView(\"mean_rating\")\n",
    "\n",
    "sqlDF = spark.sql(\"select test.*, mean_rating.prediction \\\n",
    "                   from test join mean_rating \\\n",
    "                   on test.movieId = mean_rating.movieId\")\n",
    "sqlDF.show(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To evaluate the model performance on the testing set, we will use root-mean-square error (RMSE) as the metric."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Define a function to calculate RMSE\n",
    "\n",
    "from pyspark.ml.evaluation import RegressionEvaluator\n",
    "evaluator = RegressionEvaluator(metricName=\"rmse\", labelCol=\"rating\",\n",
    "                                predictionCol=\"prediction\")\n",
    "\n",
    "def RMSE(predictions):\n",
    "    return evaluator.evaluate(predictions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using the mean rating of each movie as the prediction, the testing RMSE is 0.999525001621\n"
     ]
    }
   ],
   "source": [
    "print 'Using the mean rating of each movie as the prediction, the testing RMSE is ' + str(RMSE(sqlDF))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model Selection and Evaluation\n",
    "\n",
    "Now we can run the ALS algorithm. Using this model, we can do a grid search to find the optimal hyperparameters. We will use the RMSE of the validation set to evaluate each model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Define a function to perform grid search and find the best ALS model\n",
    "# based on the validation RMSE\n",
    "\n",
    "from pyspark.ml.recommendation import ALS\n",
    "\n",
    "def GridSearch(train, valid, num_iterations, reg_param, n_factors):\n",
    "    min_rmse = float('inf')\n",
    "    best_n = -1\n",
    "    best_reg = 0\n",
    "    best_model = None\n",
    "    for n in n_factors:\n",
    "        for reg in reg_param:\n",
    "            als = ALS(rank = n, \n",
    "                      maxIter = num_iterations, \n",
    "                      seed = 0, \n",
    "                      regParam = reg,\n",
    "                      userCol=\"userId\", \n",
    "                      itemCol=\"movieId\", \n",
    "                      ratingCol=\"rating\", \n",
    "                      coldStartStrategy=\"drop\")            \n",
    "            model = als.fit(train)\n",
    "            predictions = model.transform(valid)\n",
    "            rmse = RMSE(predictions)     \n",
    "            print '{} latent factors and regularization = {}: validation RMSE is {}'.format(n, reg, rmse)\n",
    "            if rmse < min_rmse:\n",
    "                min_rmse = rmse\n",
    "                best_n = n\n",
    "                best_reg = reg\n",
    "                best_model = model\n",
    "                \n",
    "    pred = best_model.transform(train)\n",
    "    train_rmse = RMSE(pred)\n",
    "    print '\\nThe best model has {} latent factors and regularization = {}:'.format(best_n, best_reg)\n",
    "    print 'traning RMSE is {}; validation RMSE is {}'.format(train_rmse, min_rmse)\n",
    "    return best_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6 latent factors and regularization = 0.05: validation RMSE is 1.02203363995\n",
      "6 latent factors and regularization = 0.1: validation RMSE is 0.954438052853\n",
      "6 latent factors and regularization = 0.2: validation RMSE is 0.924770729779\n",
      "6 latent factors and regularization = 0.4: validation RMSE is 0.985705320681\n",
      "6 latent factors and regularization = 0.8: validation RMSE is 1.19828898699\n",
      "8 latent factors and regularization = 0.05: validation RMSE is 1.02972976705\n",
      "8 latent factors and regularization = 0.1: validation RMSE is 0.951760819297\n",
      "8 latent factors and regularization = 0.2: validation RMSE is 0.922537908145\n",
      "8 latent factors and regularization = 0.4: validation RMSE is 0.985313259158\n",
      "8 latent factors and regularization = 0.8: validation RMSE is 1.19829732375\n",
      "10 latent factors and regularization = 0.05: validation RMSE is 1.03636326726\n",
      "10 latent factors and regularization = 0.1: validation RMSE is 0.950379421009\n",
      "10 latent factors and regularization = 0.2: validation RMSE is 0.923438930878\n",
      "10 latent factors and regularization = 0.4: validation RMSE is 0.986343222497\n",
      "10 latent factors and regularization = 0.8: validation RMSE is 1.1982784026\n",
      "12 latent factors and regularization = 0.05: validation RMSE is 1.0515627774\n",
      "12 latent factors and regularization = 0.1: validation RMSE is 0.952025747054\n",
      "12 latent factors and regularization = 0.2: validation RMSE is 0.924448021229\n",
      "12 latent factors and regularization = 0.4: validation RMSE is 0.987186223587\n",
      "12 latent factors and regularization = 0.8: validation RMSE is 1.19828044842\n",
      "\n",
