personalization_project1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# IEOR 4571 - Personalization - Project 1\n",
    "\n",
    "#### Team members: \n",
    "Name, UNI/email, Github ID\n",
    "* Megala Kannan, msk2245@columbia.edu, thisismeg\n",
    "* Hojin Lee, hl3328@columbia.edu, hjlee9295\n",
    "* Jung Ah Shin, js5569@columbia.edu, juliajungahshin\n",
    "* Tiffany Zhu, tz2196@columbia.edu, tlzhu19\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TOC:\n",
    "* [1. Introduction](#1)\n",
    "* [2. Data Exploration](#2)\n",
    "* [3. Modeling](#3)\n",
    "    * [3.1 Baseline Model](#3-1)\n",
    "        * [3.1.1 Accuracy of Baseline Model](#3-1-1)\n",
    "        * [3.1.2 Coverage of Baseline Model](#3-1-2)\n",
    "    * [3.2 Neighborhood-Based Collaborative Filtering](#3-2)\n",
    "        * [3.2.1 Tuning Hyperparameters](#3-2-1)\n",
    "        * [3.2.2 Accuracy of KNN Means Model](#3-2-2)\n",
    "        * [3.2.3 Coverage of KNN Means Model](#3-2-3)\n",
    "    * [3.3 Model-Based Collaborative Filtering](#3-3)\n",
    "        * [3.3.1 Tuning Hyperparameters](#3-3-1)\n",
    "        * [3.3.2 Accuracy of ALS Model](#3-3-2)\n",
    "        * [3.3.3 Coverage of ALS Model](#3-3-3)\n",
    "* [4. Evaluation](#4)\n",
    "    * [4.1 Accuracy](#4-1)\n",
    "        * [4.1.1 RMSE](#4-1-1)\n",
    "        * [4.1.2 NDCG](#4-1-2)\n",
    "    * [4.2 Coverage](#4-2)\n",
    "    * [4.3 User Distribution](#4-3)\n",
    "* [5. Conclusion](#5)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "from surprise import KNNWithMeans\n",
    "from surprise import Dataset\n",
    "from surprise import accuracy\n",
    "from surprise.model_selection import train_test_split as s_train_test_split\n",
    "from surprise.model_selection import KFold\n",
    "from surprise import Reader\n",
    "\n",
    "from pyspark.mllib.recommendation import ALS\n",
    "from pyspark.sql import SparkSession\n",
    "from pyspark.sql import SQLContext\n",
    "from pyspark.ml.tuning import (CrossValidator, ParamGridBuilder)\n",
    "\n",
    "import pyspark.sql.functions as sql_func\n",
    "from pyspark.sql.types import *\n",
    "from pyspark.ml.recommendation import ALS, ALSModel\n",
    "from pyspark.context import SparkContext\n",
    "from pyspark.sql.session import SparkSession\n",
    "from pyspark.mllib.evaluation import RegressionMetrics, RankingMetrics\n",
    "from pyspark.ml.evaluation import RegressionEvaluator, BinaryClassificationEvaluator, MulticlassClassificationEvaluator\n",
    "from pyspark.sql.functions import col\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import datetime\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.preprocessing import LabelBinarizer, MultiLabelBinarizer\n",
    "from sklearn.metrics import make_scorer\n",
    "from math import sqrt\n",
    "\n",
    "from collections import OrderedDict "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. Introduction <a class=\"anchor\" id=\"1\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our objective is to facilitate users to consume more products by helping them discover new contents. We want our recommendation model to provide reasonably accurate and diverse recommendations so that many users have an opportunity to explore new content. In order to achieve this objective, we begin by building two brute-force collaborative filtering algorithms to recommend items to users. \n",
    "For the neighborhood-based model, we chose the item-based collative filtering, which recommends items based on item similarity. Item-based models are shown to provide better recommendation accuracy (source: \"Item-Based Collaborative Filtering Recommendation Algorithms\" paper). Furthermore, while similarity between users are prone to change depending on changes in users’ tastes, similarity between items are less likely to vary over time, thus providing a more robust recommendation model.\n",
    "For the model-based framework, we chose the vanilla Matrix Factorization and use alternating least squares algorithm to learn the latent factors. This could be done using stochastic gradiant descent (SGD) as well, however SGD is not very practical and would take a very long time to run. Additionally, we implement a simple baseline model to compare our results. For a movie A, the baseline model gives the rating for A to be the average rating of A for all users.\n",
    "\n",
    "To measure the performance of our two recommender systems, we used RMSE and NDCG. We were interested in the RMSE since we want to minimize the error between the predicted ratings and the actual ratings. Our secondary accuracy metric is NDCG because we want to measure the quality of the rankings.\n",
    "\n",
    "When building a recommender system, the sparsity of the rating data and the introduction of new users or items without any interaction (cold start problem) can hinder the performance of recommender systems. Recognizing sparsity in our dataset, we decided to focus on recommending items that are less ubiquitous (items that have been rated more than once, but not rated by many users). Detailed description on exploratory data analysis of our dataset along with our sampling methods is provided below.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Data Exploration <a class=\"anchor\" id=\"2\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Original data contains 138493 users and 26744 items (Approximately 20M ratings). Original data only contains users that rated more than 20 items. \n",
    "\n",
    "2. In order to develop our Item-based CF model with a small data set (Approx. <10,000 users / <1,000 items), we sampled the data based on the following rationale:\n",
    "    \n",
    "    * Remove ubiquitous items (e.g. top 0.5% most rated items across users) as well as items that have extremely few ratings (e.g. items rated only once). Recommending items that have been rated by majority of users are likely to be redundant and have less value in terms of novelty of the recommendation. Since we aim to provide item recommendations that the user might not have experienced yet, it seemed reasonable to remove top 0.5% of items that have been rated by many users. \n",
    "    \n",
    "    * Regarding items that have extremely few ratings, these items would not contribute much in terms of item similarity, so we have decided to remove those user-item pairs with single ratings as well. \n",
    "\n",
    "\n",
    "3. Then, we randomly sampled 0.1%, 0.5%, and 1% of this dataset to train our models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "ratings_df = pd.read_csv('ratings.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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       "<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",
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       "      <td>3.5</td>\n",
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       "      <th>1</th>\n",
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       "      <th>2</th>\n",
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       "      <td>32</td>\n",
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       "      <td>1112484580</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "   userId  movieId  rating   timestamp\n",
       "0       1        2     3.5  1112486027\n",
       "1       1       29     3.5  1112484676\n",
       "2       1       32     3.5  1112484819\n",
       "3       1       47     3.5  1112484727\n",
       "4       1       50     3.5  1112484580"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ratings_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "138493 26744\n"
     ]
    }
   ],
   "source": [
    "userNum = len(ratings_df.userId.unique()) #138493 users\n",
    "itemNum = len(ratings_df.movieId.unique()) #26744 items\n",
    "\n",
    "print(userNum, itemNum)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
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       "      <th>count</th>\n",
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       "      <th>count</th>\n",
       "      <td>26744.000000</td>\n",
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       "      <th>mean</th>\n",
       "      <td>747.841123</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>3085.818268</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>3.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>18.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>205.000000</td>\n",
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       "      <th>max</th>\n",
       "      <td>67310.000000</td>\n",
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      ],
      "text/plain": [
       "              count\n",
       "count  26744.000000\n",
       "mean     747.841123\n",
       "std     3085.818268\n",
       "min        1.000000\n",
       "25%        3.000000\n",
       "50%       18.000000\n",
       "75%      205.000000\n",
       "max    67310.000000"
      ]
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     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_item_summary = pd.DataFrame(ratings_df.groupby('movieId').size(), columns=['count'])\n",
    "df_item_summary.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We first need to check what percentage the top 0.5% most rated items constitute in terms of the entire rating data. Given our 20M rating dataset, the top 0.5% most rated items (ubiquitous) take up approximately 21.7% of the entire data. Therefore, the list top_05 would contain the item indices of top 0.5% most rated items, and one_item_idx would contain the list of items with only one rating. We will be removing user-item pairs based on these two lists."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    0.217018\n",
       "dtype: float64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_item_summary = df_item_summary.sort_values(by='count', ascending=False) \n",
    "top_rated_movies = df_item_summary.nlargest(int(len(df_item_summary)*0.005), 'count') \n",
    "top_rated_movies.sum()/df_item_summary.sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "top_rated_movies is a dataframe which consists of top 0.5% of most rated movies. `count` column shows the number of movie ratings for each movie item. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 326,
   "metadata": {},
   "outputs": [
    {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>movieId</th>\n",
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       "      <th>296</th>\n",
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       "      <th>356</th>\n",
       "      <td>66172</td>\n",
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       "      <th>318</th>\n",
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       "      <th>593</th>\n",
       "      <td>63299</td>\n",
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       "      <th>480</th>\n",
       "      <td>59715</td>\n",
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      "text/plain": [
       "         count\n",
       "movieId       \n",
       "296      67310\n",
       "356      66172\n",
       "318      63366\n",
       "593      63299\n",
       "480      59715"
      ]
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     "execution_count": 326,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "top_rated_movies.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So now we remove the top 0.5% movies and the movies that were only rated once."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4105\n"
     ]
    },
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       "  <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",
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       "      <th>1</th>\n",
       "      <td>1</td>\n",
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       "      <td>3.5</td>\n",
       "      <td>1112484676</td>\n",
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       "      <th>5</th>\n",
       "      <td>1</td>\n",
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       "      <th>6</th>\n",
       "      <td>1</td>\n",
       "      <td>151</td>\n",
       "      <td>4.0</td>\n",
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       "      <td>1</td>\n",
       "      <td>653</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1094785691</td>\n",
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      ],
      "text/plain": [
       "    userId  movieId  rating   timestamp\n",
       "1        1       29     3.5  1112484676\n",
       "5        1      112     3.5  1094785740\n",
       "6        1      151     4.0  1094785734\n",
       "13       1      337     3.5  1094785709\n",
       "18       1      653     3.0  1094785691"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "top_05 = list(top_rated_movies.index.values) #133 items \n",
    "one_item_idx = df_item_summary[df_item_summary['count']==1].index.tolist() #3972\n",
    "remove_list = top_05 + one_item_idx #4105 items\n",
    "print(len(remove_list)) \n",
    "new_ratings_df = ratings_df[~ratings_df.movieId.isin(top_05)]\n",
    "new_ratings_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`new_ratings_df` is the dataset we'll be using to sample our data for training/test set. \n",
    "After removing the most rated items and items with single rating, we now have 137,542 users, 26,611 items and 15,659,851 ratings in total."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of users: 137542\n",
      "Number of movies: 26611 \n",
      "Total number rows: 15659851\n"
     ]
    },
    {
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       "<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>count</th>\n",
       "      <td>1.565985e+07</td>\n",
       "      <td>1.565985e+07</td>\n",
       "      <td>1.565985e+07</td>\n",
       "      <td>1.565985e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>6.901693e+04</td>\n",
       "      <td>1.117394e+04</td>\n",
       "      <td>3.445954e+00</td>\n",
       "      <td>1.110063e+09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>4.004482e+04</td>\n",
       "      <td>2.187546e+04</td>\n",
       "      <td>1.057272e+00</td>\n",
       "      <td>1.585046e+08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>3.000000e+00</td>\n",
       "      <td>5.000000e-01</td>\n",
       "      <td>7.896520e+08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>3.436200e+04</td>\n",
       "      <td>1.256000e+03</td>\n",
       "      <td>3.000000e+00</td>\n",
       "      <td>9.749575e+08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>6.908200e+04</td>\n",
       "      <td>2.712000e+03</td>\n",
       "      <td>3.500000e+00</td>\n",
       "      <td>1.108593e+09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>1.036000e+05</td>\n",
       "      <td>5.773000e+03</td>\n",
       "      <td>4.000000e+00</td>\n",
       "      <td>1.231299e+09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.384930e+05</td>\n",
       "      <td>1.312620e+05</td>\n",
       "      <td>5.000000e+00</td>\n",
       "      <td>1.427784e+09</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             userId       movieId        rating     timestamp\n",
       "count  1.565985e+07  1.565985e+07  1.565985e+07  1.565985e+07\n",
       "mean   6.901693e+04  1.117394e+04  3.445954e+00  1.110063e+09\n",
       "std    4.004482e+04  2.187546e+04  1.057272e+00  1.585046e+08\n",
       "min    1.000000e+00  3.000000e+00  5.000000e-01  7.896520e+08\n",
       "25%    3.436200e+04  1.256000e+03  3.000000e+00  9.749575e+08\n",
       "50%    6.908200e+04  2.712000e+03  3.500000e+00  1.108593e+09\n",
       "75%    1.036000e+05  5.773000e+03  4.000000e+00  1.231299e+09\n",
       "max    1.384930e+05  1.312620e+05  5.000000e+00  1.427784e+09"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_user = len(new_ratings_df.userId.unique())\n",
    "new_item = len(new_ratings_df.movieId.unique())\n",
    "print(\"Number of users: {}\\nNumber of movies: {} \\nTotal number rows: {}\".format(new_user, new_item, len(new_ratings_df)))\n",
    "new_ratings_df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since `new_ratings_df` still contains more than 1.5 million rows of data, we will now take different sized samples. More specificially, we will look at 0.1%, 0.5%, and 1% of `new_ratings_df` (randomly sampled)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample %: 0.001\n",
      "Number of users: 12878\n",
      "Number of movies: 4515 \n",
      "Total number rows: 15660\n",
      "\n",
      "\n",
      "Sample %: 0.005\n",
      "Number of users: 41704\n",
      "Number of movies: 8312 \n",
      "Total number rows: 78299\n",
      "\n",
      "\n",
      "Sample %: 0.01\n",
      "Number of users: 61517\n",
      "Number of movies: 10260 \n",
      "Total number rows: 156599\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "percentages = [0.001, 0.005, 0.01]\n",
    "all_sample_dfs = []\n",
    "for sample_percentage in percentages:\n",
    "    ratings_sample_df = new_ratings_df.sample(frac=sample_percentage, random_state=1)\n",
    "    all_sample_dfs.append(ratings_sample_df)\n",
    "    \n",
    "    new_user = len(ratings_sample_df.userId.unique())\n",
    "    new_item = len(ratings_sample_df.movieId.unique())\n",
    "    print(\"Sample %: {}\\nNumber of users: {}\\nNumber of movies: {} \\nTotal number rows: {}\\n\\n\".format(\n",
    "        sample_percentage, new_user, new_item, len(ratings_sample_df)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will use these three samples to run our models on."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. Modeling <a class=\"anchor\" id=\"3\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.1 Baseline Model <a class=\"anchor\" id=\"3-1\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We implement a simple baseline model to compare our results to. The baseline model gives the rating for movie A to be the average rating of A for all users."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Baseline model: Use the average rating of a movie in the training set as a predicted rating in the test set.\n",
    "# If movie trying to predict in test set doesn't exist in training, give it 0 rating?\n",
    "\n",
    "def baseline_predictor(avg_ratings, X):\n",
    "    predictions = []\n",
    "    rated_movies = avg_ratings['movieId'].values\n",
    "    \n",
    "    for index, row in X.iterrows():\n",
    "        movieId = row['movieId']\n",
    "        if movieId in rated_movies:\n",
    "            predicted_rating = avg_ratings[avg_ratings['movieId'] == movieId]['rating']\n",
    "            predictions.append(float(predicted_rating))\n",
    "        else:\n",
    "            predictions.append(0)\n",
    "    \n",
    "    final_df = X.copy()\n",
    "    final_df['rating'] = predictions\n",
    "    return final_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample % 0.001\n",
      " Start time: 2019-11-05 00:18:32.269224\n",
      "\tStart predicting at 2019-11-05 00:18:32.415593...\n",
      "\t...End predicting at 2019-11-05 00:18:49.218512.\n",
      "\tStart RMSE at 2019-11-05 00:18:49.218598...\n",
      "\t...End RMSE at 2019-11-05 00:18:49.239604.\n",
      "\tStart NDCG at 2019-11-05 00:18:49.239721...\n",
      "\t...End NDCG at 2019-11-05 00:18:53.908419.\n",
      "\tTotal Time: 0:00:21.639501\n",
      "Sample % 0.005\n",
      " Start time: 2019-11-05 00:18:53.908756\n",
      "\tStart predicting at 2019-11-05 00:18:53.953405...\n",
      "\t...End predicting at 2019-11-05 00:20:11.858349.\n",
      "\tStart RMSE at 2019-11-05 00:20:11.858883...\n",
      "\t...End RMSE at 2019-11-05 00:20:11.887136.\n",
      "\tStart NDCG at 2019-11-05 00:20:11.887266...\n",
      "\t...End NDCG at 2019-11-05 00:20:48.193302.\n",
      "\tTotal Time: 0:01:54.284705\n",
      "Sample % 0.01\n",
      " Start time: 2019-11-05 00:20:48.193496\n",
      "\tStart predicting at 2019-11-05 00:20:48.277898...\n",
      "\t...End predicting at 2019-11-05 00:23:18.446491.\n",
      "\tStart RMSE at 2019-11-05 00:23:18.446753...\n",
      "\t...End RMSE at 2019-11-05 00:23:18.483975.\n",
      "\tStart NDCG at 2019-11-05 00:23:18.484346...\n",
      "\t...End NDCG at 2019-11-05 00:24:39.082213.\n",
      "\tTotal Time: 0:03:50.889619\n"
     ]
    }
   ],
   "source": [
    "# Use baseline model to predict\n",
    "\n",
    "baseline_rmses = []\n",
    "baseline_rmses_train = []\n",
    "baseline_ndcgs = []\n",
    "baseline_ndcgs_train = []\n",
    "baseline_predicted_dfs = []\n",
    "baseline_predicted_train_dfs = []\n",
    "baseline_training_dfs = []\n",
    "baseline_test_dfs = []\n",
    "for i in range(len(percentages)):\n",
    "    start = datetime.datetime.now()\n",
    "    print('Sample % {}\\n Start time: {}'.format(percentages[i], str(start)))\n",
    "    ratings_sample_df = all_sample_dfs[i]\n",
    "\n",
    "    X = ratings_sample_df.loc[:, ratings_sample_df.columns != 'rating']\n",
    "    y = ratings_sample_df.loc[:, ratings_sample_df.columns == 'rating']\n",
    "\n",
    "    X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)\n",
    "\n",
    "    training_sample = X_train.copy()\n",
    "    training_sample['rating'] = y_train\n",
    "    avg_ratings = training_sample.groupby('movieId', as_index = False).mean()\n",
    "    baseline_training_dfs.append(training_sample)\n",
    "    \n",
    "    test_sample = X_test.copy()\n",
    "    test_sample['rating'] = y_test\n",
    "    baseline_test_dfs.append(test_sample)\n",
    "    \n",
    "    print('\\tStart predicting at {}...'.format(str(datetime.datetime.now())))\n",
    "    # test predictions\n",
    "    baseline_predicted_df = baseline_predictor(avg_ratings, X_test)\n",
    "    baseline_predicted_dfs.append(baseline_predicted_df)\n",
    "    # train predictions\n",
    "    baseline_predicted_train_df = baseline_predictor(avg_ratings, X_train)\n",
    "    baseline_predicted_train_dfs.append(baseline_predicted_train_df)\n",
    "    print('\\t...End predicting at {}.'.format(str(datetime.datetime.now())))\n",
    "    \n",
    "    print('\\tStart RMSE at {}...'.format(str(datetime.datetime.now())))\n",
    "    # RMSE on test set\n",
    "    y_actual = y_test['rating']\n",
    "    y_predicted = baseline_predicted_df['rating']\n",
    "    baseline_rmse = sqrt(mean_squared_error(y_actual.tolist(), y_predicted.tolist()))\n",
    "    baseline_rmses.append(baseline_rmse)\n",
    "    \n",
    "    # RMSE on train set\n",
    "    y_actual_train = y_train['rating']\n",
    "    y_predicted_train = baseline_predicted_train_df['rating']\n",
    "    baseline_rmse_train = sqrt(mean_squared_error(y_actual_train.tolist(), y_predicted_train.tolist()))\n",
    "    baseline_rmses_train.append(baseline_rmse_train)\n",
    "    print('\\t...End RMSE at {}.'.format(str(datetime.datetime.now())))\n",
    "    \n",
    "    \n",
    "    print('\\tStart NDCG at {}...'.format(str(datetime.datetime.now())))\n",
    "    # NDCG on test set\n",
    "    y_predicted_grouped, ground_truths = get_ratings_for_each_user(baseline_predicted_df)\n",
    "    baseline_ndcg = ndcg_score(ground_truth=ground_truths, predictions=y_predicted_grouped, k=2)\n",
    "    baseline_ndcgs.append(baseline_ndcg)\n",
    "    \n",
    "    # NDCG on train set\n",
    "    y_predicted_grouped, ground_truths = get_ratings_for_each_user(baseline_predicted_train_df)\n",
    "    baseline_ndcg_train = ndcg_score(ground_truth=ground_truths, predictions=y_predicted_grouped, k=2)\n",
    "    baseline_ndcgs_train.append(baseline_ndcg_train)\n",
    "    print('\\t...End NDCG at {}.'.format(str(datetime.datetime.now())))\n",
    "    \n",
    "    end = datetime.datetime.now()\n",
    "    print('\\tTotal Time: {}'.format(str(end-start)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.1.1 Accuracy of Baseline Model <a class=\"anchor\" id=\"3-1-1\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### RMSE of Baseline Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([1.6802065306456464, 1.1891280563833586, 1.0777108359990675],\n",
       " [0.7618152461605174, 0.8801984562025763, 0.9072231544147223])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "baseline_rmses, baseline_rmses_train"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### NDCG of Baseline Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 330,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ndcg_score(ratings, k=5, pred_col_name='predicted'):\n",
    "    ndcg = 0.0\n",
    "    for u in ratings['userId'].unique().tolist():\n",
    "        y_true = ratings[ratings['userId'] == u]['rating'].tolist()\n",
    "        u_pred = ratings[ratings['userId'] == u][pred_col_name].tolist()\n",
    "        ndcg += ndcg_at_k(y_true, u_pred, k)\n",
    "        \n",
    "    avg_ndcg = ndcg / len(ratings['userId'].unique().tolist())\n",
    "    return avg_ndcg\n",
    "\n",
    "\n",
    "def ndcg_at_k(y_true, y_score, k = 5):\n",
    "    \n",
    "    actual = dcg_at_k(y_true, y_score, k)\n",
    "    best = dcg_at_k(y_true, y_true, k) \n",
    "    ndcg = actual / best\n",
    "    return ndcg\n",
    "\n",
    "\n",
    "def dcg_at_k(y_true, y_score, k = 5):\n",
    "\n",
    "    order = np.argsort(y_score)[::-1]\n",
    "    y_true = np.take(y_true, order[:k])\n",
    "    gains = 2 ** y_true - 1\n",
    "    discounts = np.log2(np.arange(2, gains.size + 2))\n",
    "    dcg = np.sum(gains / discounts)\n",
    "    return dcg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 289,
   "metadata": {},