      "The best model has 8 latent factors and regularization = 0.2:\n",
      "traning RMSE is 0.690982221977; validation RMSE is 0.922537908145\n",
      "Total Runtime: 163.99 seconds\n"
     ]
    }
   ],
   "source": [
    "num_iterations = 10\n",
    "ranks = [6, 8, 10, 12]\n",
    "reg_params = [0.05, 0.1, 0.2, 0.4, 0.8]\n",
    "\n",
    "start_time = time.time()\n",
    "final_model = GridSearch(train, validation, num_iterations, reg_params, ranks)\n",
    "print 'Total Runtime: {:.2f} seconds'.format(time.time() - start_time)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The runtime is about 160 seconds. We will use an RDD-based approach in [Spark_MovieLens_RDD.ipynb](Spark_MovieLens_RDD.ipynb) and see if the runtime is different. So the model with 8 latent factors and lambda = 0.2 yields the best result. Let's do a second grid search around these values with more iterations (15) for each model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7 latent factors and regularization = 0.1: validation RMSE is 0.95097372416\n",
      "7 latent factors and regularization = 0.2: validation RMSE is 0.925118410924\n",
      "7 latent factors and regularization = 0.3: validation RMSE is 0.94787509625\n",
      "8 latent factors and regularization = 0.1: validation RMSE is 0.950515198158\n",
      "8 latent factors and regularization = 0.2: validation RMSE is 0.923712922344\n",
      "8 latent factors and regularization = 0.3: validation RMSE is 0.947078377034\n",
      "9 latent factors and regularization = 0.1: validation RMSE is 0.950582803733\n",
      "9 latent factors and regularization = 0.2: validation RMSE is 0.923303643645\n",
      "9 latent factors and regularization = 0.3: validation RMSE is 0.947200079093\n",
      "\n",
      "The best model has 9 latent factors and regularization = 0.2:\n",
      "traning RMSE is 0.686163366237; validation RMSE is 0.923303643645\n"
     ]
    }
   ],
   "source": [
    "num_iterations = 15\n",
    "ranks = [7, 8, 9]\n",
    "reg_params = [0.1, 0.2, 0.3]\n",
    "\n",
    "final_model = GridSearch(train, validation, num_iterations, reg_params, ranks)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So the model with 9 latent factors and lambda = 0.2 yields the best result."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see the testing error is consistent with the validation error:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The testing RMSE is 0.922537488773\n"
     ]
    }
   ],
   "source": [
    "pred_test = final_model.transform(test)\n",
    "print 'The testing RMSE is ' + str(RMSE(pred_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Although the RMSE dosen't look like a big improvement from the benchmark (RMSE ~ 1.0), this is pretty much the best we can achieve. You can check out some of the results using other models [here](http://surpriselib.com/)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualization\n",
    "\n",
    "We can make plots to compare the true and predicted ratings for the training and testing sets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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E/eXj4H2e932/dhb1IY3YCNW3Kq255NGbLyu7Kk2I4aq3aLMmb2PoJvmyp9yI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\nPTJL28b835+SXXg26uAgzaM/SPmqawk6u8bs+++YhxXF4Vk02QQMOMO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jh+3GmoE6PYUk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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108f37450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pred_train = final_model.transform(train)\n",
    "df = pred_train.toPandas()\n",
    "x = np.arange(0.5, 5.1, 0.5) # To draw the red one-to-one line below\n",
    "\n",
    "fig = plt.figure(figsize=(10,8))\n",
    "plt.tick_params(labelsize=15)\n",
    "plt.scatter(df.rating, df.prediction, s = 10, alpha = 0.2)\n",
    "plt.plot(x, x, c = 'r')\n",
    "plt.xlabel('rating', fontsize=20)\n",
    "plt.ylabel('prediction', fontsize=20)\n",
    "plt.title('Training Set', fontsize=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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owOjuDwGphHmXmmq5OtaD4utabIRKhfR3LiN99ZVYYchvd3kP3z/kkxSTWXbu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\nCZFATAghhBAiIf8/opMCC9T+LXUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108f71190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = pred_test.toPandas()\n",
    "fig = plt.figure(figsize=(10,8))\n",
    "plt.tick_params(labelsize=15)\n",
    "plt.scatter(df.rating, df.prediction, s = 10, alpha = 0.2)\n",
    "plt.plot(x, x, c = 'r')\n",
    "plt.xlabel('rating', fontsize=20)\n",
    "plt.ylabel('prediction', fontsize=20)\n",
    "plt.title('Testing Set', fontsize=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "A model with more latent factors can definitely fit the training data better, but it won't generalize wlll on the testing data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}