   "outputs": [],
   "source": [
    "baseline_ndcgs = []\n",
    "baseline_ndcgs_train = []\n",
    "for i in range(len(baseline_predicted_dfs)):\n",
    "    baseline_test_dfs[i]['predicted'] = baseline_predicted_dfs[i]['rating']\n",
    "    baseline_ndcgs.append(ndcg_score(baseline_test_dfs[i]))\n",
    "    \n",
    "    baseline_training_dfs[i]['predicted'] = baseline_predicted_train_dfs[i]['rating']\n",
    "    baseline_ndcgs_train.append(ndcg_score(baseline_training_dfs[i]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 290,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([0.997817149126054, 0.9920032469549104, 0.986059688296345],\n",
       " [0.9972093879159901, 0.9828112188334859, 0.9701805933562814])"
      ]
     },
     "execution_count": 290,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "baseline_ndcgs, baseline_ndcgs_train"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.1.2 Coverage of Baseline Model <a class=\"anchor\" id=\"3-1-2\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_schema = StructType([\n",
    "    StructField('userId',IntegerType(), False),\n",
    "    StructField('movieId',IntegerType(), False),\n",
    "    StructField('rating',FloatType(), False)])\n",
    "\n",
    "spark_baseline_predicted_dfs = []\n",
    "spark_baseline_predicted_train_dfs = []\n",
    "for i in range(len(baseline_predicted_dfs)):\n",
    "    test_df = baseline_predicted_dfs[i]\n",
    "    new_sample_df = test_df.iloc[:, test_df.columns != 'timestamp']\n",
    "    spark_baseline_predicted_dfs.append(spark.createDataFrame(new_sample_df, schema=data_schema))\n",
    "    \n",
    "    train_df = baseline_predicted_train_dfs[i]\n",
    "    new_sample_df2 = train_df.iloc[:, train_df.columns != 'timestamp']\n",
    "    spark_baseline_predicted_train_dfs.append(spark.createDataFrame(new_sample_df2, schema=data_schema))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Item Coverage (0.001% sample): 3.1%\n",
      "Item Coverage (0.005% sample): 2e+01%\n",
      "Item Coverage (0.01% sample): 2.5e+01%\n"
     ]
    }
   ],
   "source": [
    "baseline_test_item_coverages = get_item_coverage(spark_baseline_predicted_dfs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "User Coverage: (0.001% sample): 0.0%\n",
      "User Coverage: (0.005% sample): 1.9%\n",
      "User Coverage: (0.01% sample): 5.8%\n"
     ]
    }
   ],
   "source": [
    "baseline_test_user_coverages = get_user_coverage(spark_baseline_predicted_dfs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Item Coverage (0.001% sample): 3.6e+01%\n",
      "Item Coverage (0.005% sample): 5.1e+01%\n",
      "Item Coverage (0.01% sample): 5.3e+01%\n"
     ]
    }
   ],
   "source": [
    "baseline_train_item_coverages = get_item_coverage(spark_baseline_predicted_train_dfs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "User Coverage: (0.001% sample): 5.4%\n",
      "User Coverage: (0.005% sample): 3.4e+01%\n",
      "User Coverage: (0.01% sample): 5.1e+01%\n"
     ]
    }
   ],
   "source": [
    "baseline_train_user_coverages = get_user_coverage(spark_baseline_predicted_train_dfs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 300,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Catalog Coverage: 99.94739610731193%\n",
      "Catalog Coverage: 98.74476987447699%\n",
      "Catalog Coverage: 97.7080551846907%\n",
      "Catalog Coverage: 86.71763638719709%\n",
      "Catalog Coverage: 92.8416123097508%\n",
      "Catalog Coverage: 78.25727854635556%\n"
     ]
    }
   ],
   "source": [
    "baseline_catalog_coverages = []\n",
    "baseline_catalog_coverages_train = []\n",
    "for baseline_df, baseline_train_df in zip(baseline_test_dfs, baseline_training_dfs):\n",
    "    baseline_df.sort_values(by=['userId', 'predicted'])\n",
    "    ratings_dictionary = dict(baseline_df.set_index('userId').groupby(level = 0).apply(lambda x : x.to_dict(orient= 'records')))\n",
    "    N = len(baseline_df['movieId'].unique())    \n",
    "    baseline_catalog_coverages.append(calculate_catalog_coverage(ratings_dictionary, N))\n",
    "    \n",
    "    baseline_train_df.sort_values(by=['userId', 'predicted'])\n",
    "    ratings_dictionary = dict(baseline_train_df.set_index('userId').groupby(level = 0).apply(lambda x : x.to_dict(orient= 'records')))\n",
    "    N = len(baseline_train_df['movieId'].unique())    \n",
    "    baseline_catalog_train_coverages.append(calculate_catalog_coverage(ratings_dictionary, N))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.2 Neighborhood-Based Collaborative Filtering <a class=\"anchor\" id=\"3-2\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2.1 Tuning Hyperparameters <a class=\"anchor\" id=\"3-2-1\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [],
   "source": [
    "# A reader is still needed but only the rating_scale param is requiered.\n",
    "reader = Reader(rating_scale=(1, 5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "parameter 5\n",
      "Computing the cosine similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "RMSE: 1.0633\n",
      "Computing the cosine similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "RMSE: 1.0419\n",
      "Computing the cosine similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "RMSE: 1.0538\n",
      "RMSE: 1.0507\n",
      "parameter 10\n",
      "Computing the cosine similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "RMSE: 1.0585\n",
      "Computing the cosine similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "RMSE: 1.0496\n",
      "Computing the cosine similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "RMSE: 1.0500\n",
      "RMSE: 1.0535\n",
      "parameter 25\n",
      "Computing the cosine similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "RMSE: 1.0420\n",
      "Computing the cosine similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "RMSE: 1.0442\n",
      "Computing the cosine similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "RMSE: 1.0695\n",
      "RMSE: 1.0485\n",
      "percentage: 0.001, k: 25 , total time: 0:00:01.888176\n",
      "\n",
      "\n",
      "parameter 5\n",
      "Computing the cosine similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "RMSE: 1.0456\n",
      "Computing the cosine similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "RMSE: 1.0303\n",
      "Computing the cosine similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "RMSE: 1.0332\n",
      "RMSE: 1.0357\n",
      "parameter 10\n",
      "Computing the cosine similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "RMSE: 1.0385\n",
      "Computing the cosine similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "RMSE: 1.0352\n",
      "Computing the cosine similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "RMSE: 1.0461\n",
      "RMSE: 1.0335\n",
      "parameter 25\n",
      "Computing the cosine similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "RMSE: 1.0306\n",
      "Computing the cosine similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "RMSE: 1.0424\n",
      "Computing the cosine similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "RMSE: 1.0392\n",
      "RMSE: 1.0302\n",
      "percentage: 0.001, k: 25 , total time: 0:00:08.149369\n",
      "\n",
      "\n",
      "parameter 5\n",
      "Computing the cosine similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "RMSE: 1.0256\n",
      "Computing the cosine similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "RMSE: 1.0333\n",
      "Computing the cosine similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "RMSE: 1.0252\n",
      "RMSE: 1.0249\n",
      "parameter 10\n",
      "Computing the cosine similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "RMSE: 1.0246\n",
      "Computing the cosine similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "RMSE: 1.0319\n",
      "Computing the cosine similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "RMSE: 1.0254\n",
      "RMSE: 1.0240\n",
      "parameter 25\n",
      "Computing the cosine similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "RMSE: 1.0243\n",
      "Computing the cosine similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "RMSE: 1.0235\n",
      "Computing the cosine similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "RMSE: 1.0256\n",
      "RMSE: 1.0222\n",
      "percentage: 0.001, k: 25 , total time: 0:00:19.768622\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "def mean(l):\n",
    "    return sum(l) / len(l)\n",
    "\n",
    "kf = KFold(n_splits=3)\n",
    "possibleK = [5,10,25]\n",
    "\n",
    "knn_rmse_test = []\n",
    "knn_rmse_train = []\n",
    "\n",
    "for i in range(len(percentages)):\n",
    "    sampled_df = baseline_training_dfs[i]\n",
    "    data = Dataset.load_from_df(sampled_df[['userId', 'movieId', 'rating']], reader)\n",
    "    \n",
    "    knn_rmse_all_test = []\n",
    "    knn_rmse_all_train = []\n",
    "    for k in possibleK:\n",
    "        start = datetime.datetime.now()\n",
    "        print('parameter', k)\n",
    "    \n",
    "        rmses_test = []\n",
    "        rmses_train = []\n",
    "        algo = KNNWithMeans(k=k, sim_options={'name': 'cosine', 'user_based': False})\n",
    "        for trainset, testset in kf.split(data):\n",
    "            algo.fit(trainset)\n",
    "            predictions = algo.test(testset)\n",
    "            rmse_train = accuracy.rmse(predictions)\n",
    "            rmses_train.append(rmse_train)\n",
    "            \n",
    "        knn_rmse_all_train.append(mean(rmses_train))\n",
    "    \n",
    "        test_df = baseline_test_dfs[i]\n",
    "        test_df = Dataset.load_from_df(test_df[['userId', 'movieId', 'rating']], reader)\n",
    "        predictions_test = algo.test(test_df.build_full_trainset().build_testset())\n",
    "        rmse_test = accuracy.rmse(predictions_test)\n",
    "        knn_rmse_all_test.append(rmse_test)\n",
    "            \n",
    "        end = datetime.datetime.now()\n",
    "    \n",
    "    print('percentage: {}, k: {} , total time: {}'.format(percentage, k, str(end-start)))\n",
    "\n",
    "    knn_rmse_test.append(knn_rmse_all_test)\n",
    "    knn_rmse_train.append(knn_rmse_all_train)\n",
    "    \n",
    "    print('\\n')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When we ran cross validation on each sample size, the time it took increased as the sample size increased. So for the 0.01% sample, it took around 1.8 seconds. Then for the 0.05% it took about 8 seconds, and for the 0.1% sample it took about 20 seconds. So the time it took increased proportionally as the size of the sample increased."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For k-nearest neighbor item-based collaborative filtering, we explored our model to tune the hyper parameter k (number of similar items to use for rating prediction), and train/test our model based on three different sample sizes. While the RMSE values for each hyper parameter are shown below, we observed that the neighborhood of size 25 had the lowest RMSE. Furthermore, while it is reasonable to assume that the larger the dataset, the better the RMSE due to more information being fed into the model, our assumption was confirmed as we had the lowest RMSE for the largest sample data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 340,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "\n",
    "for knn_rmse in knn_rmse_test:\n",
    "    plt.plot(possibleK, knn_rmse, marker='o')\n",
    "\n",
    "plt.xlabel('size of k')\n",
    "plt.ylabel('RMSE')\n",
    "plt.title('RMSE Test vs k by Sample Size')\n",
    "plt.legend(['{}% Sample'.format(p*100) for p in percentages])\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2.2 Accuracy of KNN Means Model <a class=\"anchor\" id=\"3-2-2\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### RMSE\n",
    "The training and test RMSE for each sample size are shown below.\n",
    "The training RMSEs are similar to the test RMSEs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 322,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1.0485114418079646, 1.030237787733422, 1.0221884957312877]"
      ]
     },
     "execution_count": 322,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Test RMSE\n",
    "[min(rmse) for rmse in knn_rmse_test]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 323,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1.0518893325021512, 1.036380478568988, 1.02445603362914]"
      ]
     },
     "execution_count": 323,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Train RMSE\n",
    "[min(rmse) for rmse in knn_rmse_train]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### NDCG"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 286,
   "metadata": {},
   "outputs": [],
   "source": [
    "knn_test_ndcgs = []\n",
    "knn_train_ndcgs = []\n",
    "for i in range(len(knn_predictions_dfs)):\n",
    "    knn_test_ndcgs.append(ndcg_score(knn_predictions_dfs[i]))\n",
    "    knn_train_ndcgs.append(ndcg_score(knn_predictions_train_dfs[i]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The test and training NDCG for each sample size are below"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 287,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([0.9978727696881597, 0.9910469106317076, 0.9846030842377707],\n",
       " [0.997193243792226, 0.9828317606370831, 0.9704348594323414])"
      ]
     },
     "execution_count": 287,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "knn_test_ndcgs, knn_train_ndcgs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2.3 Coverage of KNN Means Model <a class=\"anchor\" id=\"3-2-3\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_knn_df(predictions_test):\n",
    "    knn_predictions_list = []\n",
    "    for i in range(len(predictions_test)):\n",
    "        # userId, movieId, rating, predicted\n",
    "        knn_predictions_list.append(list(predictions_test[i][:-1]))\n",
    "        \n",
    "    return pd.DataFrame(knn_predictions_list, columns = ['userId', 'movieId', 'rating', 'predicted'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 271,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing the cosine similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "Computing the cosine similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "Computing the cosine similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "Item Coverage (0.001% sample): 2.2%\n",
      "Item Coverage (0.005% sample): 1.9e+01%\n",
      "Item Coverage (0.01% sample): 2.5e+01%\n",
      "User Coverage: (0.001% sample): 0.14%\n",
      "User Coverage: (0.005% sample): 2.2%\n",
      "User Coverage: (0.01% sample): 5.5%\n",
      "Item Coverage (0.001% sample): 3.4e+01%\n",
      "Item Coverage (0.005% sample): 5.4e+01%\n",
      "Item Coverage (0.01% sample): 5.9e+01%\n",
      "User Coverage: (0.001% sample): 6.2%\n",
      "User Coverage: (0.005% sample): 3.2e+01%\n",
      "User Coverage: (0.01% sample): 4.9e+01%\n"
     ]
    }
   ],
   "source": [
    "knn_predictions_dfs = []\n",
    "knn_predictions_train_dfs = []\n",
    "spark_knn_predicted_dfs = []\n",
    "spark_knn_predicted_train_dfs = []\n",
    "\n",
    "best_ks = [25, 25, 25]\n",
    "for i in range(len(baseline_training_dfs)):\n",
    "    train_df = baseline_training_dfs[i]\n",
    "    train_df = Dataset.load_from_df(train_df[['userId', 'movieId', 'rating']], reader)\n",
    "    algo = KNNWithMeans(k=best_ks[i], sim_options={'name': 'cosine', 'user_based': False})\n",
    "    algo.fit(train_df.build_full_trainset())\n",
    "    test_df = baseline_test_dfs[i]\n",
    "    test_df = Dataset.load_from_df(test_df[['userId', 'movieId', 'rating']], reader)\n",
    "    predictions_test = algo.test(test_df.build_full_trainset().build_testset())\n",
    "    \n",
    "    # for test set\n",
    "    knn_predictions_df = create_knn_df(predictions_test)\n",
    "    knn_predictions_dfs.append(knn_predictions_df)\n",
    "    test_df = knn_predictions_df\n",
    "    new_sample_df = test_df.iloc[:, test_df.columns != 'predicted']\n",
    "    spark_knn_predicted_df = spark.createDataFrame(new_sample_df, schema=data_schema)\n",
    "    spark_knn_predicted_dfs.append(spark_knn_predicted_df)\n",
    "    \n",
    "    # for train set\n",
    "    predictions_train = algo.test(train_df.build_full_trainset().build_testset())\n",
    "    knn_predictions_train_df = create_knn_df(predictions_train)\n",
    "    knn_predictions_train_dfs.append(knn_predictions_train_df)\n",
    "    new_sample_df = knn_predictions_train_df.iloc[:, knn_predictions_train_df.columns != 'predicted']\n",
    "    spark_knn_predicted_train_df = spark.createDataFrame(new_sample_df, schema=data_schema)\n",
    "    spark_knn_predicted_train_dfs.append(spark_knn_predicted_train_df)\n",
    "    \n",
    "knn_item_coverages_test = get_item_coverage(spark_knn_predicted_dfs)\n",
    "knn_user_coverages_test = get_user_coverage(spark_knn_predicted_dfs)\n",
    "\n",
    "knn_item_coverages_train = get_item_coverage(spark_knn_predicted_train_dfs)\n",
    "knn_user_coverages_train = get_user_coverage(spark_knn_predicted_train_dfs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Item coverage**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 324,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([2.2411953041622197, 18.60885275519422, 24.809413324494532],\n",
       " [33.778014941302025, 54.245709123757905, 59.46304275770633])"
      ]
     },
     "execution_count": 324,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "knn_item_coverages_test, knn_item_coverages_train"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**User Coverage**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 273,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([33.778014941302025, 54.245709123757905, 59.46304275770633],\n",
       " [6.159052453468697, 32.18201754385965, 49.35579781962339])"
      ]
     },
     "execution_count": 273,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "knn_user_coverages_test, knn_user_coverages_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 303,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Catalog Coverage: 99.94739610731193%\n",
      "Catalog Coverage: 98.74476987447699%\n",
      "Catalog Coverage: 98.30885625278148%\n",
      "Catalog Coverage: 86.73059479072178%\n",
      "Catalog Coverage: 94.4639571834755%\n",
      "Catalog Coverage: 78.23663018790006%\n"
     ]
    }
   ],
   "source": [
    "knn_catalog_coverages = []\n",
    "knn_catalog_coverages_train = []\n",
    "for knn_predictions_df, knn_predictions_train_df in zip(knn_predictions_dfs, knn_predictions_train_dfs):\n",
    "    knn_predictions_df.sort_values(by=['userId', 'predicted'])\n",
    "    ratings_dictionary = dict(knn_predictions_df.set_index('userId').groupby(level = 0).apply(lambda x : x.to_dict(orient= 'records')))\n",
    "    N = len(knn_predictions_df['movieId'].unique())    \n",
    "    knn_catalog_coverages.append(calculate_catalog_coverage(ratings_dictionary, N))\n",
    "    \n",
    "    knn_predictions_train_df.sort_values(by=['userId', 'predicted'])\n",
    "    ratings_dictionary = dict(knn_predictions_train_df.set_index('userId').groupby(level = 0).apply(lambda x : x.to_dict(orient= 'records')))\n",
    "    N = len(knn_predictions_train_df['movieId'].unique())    \n",
    "    knn_catalog_coverages_train.append(calculate_catalog_coverage(ratings_dictionary, N))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Catalog Coverage**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 304,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([99.94739610731193, 98.30885625278148, 94.4639571834755],\n",
       " [98.74476987447699, 86.73059479072178, 78.23663018790006])"
      ]
     },
     "execution_count": 304,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "knn_catalog_coverages, knn_catalog_coverages_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 357,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calculate_catalog_coverage(ratingsDict, N, k=3, pred_col_name='predicted'):\n",
    "    '''\n",
    "    k: top k movies\n",
    "    N: total number of movies\n",
    "    '''\n",
    "    \n",
    "    recList = []\n",
    "    for keys in ratingsDict.keys():\n",
    "        \n",
    "        if k >= len(ratingsDict[keys]):\n",
    "            for row in ratingsDict[keys]:\n",
    "                recList.append(row['movieId'])\n",
    "        else:\n",
    "            for index, item in enumerate(sorted(ratingsDict[keys], key=lambda x: -x[pred_col_name])):\n",
    "                if index+1 <= k:\n",
    "                    recList.append(item['movieId'])\n",
    "                else:\n",
    "                    pass\n",
    "\n",
    "    recommended_set = set(recList)\n",
    "\n",
    "    coverage = (len(recommended_set) / N) * 100\n",
    "    print('Catalog Coverage: {}%'.format(coverage))\n",
    "    return coverage"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.3 Model-Based Collaborative Filtering: Matrix Factorization Using PySpark's Alternating Least Squares (ALS) <a class=\"anchor\" id=\"3-3\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use the Alternating Least Square (ALS) model in PySpark with the same samples we used for the baseline model and the neighborhood-based model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Spark Session\n",
    "spark =SparkSession.builder.appName('ALS').getOrCreate()\n",
    "sc = spark.sparkContext\n",
    "sqlContext = SQLContext(sc)\n",
    "\n",
    "# Load ratings data into PySpark dataframe\n",
    "data_schema = StructType([\n",
    "    StructField('userId',IntegerType(), False),\n",
    "    StructField('movieId',IntegerType(), False),\n",
    "    StructField('rating',FloatType(), False)])\n",
    "\n",
    "movie_ratings = spark.read.csv('ratings.csv', \n",
    "                               header=True, schema=data_schema).cache()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We convert our samples (Pandas dataframes) into Spark dataframes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create Spark DF from Pandas DF\n",
    "all_sample_spark_dfs = []\n",
    "for sample_df in all_sample_dfs:\n",
    "    new_sample_df = sample_df.iloc[:, sample_df.columns != 'timestamp']\n",
    "    spark_sample_df = spark.createDataFrame(new_sample_df, schema=data_schema)\n",
    "    all_sample_spark_dfs.append(spark_sample_df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "# ALS model without tuning parameters\n",
    "als = ALS(maxIter=5, userCol=\"userId\", itemCol=\"movieId\", ratingCol=\"rating\",\n",
    "          coldStartStrategy=\"drop\", nonnegative= True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.3.1 Tuning Hyperparameters <a class=\"anchor\" id=\"3-3-1\"></a>\n",
    "\n",
    "There are 3 hyperparameters to tune. First, we will tune `rank`, then `regParam`, and then `maxIter`. We use RSME to tune our parameters and cross validation with 3 folds. We do this on our traning set.\n",
    "\n",
    "_Cross validation set up_ : The input data was split into train and test set ( 80-20). The train set is then used for cross validation. 3-fold cross validation is implemented to tune the hyper parameters by splitting into training and validation sets for each fold.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "def tune_parameter(cv_func, paramGrid, percentages, all_training_sets):\n",
    "    \n",
    "    training_times = []\n",
    "    cvModels = []\n",
    "    results = []\n",
    "\n",
    "    for i in range(len(percentages)):\n",
    "        start_1 = datetime.datetime.now()\n",
    "        cvModel = cv_func.fit(all_training_sets[i])\n",
    "        end_1 = datetime.datetime.now()\n",
    "\n",
    "        cvModels.append(cvModel)\n",
    "        training_times.append(str(end_1 - start_1))\n",
    "        results.append(list(zip(cvModel.avgMetrics, paramGrid)))\n",
    "\n",
    "        print(str(end_1 - start_1))\n",
    "    \n",
    "    return training_times, cvModels, results\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 336,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_rmse_vs_param(cvModels, param_list, xlabel):\n",
    "    real_percetanges = [ percent * 100 for percent in percentages]\n",
    "    plt.figure(figsize=(10, 6))\n",
    "    for cvModel in cvModels: \n",
    "        plt.plot(param_list, cvModel.avgMetrics, marker='o')\n",
    "\n",
    "    plt.xlabel(xlabel)\n",
    "    plt.ylabel('RMSE')\n",
    "    plt.title('RMSE vs {} by Sample Size'.format(xlabel))\n",
    "    plt.legend(['{}% Sample'.format(p) for p in real_percetanges])\n",
    "    plt.grid(True)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "####  Tuning Rank"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The rank are the latent factors, so we must tune this. We choose values 5, 10, and 20 to use to tune."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 343,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0:02:00.794607\n",
      "0:02:24.804511\n",
      "0:03:05.277963\n"
     ]
    }
   ],
   "source": [
    "# tuning rank\n",
    "rank_list = [5, 10, 20]\n",
    "paramGrid = (ParamGridBuilder().addGrid(als.rank, rank_list).build())\n",
    "\n",
    "crossval = CrossValidator(estimator=als,\n",
    "                          estimatorParamMaps=paramGrid,\n",
    "                          evaluator=RegressionEvaluator(metricName=\"rmse\",\n",
    "                                                        labelCol=\"rating\"),\n",
    "                          numFolds=3)\n",
    "\n",
    "training_times, cvModels, results = tune_parameter(crossval, paramGrid, percentages, all_training_sets)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As sample size increased, it took longer to tune rank. Since our samples were 0.01%, 0.05%, and 0.1% for each increase in sample it took about 30 seconds longer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 337,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_rmse_vs_param(cvModels, rank_list, 'Rank')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We get the rank to "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2.5208710351886188, 2.406703436515813, 2.4000997089692673]\n",
      "[1.8150041302424498, 1.8027648590484402, 1.7171846553955805]\n",
      "[1.5620705118289568, 1.5696040226692172, 1.5252708665364574]\n"
     ]
    }
   ],
   "source": [
    "for cv in cvModels:\n",
    "    print(cv.avgMetrics)\n",
    "best_rank=20"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Tuning Regularization Parameter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the best rank we just found, we next tune the regularization parameter. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0:01:36.267541\n",
      "0:02:05.043913\n",
      "0:02:47.549340\n"
     ]
    }
   ],
   "source": [
    "reg_list = [0.001, 0.05, 0.1, 0.2]\n",
    "\n",
    "# Use the best rank found above\n",
    "als= ALS(maxIter=5, rank=best_rank, userCol=\"userId\", itemCol=\"movieId\", ratingCol=\"rating\",\n",
    "          coldStartStrategy=\"drop\", nonnegative= True)\n",
    "\n",
    "paramGrid_2 = ParamGridBuilder().addGrid(als.regParam, reg_list).build()\n",
    "\n",
    "crossval_2 = CrossValidator(estimator=als,\n",
    "                          estimatorParamMaps=paramGrid_2,\n",
    "                          evaluator=RegressionEvaluator(metricName=\"rmse\",\n",
    "                                                        labelCol=\"rating\"),\n",
    "                          numFolds=3)\n",
    "\n",
    "\n",
    "training_times2, cvModels2, results2 = tune_parameter(crossval_2, paramGrid_2, percentages, all_training_sets)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similar to as what we saw with tuning the rank parameter, as the sample size increased, the time it took did as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 338,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_rmse_vs_param(cvModels2, reg_list, 'regParam')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2.6062633832232525, 2.376728250989886, 2.4000997089692673, 2.4437349470727225]\n",
      "[2.7371086361759316, 1.741988486087179, 1.7171846553955805, 1.6524823516106966]\n",
      "[2.91276271711076, 1.6213390509996386, 1.5252708665364574, 1.398496263249813]\n"
     ]
    }
   ],
   "source": [
    "for cv in cvModels2:\n",
    "    print(cv.avgMetrics)\n",
    "best_reg = 0.2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Tuning Number of Iterations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0:01:27.539845\n",
      "0:02:29.413635\n",
      "0:03:16.695436\n"
     ]
    }
   ],
   "source": [
    "iter_list = list(range(5,25,5))\n",
    "\n",
    "# Use the best rank and best regParam found above\n",
    "als= ALS(rank=best_rank, regParam=best_reg, userCol=\"userId\", itemCol=\"movieId\", ratingCol=\"rating\",\n",
    "          coldStartStrategy=\"drop\", nonnegative= True)\n",
    "                 \n",
    "paramGrid_3 = ParamGridBuilder().addGrid(als.maxIter, iter_list).build()\n",
    "\n",
    "crossval_3 = CrossValidator(estimator=als,\n",
    "                          estimatorParamMaps=paramGrid_2,\n",
    "                          evaluator=RegressionEvaluator(metricName=\"rmse\",\n",
    "                                                        labelCol=\"rating\"),\n",
    "                          numFolds=3)\n",
    "\n",
    "\n",
    "training_times3, cvModels3, results3 = tune_parameter(crossval_3, paramGrid_3, percentages, all_training_sets)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 339,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_rmse_vs_param(cvModels3, iter_list, 'maxIter')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2.4305742906384324, 2.4305742906384324, 2.4305742906384324, 2.4305742906384324]\n",
      "[1.4810357844270297, 1.4810357844270297, 1.4810357844270297, 1.4810357844270297]\n",
      "[1.295138360350374, 1.295138360350374, 1.295138360350374, 1.295138360350374]\n"
     ]
    }
   ],
   "source": [
    "for cv in cvModels3:\n",
    "    print(cv.avgMetrics)\n",
    "best_iter = 10 # default"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.3.2 Accuracy of ALS Model <a class=\"anchor\" id=\"3-3-2\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The primary accuracy metric chosen was RMSE. For matrix factorisation error metrics is a good baseline to calculate how well our model is predicting compared to the true value. However for our business case RMSE can suffer from long tail problem ie, average error will focus primarily on popular items and unobserved items are factored fewer times.\n",
    "For checking the accuracy in the test dataset a secondary ranking metric is used. NDCG was implemented and this is a utility based metric that takes into account both the ground truth relevance of an item and its position in the ranking list. NDCG is useful when we want the  recommender system to return some relevant results, and order is important. We want to make sure our top n predictions for the user is as accurate as possible and hence pay great importance to the order of the top recommended movies. Hence higher the accuracy, more perfect the recommendations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### RMSE \n",
    "\n",
    "For training RMSE we have:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2.4305742906384324, 1.4810357844270297, 1.295138360350374]"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_als_rmses_train = []\n",
    "for cv in cvModels3:\n",
    "    best_als_rmses_train.append(min(cv.avgMetrics))\n",
    "\n",
    "best_als_rmses_train"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the test RMSE, we used the fitted model to find the predictions and calculate RMSE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "best_als_models = []\n",
    "best_predictions_test = []\n",
    "best_predictions_train = []\n",
    "best_als_rmses = []\n",
    "\n",
    "evaluator = RegressionEvaluator(metricName=\"rmse\", labelCol=\"rating\",\n",
    "                                predictionCol=\"prediction\")\n",
    "\n",
    "for i in range(len(percentages)):\n",
    "    best_als= ALS(rank=best_rank, regParam=best_reg, maxIter=best_iter, userCol=\"userId\", \n",
    "                  itemCol=\"movieId\", ratingCol=\"rating\", coldStartStrategy=\"drop\", nonnegative= True)\n",
    "\n",
    "    best_als_model = als.fit(all_training_sets[i])\n",
    "    als_predictions_test = best_als_model.transform(all_test_sets[i])\n",
    "    als_predictions_train = best_als_model.transform(all_training_sets[i])\n",
    "    rmse = evaluator.evaluate(als_predictions_test)\n",
    "        \n",
    "    best_als_models.append(best_als_model)\n",
    "    best_predictions_test.append(als_predictions_test)\n",
    "    best_predictions_train.append(als_predictions_train)\n",
    "    best_als_rmses.append(rmse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2.240793381700844, 1.3432920600923228, 1.2190040017124122]"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_als_rmses"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### NDCG"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 294,
   "metadata": {},
   "outputs": [],
   "source": [
    "# convert pyspark df to pandas df\n",
    "\n",
    "als_predicted_test_dfs = []  # pandas DF\n",
    "als_predicted_train_dfs = []  # pandas DF\n",
    "als_test_ndcgs = []\n",
    "als_train_ndcgs = []\n",
    "\n",
    "for (best_prediction_test, best_prediction_train) in zip(best_predictions_test, best_predictions_train):\n",
    "    # convert test predictions to pandas df\n",
    "    als_predicted_test_df = best_prediction_test.toPandas()\n",
    "    als_predicted_test_dfs.append(als_predicted_test_df)\n",
    "    \n",
    "    # convert train predictions to pandas df\n",
    "    als_predicted_train_df = best_prediction_train.toPandas()\n",
    "    als_predicted_train_dfs.append(als_predicted_train_df)\n",
    "    \n",
    "    # ndcg calculation for test predictions\n",
    "    als_ndcg = ndcg_score(als_predicted_test_df, pred_col_name='prediction')\n",
    "    als_test_ndcgs.append(als_ndcg)\n",
    "    \n",
    "    # ndcg calculation for train predictions\n",
    "    als_ndcg_train = ndcg_score(als_predicted_train_df, pred_col_name='prediction')\n",
    "    als_train_ndcgs.append(als_ndcg_train)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first set of NDCG values are the test values (1 for each sample size). The second set of NDCG values are the train values (1 for each sample size)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 295,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([0.997590513711344, 0.9875547953500886, 0.9818723611854507],\n",
       " [0.999983875298656, 0.9996355651277133, 0.998614716431413])"
      ]
     },
     "execution_count": 295,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "als_test_ndcgs, als_train_ndcgs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.3.3 Coverage of ALS Model <a class=\"anchor\" id=\"3-3-3\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_item_coverage(best_predictions_test, k=5):\n",
    "    als_item_coverages_test = []\n",
    "    for i in range(len(best_predictions_test)):\n",
    "        prediction = best_predictions_test[i]\n",
    "        percentage = percentages[i]\n",
    "        predictions_grouped_by_movieIds = prediction.filter(prediction['rating'] >= 3.0).groupby(['movieId'])\n",
    "        pred_df = predictions_grouped_by_movieIds.agg(sql_func.count(col('userId')))\n",
    "        pred_df2 = pred_df.filter(pred_df['count(userId)'] >= k)\n",
    "        n_movie = pred_df2.count()\n",
    "\n",
    "        potential_recommended_movies = all_test_sets[i].select(\"movieId\").distinct()\n",
    "        N_movie = potential_recommended_movies.count()\n",
    "\n",
    "        coverage = (n_movie/N_movie) * 100\n",
    "        als_item_coverages_test.append(coverage)\n",
    "        print('Item Coverage ({0:.2}% sample): {1:.2}%'.format(percentage, coverage))\n",
    "    \n",
    "    return als_item_coverages_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Item Coverage (0.001% sample): 0.0%\n",
      "Item Coverage (0.005% sample): 9.6%\n",
      "Item Coverage (0.01% sample): 2.1e+01%\n"
     ]
    }
   ],
   "source": [
    "als_item_coverages_test = get_item_coverage(best_predictions_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Item Coverage (0.001% sample): 3.5e+01%\n",
      "Item Coverage (0.005% sample): 5.5e+01%\n",
      "Item Coverage (0.01% sample): 5.9e+01%\n"
     ]
    }
   ],
   "source": [
    "als_item_coverages_train = get_item_coverage(best_predictions_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_user_coverage(best_predictions_test, k=3):\n",
    "    als_user_coverages_test = []\n",
    "    for i in range(len(best_predictions_test)):\n",
    "        prediction = best_predictions_test[i]\n",
    "        percentage = percentages[i]\n",
    "        predictions_grouped_by_userIds = prediction.filter(prediction['rating'] >= 3.0).groupby(['userId'])\n",
    "        pred_df = predictions_grouped_by_userIds.agg(sql_func.count(col('movieId')))\n",
    "        pred_df2 = pred_df.filter(pred_df['count(movieId)'] >= k)\n",
    "        n_user = pred_df2.count()\n",
    "\n",
    "        potential_recommended_users = all_test_sets[i].select(\"userId\").distinct()\n",
    "        N_user = potential_recommended_users.count()\n",
    "\n",
    "        coverage = (n_user/N_user) * 100\n",
    "        als_user_coverages_test.append(coverage)\n",
    "        print('User Coverage: ({0:.4}% sample): {1:.2}%'.format(percentage, coverage))\n",
    "    \n",
    "    return als_user_coverages_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "User Coverage: (0.001% sample): 0.034%\n",
      "User Coverage: (0.005% sample): 1.8%\n",
      "User Coverage: (0.01% sample): 5.1%\n"
     ]
    }
   ],
   "source": [
    "als_user_coverages_test = get_user_coverage(best_predictions_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "User Coverage: (0.001% sample): 5.7%\n",
      "User Coverage: (0.005% sample): 3.2e+01%\n",
      "User Coverage: (0.01% sample): 5e+01%\n"
     ]
    }
   ],
   "source": [
    "als_user_coverages_train = get_user_coverage(best_predictions_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 309,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Catalog Coverage: 100.0%\n",
      "Catalog Coverage: 98.72235872235873%\n",
      "Catalog Coverage: 98.6784140969163%\n",
      "Catalog Coverage: 88.15043791859866%\n",
      "Catalog Coverage: 95.13766842413591%\n",
      "Catalog Coverage: 79.9916675346318%\n"
     ]
    }
   ],
   "source": [
    "als_catalog_coverages = []\n",
    "als_catalog_coverages_train = []\n",
    "for als_predicted_test_df, als_predicted_train_df in zip(als_predicted_test_dfs, als_predicted_train_dfs):\n",
    "    als_predicted_test_df.sort_values(by=['userId', 'rating'])\n",
    "    ratings_dictionary = dict(als_predicted_test_df.set_index('userId').groupby(level = 0).apply(lambda x : x.to_dict(orient= 'records')))\n",
    "    N = len(als_predicted_test_df['movieId'].unique())    \n",
    "    als_catalog_coverages.append(calculate_catalog_coverage(ratings_dictionary, N, pred_col_name='rating'))\n",
    "    \n",
    "    als_predicted_train_df.sort_values(by=['userId', 'rating'])\n",
    "    ratings_dictionary = dict(als_predicted_train_df.set_index('userId').groupby(level = 0).apply(lambda x : x.to_dict(orient= 'records')))\n",
    "    N = len(als_predicted_train_df['movieId'].unique())    \n",
    "    als_catalog_coverages_train.append(calculate_catalog_coverage(ratings_dictionary, N, pred_col_name='rating'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 310,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([100.0, 98.6784140969163, 95.13766842413591],\n",
       " [98.72235872235873, 88.15043791859866, 79.9916675346318])"
      ]
     },
     "execution_count": 310,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "als_catalog_coverages, als_catalog_coverages_train"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4. Evaluation <a class=\"anchor\" id=\"4\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.1 Accuracy <a class=\"anchor\" id=\"4-1\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.1.1 RMSE <a class=\"anchor\" id=\"4-1-1\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 331,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "baseline_rmses, baseline_rmses_train\n",
    "best_als_rmses, best_als_rmses_train\n",
    "\n",
    "plt.figure(figsize=(10, 6))\n",
    "\n",
    "real_percetanges = [ percent * 100 for percent in percentages]\n",
    "plt.plot(real_percetanges, baseline_rmses, marker='o')\n",
    "plt.plot(real_percetanges, [min(rmse)  for rmse in knn_rmse_test], marker='o')\n",
    "plt.plot(real_percetanges, best_als_rmses, marker='o')\n",
    "\n",
    "plt.xlabel('sampling percentage (%)')\n",
    "plt.ylabel('RMSE')\n",
    "plt.title('RMSE Test vs Sample Size')\n",
    "plt.legend(['Baseline Model', 'KNN', 'ALS'])\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For each model, as the sample size increased, the RMSE decreased. Therefore, larger data would improve the performance of our models. It is interesting to note that the matrix factorization has the highest RMSE compared to our baseline model and KNN item-based collaborative filtering. In general, the KNN item-based CF showed the best performance with the lowest RMSE scores. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.1.2 NDCG <a class=\"anchor\" id=\"4-1-2\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 332,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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aJlpiKFOmDNeuXePq1ausWLGCq1evsmvXLpycnMicOTMhISHkzJmTXbt2sWLFCvr370+1atWoW7cu+fLlY8uWLa/cl5OT0+M3My0WC2Fh1jGehw8fsmXLFhImTPjSNtKkSYOTkxNr1qxhzJgxL32xwhjz3LdBjTGMGzeO6tWrP1EeEBDwClfzauz5jNsOIIeIZBERZ6AR8GfECiKSQkQexdAfmG4rt9imTBGRgkBBYDVwE/AQkZy2c6oC0beE8Wu6+DB5pOV3jAuEBMZwNEoppdSL9a6ei4ROT46sJXSy0Lt6rmjr4+jRo4SHh5M8eXICAwNJlSoVTk5O+Pr6cubMGQAuXryIq6srzZo1o1evXuzevZtcuXJx9erVx4lbaGgohw4dilIM1apVY/z48Y8/792794X1Bw8ezPDhw58YdfTw8CBp0qRs2LABgNmzZ1OuXDmSJEmCh4cHGzduBGDu3LmPz6levTqTJk0iNDQUgOPHj3Pnzp0oXcPz2G3EzRgTJiJdgFWABZhujDkkIoOBncaYPwFPYKiIGKxTpZ1tpzsBG2wZ7W2gmTEmDEBE2gG/ichDrIlcG3tdw8tMdW5Gn9CJuMr/T5eGGQcScY8Howvh9P4ApFhrsOgGFUoppWLfh0XSATBi1TEu3rrHe0kS0rt6rsflUXXv3j0KFy4MWEedZs6cicVioWnTptSuXZvixYtTuHBhcufODcCBAwfo3bs3Dg4OODk5MWnSJJydnVm8eDHdunUjMDCQsLAwevToQb58Lx5FjMzYsWPp3LkzBQsWJCwsjIoVKzJ58uTn1i9btmyk5TNnzqRDhw7cvXuXrFmzMnbsWABmzJhBmzZtcHV1fWJ0rW3btgQEBFC0aFGMMaRMmZIlS5a8dvwvIsZEPt/9LilevLh5+qHE6LBkzwUWrfmCy8l2ctVRSBlmSHmtGCakDD3CZ1HGcphg96y4+gzFIVd1iOMLJOrzNXGb3r+4T+9h3GevZ9zy5MkTrW2qyEXnllePRHb/RGSXMaZ4ZPV154Q34OSxl6NpDnHFyQEjwhUnB46/d5gmTdNztvYCvkjwBVcC7+KwoCFXJngTemFfbIeslFJKqThME7c3MGb3GELN/SfKQs19JuwbR8OSmfi2bx8O1V3FpITtcLp6EMvPlTgxtRUhN6JvvRyllFJKxR+auL2B/+5E/vboo3KLg1C7SGY69BnB/o98WZbwQzKd+5OHY4uyY2Y/goNvx2S4SimllIrjNHF7A2kSpYm03NXRlfCH4Y8/iwiVCuXkgz4zOPjhag4mLE6JfydxZ2QhVs4dza07ITEVslJKKaXiME3c3kD3ot1xsbg8UWYRC3fC7tB1XVeCHjy5QrKIULRIcUr2Xc7xmou4lyAl3icGceGH0sxZMJcrtzWBU0oppdTzaeL2Bnyy+jCo7CDSJkqLIKRNlJbvyn/HV6W/YsvFLTRb0Yyzt89Gem7OktXJ3HcrFyuP5T2nYJod7cS+kbUYvXAF527cjeErUUoppVRcoInbG/LJ6sPq+qvZ33I/q+uvxierDx/n+pgp1aZwI+QGjZc3ZuulrZGf7ODAexVbkrTvAW6W7kdFx4N0OdyMf0a35st56zl55dk9zZRSSqm3jZub2+PfV6xYQY4cOTh79iyDBg3C1dWVK1euRFpXRPj8888ffx45ciSDBg2KkZjjKk3c7KREmhLM85lHKtdUdFjTgflH5/PcNfOcEpLUuz8JPttHaMEmtLSsptexRswb25/Os7Zy4LzuwqCUUiqa7F8Eo/PDoCTWf/cviram165dS9euXVm5ciUZM2YEIEWKFPz444+R1k+QIAG///47165di7YY3nWauNlRBvcMzKk5hwrpKvD9tu/5duu3hIaHPv8E99S41huPQ8eNJMpcgoGOs+lzuiXjJ46mxbRtbDt9PeaCV0op9e7ZvwiWdYPAc4Cx/rusW7Qkbxs2bKBdu3YsX76cbNmyPS5v06YNCxcu5MaNG8+c4+joSPv27Rk9evQb9x9f6F5MdpbIKRFjKo9h3J5xTD0wlX8D/2WU5yiSuiR9/kmp8+HUagmc/If0qwbw07XR7Dq3iq9/bkLCTMXo5JUdz5wpn7vJrVJKqXjq737w34HnHz+/A8KfXH+U0HuwtAvsmhn5OWkKQI1hL+z2/v371KlTBz8/v8fbWj3i5uZGmzZtGDNmDN98880z5z7amqpPnz4v7ENZ6YhbDHAQB7oX7c7QCkPZf3U/jZc35sTNEy8+SQRyVMXScTP4jKKo6xX+SvAlba4M44sZK6k1biMrDlwi/OG7v2WZUkqpaPJ00vay8lfk5ORE2bJlmTZtWqTHu3XrxsyZM7l9+9n1SxMnTkyLFi0e7wOqXkxH3GJQray1yOSeie6+3Wm2ohnDKgzDK6PXi0+yOEKJT5ACDWDjKLy3TKSq61bmB9Wh11xvRqZMTsdK2fiwSDqcLJqHK6VUvPaSkTFG57dNkz7FIwO0Xh7lbh0cHFi0aBFVqlTh+++/54svvnjieJIkSWjSpAkTJ06M9PwePXpQtGhRWrduHeUY4gv9Sx/DCqQswHyf+WTxyEJ33+5MPTD1+S8tROSSGKoMQrrswDFvbZqHLmK3R19qh6+l7+K9eI7wY9aWAEJCw1/WklJKqfjq/YHglPDJMqeE1vI35Orqyl9//cXcuXMjHXnr2bMnP/30E2FhYc8cS5YsGR9//PFzR+zU/9PELRakTpSaX7x/wTuLN2N2j6Hfhn6EhL3i4rtJM0H9afDJP7ikzMJnd8eyP80QqrkcZuDSQ5Qf7stk/1MEhbzgJQillFLxU8GPofZY6wgbYv239lhreTRIliwZK1euZMiQISxduvSJYylSpKBu3brcvx/5tOznn3+ub5e+Ap0qjSUuji4MrzCcnElzMmb3GM7ePsuYymNI5Zrq1RrIUAI+WQ2Hl+C25mu+vjWAbtk8GRbelGF/32ei70lalc1M63JZSJrI2b4Xo5RSKu4o+HG0JWqPBAcHP/49Q4YM/PvvvwDUqVPniXqjRo1i1KhRkZ6XOnVq7t7VBehfRkfcYpGI0LZAW8Z4jeFU4Cka/9WYg9cOvk4DkK8udNkBVb8l6bXdDL/cgZ1F/qZqZgtj152k3PB1DPnrMJd1Oy2llFIqztPE7S1QOWNl5tScg5PFiVYrW7H89Gs+IOqYAMp1g257oHgbUhydx4+XWrPD8yA+eZIyY3MAFYb78sUfBzh7Xf/fjFJKKRVXaeL2lsiZNCfzfOaRP0V++m3ox5jdY3hoHr5eI4lSgM9I6LQFMpUl5dbvGXG5LdtqB9KgWDoW7zyP149+fLZwL8cv63ZaSimlVFyjidtbJJlLMn6u+jP1ctRj6oGp9PDtwZ3QO6/fUMpc0GQhtFgKCTxIsaoD393oydbmbrQpl5lVh/6j2uj1tJ+1k33nbkX/hSillFLKLjRxe8s4WZz4uszX9CvZj/Xn19NsRTPOB52PWmNZPeFTf/hgPNw6S7IFtRhwdwRbOmSn+/s52PbvDepM2ETzadvYcur6qy1LopRSSqlYo4nbW0hEaJqnKZOqTOLy3cs0Xt6YHf/tiFpjDhYo2hy67oZKfeHY33hMK8tnzGVTj+L0r5GbI5eCaPzzVupN2sy6o5c1gVNKKaXeUpq4vcXKvFeG+T7zSZIgCe1Xt+fX479GvbEEbuD1BXTdBfnrwab/4fZTcT5NuI6NvSvwbZ18XL59nza/7KTm2I0s23dRt9NSSin1yv744w9EhKNHjwIQEBBA/vz5n6m3detWSpUqReHChcmTJw+DBg2K4UjjNk3c3nKZEmdins88Sr1XisFbBvP9tu8Je/jsqtOvzCMd1J0E7f0gZR5Y0QuXnyvQPPlx/HpV4scGhXgQFk7X+XuoMsqfRTvO8SDsNV+SUEop9dZafno51RZXo+DMglRbXO31VzJ4jvnz51O+fHkWLFjwwnotW7ZkypQp7N27l4MHD/Lxx9G7pty7ThO3OMDd2Z0JlSfQMm9L5h+dT4d/OhB4P/DNGn2vCLT6CxrNg4dhMK8BTvPqUS/dLVZ/VolJTYvi6myhz2/78Rzhyy+b/uV+uI7AKaVUXLb89HIGbR7EpTuXMBgu3bnEoM2D3jh5Cw4OZtOmTUybNu2liduVK1dImzYtABaLhbx5875R3/GN7pwQR1gcLPQq0YvsSbMzeMtgmixvwrj3x5HVI2vUGxWB3D6QvSrsnAZ+w+CnCliKNKOG15d4dy2P//GrTPQ9xaBlh3F3hpMOJ2leJhOJXZyi7+KUUkpFi+Hbh3P0xtHnHt9/dT8PHj54oiwkPISBmway+PjiSM/JnSw3fUv2fWG/S5Yswdvbm5w5c5IsWTJ2795NsmTJIq372WefkStXLjw9PfH29qZly5a4uLi85MrUIzriFsd8mP1DplefTnBoME2XN2XD+Q1v3qijM5TuaF3At1RH2DsfxhZB1o/EM4sbizqUYdGnZcic2MKIVccoN2wdI1cd43pw5PvNKaWUejs9nbS9rPxVzZ8/n0aNGgHQqFEj5s+f/9y6AwcOZOfOnVSrVo158+bh7e39Rn3HNxIf3iAsXry42blzZ2yHEa0uBV+im283jt88Ts9iPWmRtwUiEj2NXz8F/3wNR5ZB4nTw/kAo8DF+69eTIkcRJvieZOWh/3BxtNC4ZEbaVcxCWo+E0dO3shs/Pz88PT1jOwz1BvQexn32uIdHjhwhT548r1S32uJqXLpz6ZnytInSsrr+6ij1f/36ddKnT0+qVKkQEcLDwxER/P39qV27NgcPPn8rx7CwMFKmTMnJkydJnjx5lPqPSUFBQbi7u0drm5HdPxHZZYwpHll9HXGLo9K6pWWm90zez/g+I3eO5KtNX/Eg/M3+H9NjybNBwznQagW4pYI/PoWfvfC4dYj86TyY1KwYaz6rSM0CaZm5JYCKP/jS//f9BFyLwmLBSimlYkz3ot1xsTw5LelicaF70e5RbnPx4sW0aNGCM2fOEBAQwLlz58iSJQvnz0e+Buny5csfLzt14sQJLBYLSZIkiXL/8Y1dEzcR8RaRYyJyUkT6RXI8k4isFZH9IuInIukjHBsuIgdtPw0jlIuIfCcix0XkiIh0s+c1vM1cnVwZWWkknQp1YumppXyy6hOu3bsWfR1kLgdt10HdKXDnKkX2fgELmsL1U2RP5c6PHxfCr5cnjUpk5LfdF6j8ox/d5u/h6H+3oy8GpZRS0cYnqw+Dyg4ibaK0CELaRGkZVHYQPll9otzm/PnzqVu37hNl9erV4/vvv+fYsWOkT5/+8c+vv/7K7NmzyZUrF4ULF6Z58+bMnTsXi8XyppcWb9htqlRELMBxoCpwHtgBNDbGHI5Q51fgL2PMTBGpDLQ2xjQXER+gB1ADSAD4A5WNMbdFpDXgBbQyxjwUkVTGmCsviuVdnCp92uqA1QzYOIAkLkkY6zWWPMlfbdj8lT24y+n5vch6fgmEP4CS7aBib3C1Pnx6JSiEaRv+Zc7WM9x5EE6VPKnp7JWNIhmTRm8cKsp0mi3u03sY98X2VKl6M+/6VGlJ4KQx5rQx5gGwAKjzVJ28wFrb774RjucF/I0xYcaYO8A+4NHTix2BwcZYd2B/WdIWX1TLXI1ZNWYB0HJlS1YHRO1ZhedyduVspo+tLzAUbgzbJsPYIrB1EoQ9IJW7C/1r5mFTv8p8ViUnO8/coO7EzTT5eSubT17T3RiUUkqpaGDPEbf6gLcxpq3tc3OglDGmS4Q684BtxpgxIvIR8BuQAigGfI11tM4V2A5MMMb8KCLXgVFAXeAq0M0YcyKS/tsD7QFSp05d7GXryrwrboffZurVqfx7/19qeNTA28MbB4me/Dw4OBg3NzcAEgUHkO3UDJLd3MvdhGk5nbUV11KUsi4xAoSEGXzPhbEyIJTA+4asHg7UzuZEoZQWHKLrJQr1WiLePxU36T2M++xxDz08PMiePXu0tqkiFx4eHu3TuidPniQw8Mm1Wb28vJ474mbPddwi++v8dJbYCxgvIq2A9cAFIMwYs1pESgCbsSZnW4BH2wUkAEKMMcVtyd50oMIzHRkzBZgC1qnS+DS94B3uzeAtg1l6ailhScIYUm4Irk6ub9zuM0P8piWc/CPBTY4AACAASURBVAfXVQPIf2goZCoH1b+zLu6LdYj0m9BwFu86z2T/U4zZfY/cadzp6JkNnwJpcbTouzExSafZ4j69h3GfvaZKo3v6TkXOHlOlLi4uFClS5JXr2/Mv53kgQ4TP6YGLESsYYy4aYz4yxhQBBtjKAm3/fmeMKWyMqYo1CXw0qnYe68gcwB9AQftdQtzkbHHm23Lf0qt4L9aeXUvLlS25FPzs699vTARyVIWOm8HnR7h6DKZ4wh8dIPACAC5OFpqVzoRfL09GNyxE+END9wV7eX+UPwu2n+V+WHj0x6WUUvGMPo4SN0XlvtkzcdsB5BCRLCLiDDQC/oxYQURSiDyex+uPdfQMEbGISHLb7wWxJmePHtpaAlS2/V4J6wsQ6ikiQst8LRlfeTzng87TaHkj9l7Za5/OLI5Qoi102w3lesDB32FcMVj3HdwPBsDR4kDdIulZ1aMik5sVI7GLE/1+P0ClH/yYvvFf7j54g/1XlVIqHnNxceH69euavMUxxhiuX7/+2rtG2G2q1BgTJiJdgFWABZhujDkkIoOBncaYPwFPYKiIGKxTpZ1tpzsBG2wLyt4GmhljHv1lHwbMFZHPgGCgrb2u4V1QIX0F5tacS9d1XWmzqg0Dywzkw+wf2qczFw+o+g0UbwNrv4H1P8DumVD5SyjcFBwsODgI3vnTUD1fajacuMYE35MM/usw431P0qZcZpqXyYxHQt1OSymlXlX69Ok5f/48V69eje1Q3nkhISHRuj2Xi4sL6dOnf3nFCHTnhHgi8H4gn/t/zrZL22iRtwU9i/XE4vB6D1i+9rMZ53bAqi/g/HZInR+qDYFsXs9U2xlwgwm+J/E9dhX3BI40L5OJNuWzkMItwWvFp15Mn4+K+/Qexn16D+O2mLp/unOCwiOBB5OqTKJJ7ibMOjyLzus6E/QgyL6dZigBn6yG+jPg/m2Y/SHM/dj6LFwExTMnY0brkizvVp6KuVIyyf8U5YatY9Cfh7h46559Y1RKKaXiEE3c4hEnByf6l+rPwDID2XZxG01XNOXM7TP27VQE8n8EnXdA1cFwdgtMLAPLe8GdJ3d5yPeeBxOaFOWfnpX4oNB7zNl6hkojfOmzeB+nrwbbN06llFIqDtDELR5qkLMBU6pN4WbITZosb8KWi1vs36mTC5Trbl3At3gb2DnduoDvpjEQGvJE1Wwp3RjRoBD+fbxoUjIjS/depMoof7rM283hi7qdllJKqfhLE7d4qkSaEsz3mU8q11R0/Kcjc4/MjZk3khKlAJ+R0GkLZCwDawbChBLWN1Gf6j9dkoR8Uyc/G/tW5tNK2fA7dpWaYzfQ5pcd7Dpz0/6xKqWUUm8ZTdzisfTu6ZlTcw4V0ldg2PZhfLPlG0LDQ2Om85S5oOkiaL4EEiSGxa1hWjXrCw1PV3VPQF/v3GzqW5nPq+Zkz9mb1Ju0mUZTtrDxhG6npZRSKv7QxC2eS+SUiDFeY2hXoB2/nfiNdmvacSPkRswFkM0LPl0PH4yHW2dgWhVY3AZuPvvsnYerE13fz8HGvpX50icP/167Q7Np2/hwwiZWHfqPhw81gVNKKfVu08RN4SAOdCvajWEVhnHw2kGaLG/C8ZsxuK6xgwWKNoeuu6FiHzi6AsaXgDVfQ0jgM9UTJXCkbYWsrO/jxdCPCnDzbiifzt6F95j1LNlzgbDwhzEXu1JKKRWDNHFTj/lk9eEX7194EP6A5iuas+7supgNIIEbVB4AXXdZ30Td9D8YWxR2TIPwZ3dWSOBooXHJjKz7vBJjGhUGoMfCvVT+0Z9523Q7LaWUUu8eTdzUE/KnyM+CWgvI6pGVHr49+Hn/zzH/DJlHOqg7Gdr7QcrcsLwnTC4HJ9Y88wIDWLfTqlM4HSu7V2RK82IkdXXiiz8OUPEHX6ZuOM2d+7qdllJKqXeDJm7qGalcUzHDewY1stRg7J6x9N3Ql5CwkJefGN3eKwKt/oKGcyH8AcytD7PrwuVDkVZ3cBCq5UvDks7lmNu2FFlTuDFk+RHKD1/H2LUnCLwbQy9eKKWUUnZit71KVdzm4ujCsArDyJE0B2N3j+Xs7bM0cmkU84GIQJ5akKMa7JwGfsNgcnko0hy8BoB76khOEcplT0G57CnYdeYmE31PMmrNcX7yP0WzMploWz4rKd11Oy2llFJxj464qecSEdoWaMsYrzH8G/gvI/4bwYGrB2InGEdnKN3RuoBvqQ6wdx6MKwrrR0Do87fFKpYpKdNalWBFtwpUzpOan9efpvzwdQxcepDzN+/G4AUopZRSb04TN/VSXhm9mFNzDo440mplK5afXh57wbgmA++h0HkbZPWEdUNgXDHYtxAePv9t0rzvJWZc4yKs/dyTDwunY/72s3iO8KPXr/s4eUW301JKKRU3aOKmXkmOpDnonbY3BVMWpN+Gfvxv1/94aGJx2Y3k2aDRXGi1AhKlhD/aw9TKcGbzC0/LkiIRw+sXxL+3F81KZ+Kv/RepOtqfTnN3cfDCs0uPKKWUUm8TTdzUK3OzuDGl6hQa5GzAtIPT6L6uO3dC78RuUJnLQTtfqPsTBF2GGTVgYTO4fuqFp72XJCGDPsjHxr6V6eSZjQ3Hr1Fr3EZazdjOzoAYXIBYKaWUeg2auKnX4mRx4qvSX/FFqS/YcGEDzVY041zQudgNysEBCjWyrv/m9SWcXAcTSsHKL+Dei/c0TeGWgN7Vc7OxX2V6V8/F/vOB1J+8hY9/2oL/8au6nZZSSqm3iiZu6rWJCI1zN2Zy1clcuXuFJsubsOO/Z/cYjXHOrlCpN3TbDYUbw9aJMLYIbJ0EYQ9eeKpHQic6e2VnU9/KfF07L+du3KXl9O18MH4TKw9e0u20lFJKvRU0cVNRVjptaeb5zCOpS1Lar27PomOLYjskK/c08ME46LAB0haClf1gYmk4ujzSBXwjSuhsoXW5LPj39mJ4vQIEhYTSYc5uqv1vPb/vPk+obqellFIqFmnipt5IpsSZmFtzLqXfK823W7/lu63fEfrwLVnoNk0BaL4EmvwKDo6woAn8Ugsu7n3pqc6ODjQskZF/elZibOMiODoIPRftw2ukH7O3niEkVLfTUkopFfM0cVNvzN3ZnfGVx9MqXysWHFtAxzUdCbz/lryhKQI5q0HHzeDzI1w9AlM84Y+OcPviS093tDjwQaH3+Lt7Baa2KE4KtwR8teQgFX7wZcr6UwTrdlpKKaVikCZuKlpYHCx8XvxzhpQbwu4ru2m8vDGnb52O7bD+n8URSrS1LuBbrhscXGzdwN73e7j/8nXcRIQqeVPzR6eyzGtXipyp3fh+xVHKDVvH6DXHuXX3xc/QKaWUUtFBEzcVrepkr8P06tO5G3qXpiuasv78+tgO6UkuHlB1MHTZAblqgP9w6wK+u2fDw5dPf4oIZbOlYG7b0vzRqSwlsyRjzNoTlBu2ju9XHOHK7VjY01UppVS8oYmbinaFUxVmQa0FZHDPQJe1Xfjl4C9v37IaSTNDgxnwyRpIkgH+7AI/VYLTfq/cRJGMSfm5RXFW9qhAlbypmbrhNOV/8OXLJQc4d0O301JKKRX9NHFTdpEmURp+8f6Fqpmq8uOuH/ly05fcD78f22E9K0NJa/JWfzrcD4RZdWBeQ7h6/JWbyJ0mMWMaFcG3lyf1iqZj4Y5zeI70o+fCvZy8EmTH4JVSSsU3mrgpu3F1cmVkpZF0KtyJP0/9SZtVbbh271psh/UsEchfDzrvgCrfWLfNmlgalveCO9dfuZlMyRMx9KOCrO/jRauymfn74H9UHb2eDrN3ceD8W/KyhlJKqThNEzdlVyJCx0IdGeU5ihM3T9Dor0Ycvn44tsOKnJMLlO9hfYGheGvYOd26gO+msRD26qOFaT0S8lWtvGzs60UXr+xsOnWN2uM30mL6dradfvVEUCmllHqaJm4qRlTNVJVZNWYhIrT8uyWrAlbFdkjPlyiFdemQTlsgY2lY8xWMLwGH/njpAr4RJXdLwOfVcrG5X2X6eOfi0IVAGk7ZSoPJm/E9duXte+5PKaXUW08TNxVjcifLzXyf+eROlpte/r2YsHcCD81bvBNBylzQdBE0/wOc3eDXVjC9Opzf+VrNuLs40ckzOxv7VmZQ7bxcuHmP1jN2UGvcRlYcuES4bqellFLqFdk1cRMRbxE5JiInRaRfJMczichaEdkvIn4ikj7CseEictD20zCSc8eJyMsX4FJvlRQJUzCt+jQ+zP4hk/dNppd/L+6GvuVvYGarbN0+q/ZYuPEvTH0fFn8Ct86+VjMJnS20KpcFv95e/FC/IPcehNNp7m6qjvbn153ndDstpZRSL2W3xE1ELMAEoAaQF2gsInmfqjYSmGWMKQgMBobazvUBigKFgVJAbxFJHKHt4kASe8Wu7MvZ4szgsoPpXbw3a8+upcXfLbgY/PJdDGKVgwWKtbRuYF+xt3Xf03HF4Z9BEHL7tZpydnTg4+IZWNOzEuObFCGBo4Xei/fjOcKPWVsCdDstpZRSz2XPEbeSwEljzGljzANgAVDnqTp5gbW2330jHM8L+Btjwowxd4B9gDc8TghHAH3sGLuyMxGhRb4WTHh/AheCL9B4eWP2XNkT22G9XAJ3qPwldN0J+erCxtHWFxh2Tofw19v+yuIg1Cr4Hiu6lWd6q+KkTpyAgUsPUX64L5P9TxEU8pbs+aqUUuqtIfZ6QFpE6gPexpi2ts/NgVLGmC4R6swDthljxojIR8BvQAqgGPA1UBVwBbYDE4wxP4pId8DBGDNaRIKNMW7P6b890B4gderUxRYsWGCX64xPgoODcXOL9Ot+I/+F/seUK1O4EXaDRskbUdqtdLT3YS/ut0+Q7dQMkgQe4o5rBk5la8ON5EWj1JYxhmM3H/LXqVAOXg/H1RGqZHKiWiYn3JzljWO11/1TMUfvYdyn9zBui6n75+XltcsYUzyyY/ZM3BoA1Z9K3EoaY7pGqPMeMB7IAqwH6gH5jDGBIjIAaABcBa5gTd5+BRYBnsaYsBclbhEVL17c7Nz5eg+Uq2f5+fnh6elpl7YD7wfSy78XWy9tpXne5vQs1hNHB0e79BXtjIGjf8GagXDjtPWZuGpDIHW+KDe579wtJvqdZNWhy7g6W2hSMiPtKmYldWKXKLdpz/unYobew7hP72HcFlP3T0Sem7jZc6r0PJAhwuf0wBMPMhljLhpjPjLGFAEG2MoCbf9+Z4wpbIypCghwAigCZAdOikgA4CoiJ+14DSqGeCTwYFKVSTTN05TZh2fTZW0Xbj94vWfHYo0I5KkNnbZB9aFwYTdMLg/LukPwlSg1WShDEn5qXpzVn1Wker40zNgcQIXhvnzxxwHOXn/LX+ZQSillN/ZM3HYAOUQki4g4A42APyNWEJEUIvIohv7AdFu5RUSS234vCBQEVhtjlhtj0hhjMhtjMgN3jTHZ7XgNKgY5OjjSr2Q/vi7zNdsubaPp8qYEBAbEdlivztEZynSyLuBbqgPsmWN9/m39SAi9F6Umc6Z2Z3TDwvh+7kn94ulZvPM8Xj/68dnCvRy/rNtpKaVUfGO3xM0YEwZ0AVYBR4BFxphDIjJYRD6wVfMEjonIcSA18J2t3AnYICKHgSlAM1t7Kh6on7M+P1f7mcD7gTRZ0YTNFzfHdkivxzUZeA+1jsBl9YR131rfQN2/CB5GbcmPjMld+b5uATb09aJNucysOvQf1Uavp/2snew7dytaw1dKKfX2sus6bsaYFcaYnMaYbMaY72xlA40xf9p+X2yMyWGr09YYc99WHmKMyWv7KW2M2fuc9vUJz3dU8TTFmV9rPmkSpaHTP52Ye2Ru3NtpIEV2aDQXWi2HRMnh93bWNeDObIlyk6kTuzDAJy+b+lam2/s52Hr6OnUmbKL5tG1sOXU97n1HSimlXovunKDeWunc0jG7xmwqpq/IsO3D+GbLN4SGx8ElMjKXh3Z+UPcnCPoPZnjDwubWFxmiKGkiZ3pWzcmmfpXpVyM3Ry4F0fjnrdSfvIV1Ry9rAqeUUu8oTdzUWy2RUyL+5/U/2hVox28nfqPt6rbcCLkR22G9PgcHKNQIuu4CrwFwci2MLwmrBsC9m1Fu1t3FiQ6VsrGxrxff1snHf4EhtPllJzXHbmTZvou6nZZSSr1jNHFTbz0HcaBb0W4MrzCcQ9cP0fivxhy7cSy2w4oaZ1eo1Me6A0OhRrBlgvUFhq2T4Q1GE12cLDQvkxm/3p6MbFCI+2HhdJ2/hyqj/Fm04xwPwnQ7LaWUehdo4qbijJpZa/KL9y+EPQyj+d/NWXt27ctPelu5p4E64617oKYpCCv7wsTScHSFdV24KHKyOFC/WHrWfFaJiU2L4upsoc9v+/Ec4cuaM6Hce6DbaSmlVFymiZuKU/KnyM/8WvPJniQ7PXx7MGX/lLj9PFeaAtBiKTRZBOIACxrDzNpwMdL3cV6ZxUGoWSAtf3Utzy+tS5AuaULmHnlA+eHrmOB7ktu6nZZSSsVJmripOCeVayqmV5+OT1Yfxu0ZR9/1fbkXFrV10t4KIpCzOnTcDDVHwpXDMMUT/ugIty++9PQXNy145krFrx3K0r+kC/nTeTBi1THKDVvHyFXHuB58P3quQSmlVIzQxE3FSS6OLgwtP5TuRbuzMmAlrVa24vKdy7Ed1puxOEHJdtB1N5TtCgcXw7hi4DsUHtx54+ZzJbMws01JlnUpT/nsKZjgd5Lyw30ZvOwwlwLjcOKrlFLxiCZuKs4SEdoWaMvYymMJCAyg0fJG7L+6P7bDenMJk0C1b6HLDutInP8wGFvUuhPDwzd/Rq1Aeg8mNSvGms8qUqNAGmZuCaDiD770/30/AdfePEFUSillP5q4qTjPM4Mnc2rOIYElAa1XtmbZqWWxHVL0SJoZGvwCbVaDR3pY2hmmVILT/tHSfPZU7oz6uDB+vTxpWCIDv+2+QOUf/eg2fw9H/4sj+8QqpVQ8o4mbeifkSJqD+T7zKZiyIF9s/ILRu0YTHg2jU2+FjKWg7T9QbxrcC4RZH8C8RnDtRLQ0nyGZK0M+LMDGPl60q5CVtUcu4/2/DbSduZM9Z6O+xpxSSqnop4mbemckdUnKlKpTaJCzAdMPTqe7b3eCHwTHdljRQwQK1LdOn1YZBAEbrcuHrOgNd65HSxepErvQv2YeNvWrTI8qOdgRcIO6EzfT5OetbD55LW6/vauUUu8ITdzUO8XJ4sTAMgMZUGoAGy9spPnfzTkXdC62w4o+Ti5Q/jPotgeKtoQdU60L+G4eB2HR84ZoEldnelSxbqc1oGYeTlwJpsnUbdSduJk1hy/zUHdjUEqpWKOJm3onNcrdiMlVJ3Pl7hUaL2/M9kvbYzuk6OWWEmqNsi4hkqEkrP4SJpSEQ0veaAHfJ7pI4Ei7ilnZ0MeLIR/m51rwfdrN2knNsRtYuvcCYeG6G4NSSsU0TdzUO6t02tLM95lPcpfkfLrmUxYdWxTbIUW/VHmg2WJo9js4JYJfW8J0bzi/K9q6cHGy0Kx0Jnx7eTLq40KEPTR0X7CX90f5s2D7We6HvSPPEiqlVBygiZt6p2VMnJE5NedQ5r0yfLv1W4ZsHULow3dw14Ds71u3z6o9Fm6chqmV4be2cCv6pomdLA58VDQ9q3tUZHKzYiR2caLf7weo9IMf0zf+y90HYdHWl1JKqchp4qbeee7O7oyrPI7W+Vqz8NhCOqzpwK2QW7EdVvRzsECxltYN7Cv0giPLrAv4/vMNhETf8h4ODoJ3/jT82aUcs9qUJGNyVwb/dZjyw30Zv+4EgffewcRYKaXeEpq4qXjB4mChZ/GefFf+O/Zc2UOTFU04detUbIdlHwnc4f2voOsuyPchbBwF44qS9uJKCI++UTERoWLOlCz6tAy/dihDofQejFx9nPLD1vHDyqNc0+20lFIq2mnipuKVD7J9wPTq07kbepemK5qy/vz62A7JfjzSw0dToJ0vJM9BruOTYHJ5OPlPtHdVInMyZrQuyV9dy1MxZ0om+Z+i/PB1DPrzEBdv6XZaSikVXTRxU/FO4VSFWVBrARndM9JlbRdmHJzxbq9Rlq4otF7BwXz9ICwE5tSD2R/B5cPR3lX+dB5MaFqUf3pWolbB95iz9QyVRvjSZ/E+Tl99R9bUU0qpWKSJm4qX0iRKw8waM6mWuRqjdo1iwMYB3A9/h6f2RLiWsgx03g7Vv4cLO2FyOVjWHYKvRHt32VK6MbJBIfx6e9KkZEaW7r1IlVH+dJm3m8MXdTstpZSKKk3cVLyV0DEhIyqOoHPhziw7vYw2q9pw9e7V2A7LvhydoUxn6LYXSn5q3bh+bBHY8COERv+UZvqkrnxTJz8b+1amfcVs+B27Ss2xG2jzyw52ndHttJRS6nVp4qbiNRGhQ6EOjPIcxYmbJ2i0vBGHrh+K7bDszzUZ1BgGnbZBVk9YOxjGl4D9v8LD6F9YN6V7AvrVyM2mvpXpWTUnu8/epN6kzTSasoWNJ3Q7LaWUelWauCkFVM1UlVk1ZmERC63+bsXKgJWxHVLMSJEdGs2Fln9BwqTwe1uYVgXObrVLdx6uTnR7Pweb+lbmS588/HvtDs2mbePDCZtYdeg/3U5LKaVeQhM3pWxyJ8vNfJ/55Emeh97+vRm/ZzwPTTzZ1ilLBWjvDx9OhtuXYHp1WNTCupivHSRK4EjbCllZ38eL7+sW4ObdUD6dvQvvMetZske301JKqefRxE2pCJInTM7UalOpm70uP+3/iZ5+Pbkbeje2w4oZDg5QuLF1/TevAXBiDYwvCasGwD37LFicwNFCk1IZWfd5Jf7XsDAAPRbupfKP/szbpttpKaXU0zRxU+opzhZnvin7DX1K9MH3nC/N/27OxeCLsR1WzHF2hUp9oOtuKNQQtkywvsCwbQqE22dXBEeLAx8WScfK7hWZ0rwYSV2d+OKPA1T8wZepG05z575up6WUUqCJm1KREhGa523OxPcncin4Eo2XN2b35d2xHVbMSpwW6kyAT9dDmvzwd2+YWAaOrgA7vUzg4CBUy5eGJZ3LMeeTUmRN4caQ5UcoP3wdY9eeIPCubqellIrfNHFT6gXKpSvHXJ+5uDu788nqT/j9xO+xHVLMS1sQWvwJjReCCCxoDDNrw6V9dutSRCifIwXz25fmt45lKZoxKaPWHKfc8HUM+/soV4Pe4TX3lFLqBeyauImIt4gcE5GTItIvkuOZRGStiOwXET8RSR/h2HAROWj7aRihfK6tzYMiMl1EnOx5DUpl8cjC3JpzKZG6BF9v/prh24cT9jCeTd2JQC5v6LgZao6Ey4fgp0qwpLP1ZQY7KpYpKdNalWBFtwp45krJT+ut22kNXHqQ8zetzx8u2XOBcsPWkaXfcsoNW8eSPRfsGpNSSsUWuyVuImIBJgA1gLxAYxHJ+1S1kcAsY0xBYDAw1HauD1AUKAyUAnqLSGLbOXOB3EABICHQ1l7XoNQjHgk8mFhlIs3yNGPOkTl0XtuZ2w/i4Q4AFico2Q667YGyXeHAIhhXFPyGwYM7du0673uJGd+kKGt7VuLDwumYv/0sniP8+HjyZvr+tp8Lt+5hgAu37tH/9wOavCml3kn2HHErCZw0xpw2xjwAFgB1nqqTF1hr+903wvG8gL8xJswYcwfYB3gDGGNWGBtgO5AepWKAo4MjfUv2ZVCZQWz/bztNlzclIDAgtsOKHQmTQLVvrVto5agGfkNhXDHYM9cuC/hGlDWlG8PrF8S/txfNSmdie8BN7oc92ee90HBGrDpm1ziUUio2iL1WLBeR+oC3Maat7XNzoJQxpkuEOvOAbcaYMSLyEfAbkAIoBnwNVAVcsSZoE4wxP0Y41wnYBnQ3xmyIpP/2QHuA1KlTF1uwYIFdrjM+CQ4Oxs3NLbbDeCucDDnJtKvTCDfhtE7ZmjwJ88R2SC9lz/uXOPAI2U9OJ3HQcYLcsvJ/7N15WFVV+//x9zqHWUYBAeGoCDigoihDmgOC84RDimY+VpY+pWVqqWWDWWplOTVoWVppilMGzjNaToDzrOCEs2lqztP+/bGpn49fFTNhn4P367r2FZxzNn5OW/Bmrb3ulR3yHGe9IvLlz7rTswvuPdL3faMiBZKhoMj3oO2Ta2jbCur61a1bd72maVF3ey4/C7e2QMM7CrcYTdNeue01xYEvgGBgJdAGqKBp2jml1ACgLXAKOAmka5o26rZzxwEXNU17La8sUVFRWmZm5qN7c4+ptLQ04uLijI5hNY5cOMIry14h+2w2b0S9QcfyHVFKGR3rnvL9+mkabJsJSwbCuRwo2wTqDwKfsPz7M4EnP1rGkbN332e1cUV/kqIt1ArzxWyy3mvzoOR70PbJNbRtBXX9lFL3LNzyc6r0MGC57fMg4H+aYWmadlTTtNaapkUCA3IfO5f738GaplXRNK0+oIC9f52nlHoP8AV652N+Ie4r0DWQSY0nERcUx8cZHzNwzUCu51OfM5ugFFR6CnpkQMJ7sP9X+OoJmNcXLp3Jtz/2jYZlcbY3/89jjnYm4sr4sG7/GZ6dkEGtj5cxYvGevxczCCGErbLLx6+dAYQppYKBI0B74OnbX6CU8gHOaJp2C3gTGJ/7uBnw1DTttFIqAogAFuU+9wLQEEjIPU8Iw7jYuzCi7gi+3PQl32z5hgPnDjA8bjjezt5GRzOOvTPU6g2RnSBtCGSMgy3JUPsNiOkKdo6P9I9rGRkIwLCFuzl69jLFPZ15o2FZWkYGcvXGTZbsOElyxiFGL9vL6GV7qRXmS/toC/XK++FgJx2RhBC2Jd8KN03TbiilegALATMwXtO07UqpQUCmpmmpQBwwVCmloU+Vds893R74NXfa6TzwjKZpf/VfGAscBNbkPv+zpmmD8ut9CJEXkzLxSuQrhHqG8s6qd+gwtwOfx39O2aJljY5mLFdfaDZCL9YWvQOL3oaMb/Xp0/It9BG6R6RlZODfBdztHO3MNI0IoGlEADln258XdAAAIABJREFULjF9/WGmZ+bw8k8b8C7iQOuqgSRFWwgt5vbIsgghRH7KzxE3NE2bB8y747F3b/t4BjDjLuddQV9Zerevma+ZhXhYjYMbU8KtBK8uf5VO8zsxtOZQEkomGB3LeMXKwzMzIGuJXsBN+w+UqA4NB0NgtQKLYSnqQu/6ZeiZEMbKvaeYmp7DhFUHGPfrfqJKepEUbaFpRAAuDvIjRghhvWSeQIhHqIJPBZKbJhPqGcpraa/x9eavya8FQDYntB50+xWaj4LTWTAuHma+CGdzCjSG2aSoW7YYYztVY82bCbzZuBxnLl7jjRlbiB28lAGztrL18Dm5bkIIqySFmxCPmK+LLxMaTaBZ6WZ8sekL+q7sy+Ubd1/1+Ngx20G1Z/UGvrVeh52p8EUULB0EV/8s8Di+bo50qxPC0j51mNatOvUr+DFj/WGaf/EbTUf/xo9rDsj+qEIIqyKFmxD5wNHsyJCaQ+hVrRcLDyzk2QXPcvzicaNjWQ9HN0h4B3pk6ve7/foZjI6EzAlws+C3E1NKERNclOHtqpA+oB4ftKyIUvBuynZihiyh19RNrN13WkbhhBCGk8JNiHyilOL5is/zefznHDh3gA5zO7D5VP5tzG6TPC3QZhy8uAy8Q2HOa/B1Lchamve5+cTD2Z5OT5Rk7qu1mPNKTdpGBbFkxwnaf7OW+M9WMCYtm5N/XjEsnxDi8SaFmxD5rI6lDj81+QknsxPPL3ie2dmzjY5kfQKrwXPzod2PcP0yTGoNk9rAyZ2GxqoY6MGHLSuRPqAen7WtjK+rIx8v2EX1ocvo+mMmy3ad4MZN6UokhCg4snxKiAIQ6hXKlKZT6L2iN2/99hZ7z+6lZ2RPzCZz3ic/LpSC8EQo0wjSx8HKT2BMDajaGeq+Ba7FDIvm7GCmTbUg2lQLIvvUBaZl5jBz/WEW7TiBv7sTbaOCaBdlwVLUxbCMQojHg4y4CVFAPJ08+br+1ySVTWLCtgm8uvxVLly7YHQs62PnCDV6wKub9B5wGyfC6Krw63C4bvwUZYivK282Ls/q/gmMfaYq5QLc+GJ5FrU+Wc4z365j9uajXL1x0+iYQohCSgo3IQqQvcmet594mwGxA1h1ZBXPzHuGnPMF2w7DZrgUhcYfw8vrILg2LH1fX4G6dYa+L6rBHOxMNKoYwPfPxbCqXzy96pVh/+8XeWXKRp4YspRBs3ew50TBr5QVQhRuUrgJYYD25drzdf2v+f3K73SY14F1x9YZHcl6+YRCh8nQeQ44e8HMLvBtAhxaa3SyvxX3dKZnvTBW9q3Lj8/HUCPEh4lrD9BgxEpafbWKqRmHuHi14FfLCiEKHynchDBIbEAsU5pMwdvJm26Lu5G8K9noSNYtuBZ0XQEtx8D5ozC+IUzrDGf2w5ZpMKIiDPTU/7tlmiERzSZF7TK+fNmxKmvfTODtpuX588oN+s3cSszgJfSfuYVNOWelrYgQ4qHJ4gQhDGRxt/BTk5/o92s/Bq8bTNbZLPrF9MPeZG90NOtkMkGVp/VFDKs/h1WjYOdsfWHDrdwRrXM5MPtV/eOIdoZF9XZ15IVapelSM5gNh/4gOT2HlE1HSc7IoZy/G0nRFlpFBuLp4mBYRiGE7ZERNyEM5urgyui6o3mu4nNM3T2V/y7+L2evnDU6lnVzKAJx/eGVDWDn9P+Ltr9cv6zvxmAFlFJUK1mUYW0rkz4ggSGtKuFoZ+L92TuIGbKUV6dsZHXW79y6JaNwQoi8yYibEFbAbDLTu1pvwjzDeG/1e3SY24HP4z8n1CvU6GjWzT0Arl+6+3PnDuuLGJQq2Ez34eZkz9OxJXg6tgQ7jp5nWmYOP284TOrmo5Qo6kJStIWnqgXh5+5kdFQhhJWSETchrEjzkOZMaDSByzcu88z8Z1iRs8LoSNbPI+geT2jwTR3Y+JNVtBG5U3hxdwa2qED6gHqMTKpCcU8nhi3cTfWhS3nhhwwW75DmvkKI/0sKNyGsTGXfyiQ3S6aEWwleWfYK3239Tm5mv5+Ed8He+X8fs3OGKh3hxjVIeRmGl4clA+Gs9bVecbI30zIykOSu1Vn+ehzd6oSw+fA5XvwxkxofLeOTBbs4ePqi0TGFEFZCpkqFsEL+Rfz5ofEPvLPqHUZuGEnW2SwG1hiIo9nR6GjW568FCEsH6dOjHkF6MRfRTp8qPfArrPtaX8iwahSUbaI39g2ubVXTqADBPkXo16gcveuXYfmuk0zNyGHsimy+SsumemlvIlxv8MT1mzjZy44bQjyupHATwko52zkzrPYwwjzD+GLTFxw6f4iRdUfi6+JrdDTrE9Hu7itIldILtODa+mhb5njY8APsmgO+5SDmRYhoD46uBZ/5PuzNJhpU8KdBBX+On7vCjPU5TM3MYc2+qyTvXUqryECSoi2UD3A3OqoQooDJVKkQVkwpRbfK3RgRN4K9Z/fSfm57tv++3ehYtsnTAvXeg1479F5wdk4wt48+jTq/P5zONjrhXfl7ONEjPowVr9elb7QTtcv4MnndIRqP+pXEL1cxJf0QF6S5rxCPDSnchLAB9UrWY2LjiZiVmc4LOrNg/wKjI9kueye9F1zXNOiyBMo0hIxv4fOqMKkN7FkEt6xvUYDJpAj3NvN5h0jWvZXAu83CuXztBm/+rDf37TtjM+sP/iH3QwpRyMlUqRA2omzRskxpOoXeab15Y+Ub7D27l+5VumNS8vvXQ1EKLNH60WAwrP9en0qd3Ba8gvVp1CodwdnT6KT/h1cRB56vGcxzT5ZiU85ZpmbkkLr5KNMyDxNWzJWkaAutqwZRtIg09xWisJGf+ELYEG9nb8Y1GEer0FZ8s+Ubeqf15tK9+piJB+fmB3H9oNc2eGo8uPnDwrf0adTZr8EJ65yeVkoRWcKLj9pEkD6gHh+1rkQRRzs+nLuT2CFL6D55A7/uPSXNfYUoRGTETQgb42B24P0a71PGqwzDMofRaX4nRsePJtA10Ohots9sDxXb6MexzZA+DjZPgfUToFQtfRSubFMwW9+PTldHO9rHlKB9TAl2HT/P1IwcZm08wtwtxwjycqZdlIW2UUEEeDjn/cWEEFbrviNuSqkuSqk3bvv8iFLqvFLqT6XUS/kfTwhxN0opngl/hq8SvuLYhWN0mNOB9SfWGx2rcAmoDIlfQO+dUH8QnD0I0/4DoyJg5adw8XejE95TOX933mtegbVvJjC6QyQlvV0YvngPT360jOcmpLNg23GuS3NfIWxSXlOl/wXG3/b5SU3T3AFfoEO+pRJCPJAnA5/kp6Y/4eHowQuLXmDmnplGRyp8XIrCkz3h1U3Qfgr4lIFlH+jTqLP+C0est2B2sjfTonJxfnrhCVa+UZeX40LZcew8/520nupDlzF0/k72/y7NfYWwJXkVbiZN007f9vl0AE3TrgAy3i6EFQj2CGZSk0nE+McwcM1APk7/mBt3brou/j2TGco1gf/8At0zoNqzsHM2jIuHcQmweSrcuGp0ynsq4e3C6w3LsqpfPN91jiKyhCff/rqfup+mkfT1GmZtPMyV6zeNjimEyENehZvH7Z9omjYEQCllArzzK5QQ4p/xcPTgy4Qveab8M0zaOYmXl7zMuavnjI5VePmWgSbD9GnUxsPgyjmY1RVGVIBlH8L5o0YnvCc7s4mE8n6M+08Ua/rH07dRWY6fv0KvqZuJHryEd1O2sf2o/N0RwlrlVbgtUkp9eJfHBwGL8iGPEOIh2Zns6BfTj0E1BpFxIoNn5j3D/nP7jY5VuDm5Q2xX6J4OnWZBYJR+/9uIijCtMxxcrW+7ZaWKuTvxclwoy/vEMeXFJ0goV4zkjByajv6N5p//xqS1Bzl/5brRMYUQt8mrcHsDCFFKZSmlZuYeWUAo8Hr+xxNC/FOtwlrxXYPvOH/tPB3ndmTVkVVGRyr8TCYIiYenk6HnJqj+MuxLgwmNYWwtWP8DXLPeti0mk6J6iDcj20eS/lYC77eowPWbt3j7l23EDF5Cn2mbyThwRpr7CmEF7lu4aZp2UdO0DkAD4Pvco6Gmae01TbuQ1xdXSjVSSu3OLfz63+X5kkqppUqpLUqpNKVU0G3PfayU2pZ7JN32eLBSap1Saq9SaqpSSjpMCnGHqn5VmdJ0CgGuAby89GUm7pgo/+gWFK9S0OBDfRq1+WhAg9mv6osZFr0NZ6x7FNTTxYHONUoxv2ctUns8SeuqQSzcfpy2Y9eQMHwF36zM5vcL1nsvnxCFXV7tQBoqpZ7SNG2fpmmzc49spVRHpVT9PM41A18CjYFwoINSKvyOl30K/KhpWgT69OvQ3HObAlWBKkAs8IZS6q/dlD8GRmiaFgb8AXT5J29YiMdFcdfiTGw8kbqWunyS8QmTT0/m2s1rRsd6fDi4QLXO8N/f4Ln5EFIX1nwFoyNhcnvIWmqVW2v9RSlFRJAnQ1pVIn1AAsOeisDLxYEh83bxxJClvDRpPWm7T3JTmvsKUaDymip9H1hxl8eXohda9xMDZOUWfdeAZCDxjteE534tgOW3PR8OrNA07YamaReBzUAjpZQC4oEZua/7AWiZRw4hHlsu9i4MjxtOt4hurL24lhcWvcDpy6fzPlE8OkpByRrQ9nt9Z4bab8CRTJjUGr6MhnVfw5XzRqe8LxcHO9pGWZj5Ug0W96rNszVKsW7/GZ6dkEGtj5cxYvEejpy9bHRMIR4L6n7TJ0qpLbmjYf/oudznnwIaaZr2Qu7nnYBYTdN63PaaycA6TdNGKaVaAzMBH6Aa8B5QH3AB0tFH734A1mqaFpp7vgWYr2laxbv8+V2BrgB+fn7VkpOT7/1/QTyQCxcu4OrqanQM8ZBWn17NjIszcDW50rVYV4IcgvI+SeQLdes6vqdWEXhkHh7nd3PD7MQJv3iOBDbhUhHLPc+zpu/B67c0Np68ycqcG2w/rbcRqehjpnaQHZHFzNiZlMEJrZM1XUPxzxXU9atbt+56TdOi7vZcXvu2OCml7DRN+5+mUEope/Lu43a379o7q8TXgS+UUs8CK4EjwA1N0xYppaKB1cApYA1w4wG/pv6gpn0DfAMQFRWlxcXF5RFX5CUtLQ35/2jD0iAxLpFXl73K6FOjGVJzCPVK1jM61WOsPjAQjmzALn0cgdtmEHh0HpSOg5iuUKaR3jvuNtb2PVgf6AvknLnE9PWHmZ6Zw5ebruBdxIE21YJoF2UhtJgUKbeztmso/hlruH55TZX+DIxTShX564Hcj8fmPnc/h4Hbf3UMAv6nuZGmaUc1TWutaVokMCD3sXO5/x2saVoVTdPqoxdse4HfAU+llN29vqYQ4t4qeFcguWkyYZ5h9ErrxdjNY2XRgtECq0KrMfpihoR34fe9kPw0jKoCv42ES2eMTpgnS1EXetcvw2/94pnwXDTRpYoy/rf91Bu+grZjVzNj/WEuXZOm0EI8CnkVbm8DJ4CDSqn1SqkNwAH0UbC38zg3AwjLXQXqALQHUm9/gVLKJ7eZL8Cb5G6vpZQyK6W8cz+OACKARZr+L8xy4KncczoDKXm+SyHE33xdfBnfaDzNSzfny01f8vqK17l8Q+5PMlwRH6jVB3pugXYTwaskLHlPX42a0l3f9N7KmU2KumWLMbZTNda8mcCbjctx+sI1Xp++mdjBSxkwaytbD5+TXxaE+BfuO1WaO0XaXyn1PnrvNtAXHOT5U17TtBtKqR7AQsAMjNc0bbtSahCQqWlaKhAHDFVKaehTpd1zT7cHftXXInAeeOa26dp+QHJuY+CNwHcP/G6FEAA4mh0ZXHMwYV5hjFg/gpw/cxgdPxr/Iv5GRxNmOwhvoR8ndkD6N7BlKmycRKR7efB+HcITwWxvdNL78nVzpFudELrWLk3GgT9IzjjEjPWH+WndIcID3GkfYyGxciAeLtb9PoSwNvddnACQO/L1NFAu96GdwJQ79jC1alFRUVpmZqbRMWyeNczti4d3r+u3ImcF/X7th5PZiVHxo6jsW7ngw4n7u3wWNk3m8opROF85Dq7+EPUcVHsO3PyMTvfAzl2+TurmoySnH2L70fM42ploUimApGgLscFFyf1lvVCTn6O2raCun1LqnosT8urjVh7Yhr7Kcw/6fWbRwFalVLn7nSuEsA11LHWY1HgSznbOPLfgOVKzU/M+SRQsZ0+o/jLrYsfA09PBvxKkDdX3Rp3RBXLSrXprrb94ONvT6YmSzH21FnNeqUnbqCCW7DhB+2/WEv/ZCsakZXPyzytGxxTCquW1qvQDoKemadNuf1Ap1QYYDLTJr2BCiIIT6hXKlKZT6LOiDwN+G8DeP/byWtXXMN+xqlEYTJmgTAP9OJ0NGd/CxkmwbQYEVIaYblCxDdg7GZ00TxUDPfgwsBIDmoQzb+sxpmbk8PGCXXy2aDcJ5YvRProEtcv4Ypa2IkL8j7wWJ1S6s2gD0DRtJvB/eqcJIWyXp5MnY+uPJalsEt9v/55Xlr3ChWt57mwnjOIdAo2G6qtRmw6HG9cg5WV9McOSgXA2x+iED8TZwUybakFM+291lvapQ5eawWQe+IPnvs/gyY+WMXzRbnLOWO8+r0IUtLwKt4sP+ZwQwgbZm+x5+4m3eTv2bdYcXUPHeR05dP6Q0bHE/Ti6QnQXeHkNdJ6t79KwahSMioDkjrBvhU1MowKE+LryZpPyrHkzgbHPVKVcgBufL8+i9rDldPpuHXO2HOXqjZtGxxTCUHlNlRZTSvW+y+MK8M2HPEIIK5BULolgj2B6r+hNh7kdGB43nNiAWKNjiftRCoJr68fZHMj8Dtb/ALvmgG85iHkRItrrhZ6Vc7Az0ahiAI0qBnDk7GVmZB5mWmYOPSZvxMvFntZVg0iKtlDGz83oqEIUuLxG3MYBbnc5XIFv8zeaEMJIMQExTGkyBV9nX7ot7kbyLtk2zmZ4WqDeQH0ateUYsHOCuX30adT5/fX742xEoKczPeuFsbJvXX58PoYaIT78uOYADUaspPVXq5iWkcPFq9LcVzw+8urj9n5BBRFCWB+Lu4VJTSbR/9f+DF43mL1/7KV/bH/sTdJ7yybYO0GVp6FyBzicCelf6wsa1o2B0Hr6YobQemDK63d445lNitplfKldxpfTF64ya+MRpqQfou/MLbw/ezstqhQnKboElYM8Hou2IuLxdd/CTSn17n2e1jRN++AR5xFCWBlXB1dG1R3F6I2jGb9tPPvO7WN43HC8nLyMjiYelFJgidaPBoNh/feQOR4mtwWvYH0atUpHve2IDfB2deSFWqXpUjOY9Qf/IDkjh182HmVKeg7l/N1IirbQKjIQTxcHo6MK8cg9yOKEOw+ALug7GAghHgNmk5le1XoxpOYQtpzaQoe5Hcj6I8voWOJhuPlBXD/otQ2eGg9u/rDwLX0adXZPOLHd6IQPTClFVKmifNq2MusGJDC4VUUc7Ey8P3sHMUOW0jN5I6uzf+fWLdtYnCHEg8hrqvSzvz5WSrkBPYHngGTgs3udJ4QonJqHNKeke0l6Lu9Jx3kd+bj2x8RZ4oyOJR6G2V7v+Vaxjb4Pavo42Jysj8aVrAmxXaFsU30LLhvg7mRPx9iSdIwtyfaj55iWkcOsjUdI2XSUkt4utIuy8FS1IPzcrb/HnRD3k+eNDUqporn7gm5BL/SqaprWT9O0k/meTghhdSJ8I5jSdAqlPErx6rJX+Xbrt7JpuK0LqAyJX+iLGeoPgnOHYNp/9JYiKz+FC6eMTviPVCjuwfuJFUkfUI+RSVUI8HBi2MLd1PhoGS/8kMmSHSe4cfOW0TGFeCh53eM2DGgNfIPejFe6cQoh8C/iz/eNvufdVe8yasMoss5m8X6N93E0OxodTfwbLkXhyZ5QvQfsWahvcL/sA1jxsT4yF/MiBFYzOuUDc7I30zIykJaRgez//SLTMnOYnnmYJTtPUMzNkbZRQbSLslDSu4jRUYV4YHmNgfcBrgJvAwNuW6mj0BcnuOdjNiGEFXO2c+aT2p8Q5hXG5xs/59D5Q4ysO5JiLsWMjib+LZMZyjXRj1N7IGMcbJoMm6dAYBTEdIUKLcHOdgr1YJ8i9GtUjt71y7B810mmZuQwJi2bL5dnUyPEm6RoCw0r+ONkL9u8Cet236lSTdNMmqY5a5rmpmma+22HmxRtQgilFF0jujIybiRZZ7PoMKcD23+3nZvbxQPwLQNNhunTqI2HwZVzMKurvsH9sg/h/FGjE/4j9mYTDSr4892z0azun8DrDcqQ88cleiZvInbIUgambmfX8fNGxxTinqy/eY8QwuollExgYuOJ2Jns6LygM/P3zzc6knjUnNz1BQvd06HTLH3kbeWnMKIiTOsMB1bZzNZaf/H3cKJHfBgrXq/LTy/EUruML5PXHaLRyF9J/HIVU9IPcUGa+worYxvLhYQQVq9s0bJMbjqZ3mm96buyL3v/2EuPyB6YlPx+WKiYTBASrx9/HNAb+m6YCDt+Ab+K+n1wldqBg4vRSR+YyaR4MtSHJ0N9+OPiNWZtPEJyxiHe/HkrH8zZQfOI4iTFWIi0eEpzX2E4+YkqhHhkvJ29+bbBt7QJa8O4reN4bflrXLx+Me8ThW3yKgUNPtSnUZuP1h+b3ROGl4OFA+DMfkPjPQyvIg48XzOYha/VZtbLNWhRuTiztxyl9VeraThyJd/9tp8zF68ZHVM8xqRwE0I8UvZme96r/h79Y/qz4vAKOs3vxOE/DxsdS+QnBxeo1hn++xs8N18fjVs7BkZHwuQkyFoKt2yr/YZSisgSXnzUJoL0AfX4qHUlXBzs+GDODp4YspQekzfw215p7isKnkyVCiEeOaUUHct3JNg9mNdXvs7Tc59meNxwovyjjI4m8pNSULKGfpw/CpkTYP0EmNQavEP11aiVO+j3y9kQV0c72seUoH1MCXYdP8/U3Oa+c7YcI8jLmaQoC09FBRHg4Wx0VPEYkBE3IUS+qRFYg8lNJuPh6MGLi15kxp4ZRkcSBcW9OMQPgF7bofU4cPaC+X31rbXmvg6ndhud8KGU83fnveYVWPtmAqM7RFLS24XPFu/hyY+W8fz3GSzcfpzr0txX5CMZcRNC5KtSHqX4qelP9F3Rl/fXvM/eP/byRvQb2Jnkx89jwc4RItrpx5EN+tZaG37Qe8MF14HYblCmkd47zoY42ZtpUbk4LSoX59DpS3pz3/U5dJt4Eh9XR56qFkRStIVgH2nuKx4tGXETQuQ7dwd3vkj4gk7hnZi8azIvLXmJc1fPGR1LFLTAqtBqjL6YIeFdOJ0FyU/DqCrw20i4dMbohA+lhLcLrzcsy6p+8XzXOYrIEp6M+3UfdT9NI+nrNczaeJgr128aHVMUElK4CSEKhJ3Jjr7RfRlUYxCZJzLpOK8j+87tMzqWMEIRH6jVB3pugXYTwaskLHlPn0ZN6a5vem+D7MwmEsr7Me4/UazpH0/fRmU5fv4KvaZuJmbwEt5L2cah81LAiX9HCjchRIFqFdaK7xp8x5/X/uSZuc/w25HfjI4kjGK2g/AW8OwceGmNvnBh28/wdW34riFsnQE3rxud8qEUc3fi5bhQlveJY8qLTxBfrhhTMnJ4d/UVWnzxGz+tO8ifV2zzvQljSeEmhChwVf2qMqXpFIq7Fqf70u78sP0HNBvrui8eMb9waD5Sn0ZtOAQunICZXfSdGdI+gj9PGJ3woZhMiuoh3oxsH0n6Wwl0LO/AtRu3GDBrGzGDl/L69M1kHjgjf//FA5PCTQhhiOKuxfmx8Y/EW+L5NPNT3ln1DtduSmPTx56zJ1TvDq9sgKeng38lSBuq7406owvkpNvc1lp/8XRxoH5Je+b3rEVK9ydpGRnI/K3HeGrsGuoNX8G4lfs4feGq0TGFlZNlXUIIw7jYu/BZ3GeM2TyGsZvHcvD8QUbUHYGPs4/R0YTRTCYo00A/TmfrW2ttnATbZkBAZb0nXMU2YG97vdOUUlS2eFLZ4snbTcszd+sxpmbkMHjeTj5ZuIv64X4kRZegZqgPZpNssSX+l4y4CSEMZVImulfpzrA6w9h1Zhcd5nZg5+mdRscS1sQ7BBoN1adRmw6HG9f0RQzDw2Hxe3D2kNEJH1oRRzvaRVmY+VINFveqTefqpViTfZrO49Op/clyRi7Zw5Gzl42OKaxIvhZuSqlGSqndSqkspVT/uzxfUim1VCm1RSmVppQKuu25T5RS25VSO5VSo1Xuzr5KqQ5Kqa255yxQSsmv5kIUAo1KNeKHxvq9bp0XdGbxwcVGRxLWxtEVorvAy2ug82x9h4bVo2FUZUjuCPtW2Ow0KkCYnxtvNwtn7VsJfPl0VUr7FmHU0r3U/HgZncenM3/rMa7dkOa+j7t8K9yUUmbgS6AxEA50UEqF3/GyT4EfNU2LAAYBQ3PPrQE8CUQAFYFooI5Syg4YBdTNPWcL0CO/3oMQomCFe4eT3CyZMK8weqf1ZsymMdzS5B8qcQelILg2tP9JbynyZE84uBp+bAFfPaFPq169YHTKh+ZoZ6ZpRAATu8Sy8o26vBIfxp4Tf/LSTxuoPnQpQ+btJOuk7b4/8e/k54hbDJClado+TdOuAclA4h2vCQeW5n68/LbnNcAJcAAcAXvgBKByjyK5I3DuwNF8fA9CiALm4+zD+IbjaRHSgq82f8XrK17n0vVLRscS1srTAvUG6tOoLceAnRPM7aP3hJvfH37PMjrhv2Ip6kLv+mX4rV88E56LJrpUUcb/tp96w1fQduxqZqw/zOVr0hvucaLyawmyUuopoJGmaS/kft4JiNU0rcdtr5kMrNM0bZRSqjUwE/DRNO20UupT4AX0Qu0LTdMG3PZ1xwMXgb3oo2//52+tUqor0BXAz8+vWnJycr68z8fJhQsXcHV1NTqGeEi2dv00TWPZ+WWknE0h0CGQrr5d8bLzMjqWoWztGhpC03A/v4fAI3PwPbUak3aD00WrciSwKWeKVgVl7K3dj+Ianr16i9VHbrDi8A1OXNJwtoOkMTUtAAAgAElEQVQnAuyoE2RHKQ/b2jrM1hTU92DdunXXa5oWdbfn8rNwaws0vKNwi9E07ZXbXlMc+AIIBlYCbYAKgC/6lGhS7ksXA/2ANcAC9IJsH/A5cFzTtA/vlyUqKkrLzMx8dG/uMZWWlkZcXJzRMcRDstXrt/LwSvqt7Iej2ZGRdUdSpVgVoyMZxlavoWH+PAHrv4fM8XDhOHiVgugXIbKjvum9AR7lNdQ0jfT9Z5iakcPcrce4euMWFYq70z7aQosqgXg42z+SP0f8fwX1PaiUumfhlp+/ehwGLLd9HsQd05qaph3VNK21pmmRwIDcx84BrYC1mqZd0DTtAjAfeAKokvuabE2vOKcBNfLxPQghDFY7qDaTmkzCxd6F5xc+T0pWitGRhK1w84O4ftBrGzw1HtwCYNEAfTXq7J5wYrvRCf8VpRSxpb0ZnlSF9AH1+CCxApoG76RsJ2bwEnpP3cS6faeluW8hk5+FWwYQppQKVko5AO2B1NtfoJTyUervces30adAAQ6RuxhBKWUP1AF2AkeAcKWUb+7r6uc+LoQoxEI8Q5jcZDJVi1Xl7VVv82nGp9y8Jff1iAdkttd7vj2/ALqt1D/enAxjasCEprAjBW7eMDrlv+LhbE+n6qWY17MWc16pSduoIBbvOEHSN2uJ/2wFY1dkc+pPae5bGORb4aZp2g30FZ8L0YuraZqmbVdKDVJKtch9WRywWym1B/ADBuc+PgPIBrYCm4HNmqbN1jTtKPA+sFIptQV9BG5Ifr0HIYT18HTyZEz9MbQv254fdvxAj2U9+PPan0bHErYmoDIkfqEvZqg/CM4dgmn/gVERsPJTuHDK6IT/WsVADz5sWYn0AfX4rG1lfF0d+Wj+LqoPXUq3iZks33WSm7dkFM5W5evOCZqmzQPm3fHYu7d9PAO9SLvzvJtAt3t8zbHA2EebVAhhC+xN9gx4YgBhXmEMXTeUjvM68nn855R0L2l0NGFrXIrqbUSq94A9CyH9G1j2Aaz4WB+Ri3kRAqsZnfJfcXYw06ZaEG2qBZF18gLTM3OYsf4wC7efIMDDibbVgmgbZcFS1MXoqOIfkC2vhBA2p13ZdgR7BNMrrRdPz32atmXaMm//PI5fPI5/EX96Vu1J09JNjY4pbIHJDOWa6MepPZAxDjZNhs1T9MItphtUaAl2jkYn/VdCi7nyZpPy9GlQlmW7TpCckcPny7P4fHkWNUN9SIq2UD/cD0c7WZVq7WTLKyGETYr2j2ZK0yk4mZ34btt3HLt4DA2NYxePMXD1QObum2t0RGFrfMtAk2H6NGrjYXDlPMzqqm9wv+xDOHfE6IT/moOdiUYVA/j+uRh+6xfPawll2HfqIj0mb+SJIUv5YM4O9p6QWxCsmRRuQgibZXGzYLpLX64rN68wasMoAxKJQsHJHWK7Qvd06DQLAqP0+99GVoJpneHAKpveWusvgZ7O9KwXxsq+dfnx+RhqhPjw45oD1B+xktZfrWJaZg4Xr9r2oo3CSKZKhRA27cSlE3d9/NjFYyw9uJTaQbWxN0s/K/EQTCYIidePPw7oW2ltmAg7fgG/ivp9cJXagYNt3yNmNilql/GldhlfTl+4yqyNR5iSfoi+M7YwaPYOmlcuTvtoCxFBHuRuGy4MJIWbEMKm+Rfx59jFY//ncZMy8Vraa3g6etIkuAmJoYmUL1pe/uERD8erFDT4EOLegq3T9cUMs3vC4nchshNEvwBFg41O+a95uzryQq3SdKkZzPqDf5CckcMvuYVcOX832kdbaBkZiKeLg9FRH1syVSqEsGk9q/bEyez0P485mZ34oMYHfJnwJbEBsUzfM52kOUm0Tm3ND9t/4PfLvxuUVtg8Bxeo1hn++xs8N18fjVs7BkZHwuQkyFoCt24ZnfJfU0oRVaoon7atzLoBCQxuVREHOxMDZ+8gZshSeiZvZHX279yStiIFTkbchBA27a/Vo6M2jLrrqtLaQbU5d/UcC/YvIDU7lU8zP2XE+hE8GfgkiSGJxFnicDDL6IH4h5SCkjX04/xRyJwA6yfApAXgHapvrVXlaf1+ORvn7mRPx9iSdIwtyfaj55iWkcOsjUdI2XSUkt4utIuy0LZaEMXcnfL+YuJfy7e9Sq2J7FX6aMg+ibZNrp9u39l9pGSnMCd7Dicvn8TdwZ3GwY1pGdqSCt4VrHoqVa6hlbtxVd+FIf0bOJwBDq5QuT3EdAXfskDhuYZXrt9kwbbjJGccYu2+M5hNirpli9E+2kJcWV/szIVzQs8a9iqVETchxGOltGdpelXrxauRr7L22FpSslL4JesXpu6eSohHCC1CW9CsdDOKuRQzOqqwNXaOENFOP45sgPRxsOFHfVFDcB2I7QZa4RiVcrI30zIykJaRgez//SLTMnOYnnmYJTtPUMzNkbZRQbSLslDSu4jRUQsdGXETD6yw/Kb4uJLrd2/nr51n4YGFpGSlsPnUZkzKRI3iNUgMSaRuibo4mq2j+apcQxt08XfY8ANkfAfnj3DFsRhOtbpD1f/ouzcUItdv3mL5rpNMzchh+e6T3NKgRog37WNK0CDcDyd722/uKyNuQghhBdwd3Glbpi1ty7Rl/7n9zM6eTWp2Km+sfAM3Bzcal2pMi9AWRPhEWPVUqrBCRXygVh+o0RN2z+Pyoo9xWvIepA2FSk/p06gBlY1O+UjYm000qOBPgwr+HD93hRnrc5iamcOrUzbi6WJPq8hAkqItlPO3/fv+jCSFmxBC3CbYI5hXq75K9yrdST+eTkp2CqnZqUzbM41S7qVIDE2kWelm+BfxNzqqsCVmOwhvweaT7sSVL6bfB7dlKmycBJZYvYAr3wLsCsdCGX8PJ3rEh/FyXCirs0+TnHGIn9YeYsKqA1SxeNI+2kKzysVxdZQy5J+S/2NCCHEXZpOZ6sWrU714dS7EXmDRwUWkZKUwasMoRm8YTfXi1WkR0oL4EvE42zkbHVfYEr9waD4S6g2ETT/p98LN7AKu/hD1HFR7FtwKxy8GJpOiZpgPNcN8OHPxGrM2HmFqxiH6/7yVQXN20DyiOEkxFiItnjKa/YCkcBNCiDy4OrjSOqw1rcNac+j8IVKzU0nNTqX/r/1xtXelYamGJIYmUsW3ivzjIx6csydU7w6xL+n939K/0adQV34K4Yn6KJwlRm89UggULeJAl5rBPP9kKTbmnGVqeg6ztxxlamYOZfxcSYouQavIQIoWKRyjjvlFCjchhPgHSriXoEdkD16u8jKZxzNJyU5h3v55zNw7k5LuJWkR0oLmpZsT4BpgdFRhK0wmKNNAP05n66tQN06CbTP0+99iukLFNmBfOEZ2lVJULeFF1RJevNM8nDmbj5KckcMHc3bw8fxdNKjgR/voEtQI8cZkKhxF66MkhZsQQjwEkzIRExBDTEAMb8W+xeKDi0nJSuHzjZ/zxcYviAmIITEkkYQSCbjY2/ZelqIAeYdAo6FQd4B+D1z6OEjpDove0VeiRncBzxJGp3xkXB3taB9TgvYxJdh1/DxTc5v7ztlyjCAvZ5KiLDwVFUSAR+EoWh8FKdyEEOJfKmJfhJahLWkZ2pKcP3OYkz2HlOwU3vrtLVzsXP6eSq1arKpMpYoH4+iqF2lRz8OBX2Hd17B6tH6UbaKPwgXXLjTTqADl/N15r3kF+jUqx6IdJ5iacYjPFu9hxJI9xOU2961brhj2hbS574OSwk0IIR4hi5uFl6q8RLfK3Vh/Yj2p2aksOLCAWVmzCHINokVoC1qEtCDQNdDoqMIWKKUXaMG14WwOZH4H63+AXXPAtxzEvAgR7fVCr5BwsjfTonJxWlQuzqHTl/Tmvutz6DrxJL5ujjxVTW/uG+zzeDb3fbzLViGEyCcmZSLaP5oPnvyAtHZpDK45mEDXQL7a9BWNZjbi+YXPk5KVwqXrl4yOKmyFp0Vfidp7J7QcA3ZOMLcPDC8P8/vD71lGJ3zkSni78HrDsqzqF8+3/4micpAn36zcR91P02j/zRp+2XiEK9dvGh2zQMmImxBC5DMXexdahOgjbUcvHGV29mxSslN4e9XbDF43mAYlG5AYmkg1v2qYlPw+LfJg76RvYF+5AxzOhPSv9QUN68ZAaD19GjW0vr7ooZCwM5uoF+5HvXA/Tpy/woz1h5mWmcNrUzfhnmKX29y3BOHFC39zXynchBCiABV3LU63yt3oGtGVjSc3kpKdom+3lZ1CoGsgzUOa06J0CyzuFqOjCmunFFii9aPBYFj/PWSOh8ntwKsURL8IkR3B2cvopI+Un7sT3euG8lKdENbuP83UjBymZOTww5qDRAR5kBRtoUXl4rg52RsdNV8UnnJcCCFsiFKKqn5Veb/G+yxvt5yhtYZicbPw9eavaTKrCZ3nd2bW3llcvH7R6KjCFrj5QVw/6LUNnhoPbgGwaAAMD4fZPeHEdqMTPnImk6JGiA+j2keS/lYCA5uHc+3GLQbM2kbM4KW8Pn0zmQfOUNj2ZJcRNyGEMJiznTPNSjejWelmHL94/O+p1HdXv8vQ9KHUK1GPFqEtuKXdMjqqsHZme73nW8U2cGyz3k5kc7I+Gleypr6YoVwzfQuuQsTTxYFnnwymc41SbDl8juSMHFI3HWHG+sOE+BahfXQJWlcNxNvV0eio/1rhunJCCGHj/Iv482LEi7xQ6QU2n9pMSnYKC/YvYPa+2XiZvdi+cTuJIYmUcC88vbxEPgmoDIlfQP1BsHGifh/c9M7gHqhvrVX1WXD1NTrlI6WUorLFk8oWT95uWp65W48xNSOHwfN28snCXdQP15v71gz1sdnmvqqwDSHeTVRUlJaZmWl0DJuXlpZGXFyc0THEQ5LrZ7uu3LjC8pzlTEifwO6ru7ml3SKyWCSJIYk0KNUANwc3oyOKB2To9+Gtm7Bnob611r7lYHaACq0htisEVjMmUwHZe+JPpmbkMHPDYf64dJ1AT2faRVloGxVEcc8Hb+5bUNdPKbVe07Souz0nI25CCGHlnOycaBzcGOeDzpSPLs+cfXqD34FrBjI0fSgJJRJIDE0k1j8Ws8lsdFxhrUxmKNdEP07tgYxxsGkybEnWC7eYblChJdjZ/nTincL83Hi7WThvNCrLkh0nSc44xMilexi5dA91yvjSPtpCfDk/HOys/9Z/KdyEEMKG+BXxo0ulLjxf8Xm2/r6V1OxU5u2fx7z98yjmUuzvtiPBHsFGRxXWzLcMNBkG8e/o98ClfwOzuuoLGqo9C9WeA4/C1yTa0c5M04gAmkYEkHPmEtPXH2Z6Zg7/nbQBH1cH2lQNol20hRBf621oLFOl4oHJVJttk+tn++51Da/evEpaThopWSmsOrqKW9otInwjSAxJpFFwI9wdCn9vK1thtd+Ht27B/jRY9w3sWQDKBOWb6aNwJWsUqq217nTzlsbKvaeYmp7Dkp0nuHFLI6ZUUZKiLTSpFICzg5lfNh5h2MLdHDl7mUBPZ95oWJaWkflX2Bo2VaqUagSMAszAt5qmfXTH8yWB8YAvcAZ4RtO0w7nPfQI0RW9ZshjoqWmappRyAL4A4oBbwABN02bm5/sQQghr5mh2pGGphjQs1ZBTl04xd99cUrJT+GDtB3yc/jHxJeJJDE2kekB1mUoVd2cyQUi8fvxxQF/IsGEi7EgBv4r6atRKbcGh8G0zZTYp6pYtRt2yxTj55xV+3nCEqRk59Jm+mYGp24kIcifz4Fmu3tBXdR85e5k3f94KkK/F273k22SuUsoMfAk0BsKBDkqp8Dte9inwo6ZpEcAgYGjuuTWAJ4EIoCIQDdTJPWcAcFLTtDK5X3dFfr0HIYSwNb4uvjxb8Vl+bvEzyU2TaVOmDWuOreGlJS/RYEYDhq8fTvbZbKNjCmvmVQoafKhvrdV8tP7Y7J761loLB8CZ/YbGy0/F3Jz4b50QlvWpw9SuT1A/3I9V2Wf+Ltr+cvn6TYYt3G1IxvwccYsBsjRN2weglEoGEoEdt70mHOiV+/Fy4JfcjzXACXAAFGAPnMh97nmgHICmabeA3/PvLQghhG1SSlHBpwIVfCrwetTrrDi8gtSsVH7c/iMTtk2gondFEkMTaRzcGA9HD6PjCmvk4ALVOkPV/8ChNfp9cGvHwJovoUxDfRSudHyh2lrrL0opYkt7E1vam1kbj3C3m8qOnr1c4LkgH+9xU0o9BTTSNO2F3M87AbGapvW47TWTgXWapo1SSrUGZgI+mqadVkp9CryAXrh9oWnaAKWUJ7AVmI4+VZoN9NA07QR3UEp1BboC+Pn5VUtOTs6X9/k4uXDhAq6u1nvDprg/uX6271Fcw/M3z5N5MZN1F9Zx9PpR7LCjoktFYovEUt65PGYlU6n5yda/Dx2unqb40QUUP7oQh+vnuORcnCOBTTjun8BNOxej4+WLPmmXOH3l/9ZK3k6Kz+Ly5z3XrVv3nve45Wfh1hZoeEfhFqNp2iu3vaY4+v1qwcBKoA1QAf2et1FAUu5LFwP90EfrTgFPaZo2UynVG4jUNK3T/bLI4oRHw2pvqhUPRK6f7XuU11DTNHad2UVKdgrz9s3jj6t/4O3kTbPSzUgMTSTMK+yR/DnifxWa78MbV/X739K/gcMZ4OAKldvrG9z7ljU63SP1y8YjvPnzVi5fv/n3Y872Zoa2rpRv97gZtTjhMHD7LslBwNHbX6Bp2lGgNYBSyhVoo2naudzRsrWapl3IfW4+8ATwK3AJmJX7JaYDXfLxPQghRKGklKK8d3nKe5enT7U+rDyykpSsFH7a+RM/7PiBcO9wWoS0oElwE7ycCtcm5eIRsHOEiHb6cWSDvrXWhh/1RQ3BdfQCrmxjvXecjfurOCvIVaX3k58T0xlAmFIqOHclaHsg9fYXKKV8lFJ/ZXgTfYUpwCGgjlLKTillj74wYaemDw/ORp8mBUjgf++ZE0II8Q/Zm+1JKJHA6PjRLG23lH7R/dA0jY/SPyJ+ejy9lvdi+aHlXL913eiowhoFVoVWY/TFDAnvwuksmNoRRlWB30bApTNGJ/zXWkYGsqp/PN83KsKq/vGGFW2QjyNumqbdUEr1ABaitwMZr2nadqXUICBT07RU9AJsqFJKQ58q7Z57+gwgHv1+Ng1YoGna7Nzn+gETlVIj0adNn8uv9yCEEI+bok5FeSb8GZ4Jf4bdZ3aTkp3C3H1zWXJoCUWditK0dFMSQxIpW7RwTYeJR6CID9TqAzV6wu55+jTqkoGQ9hFUfErfWiugstEpbV6+9nHTNG0eMO+Ox9697eMZ6EXanefdBLrd42seBGo/2qRCCCHuVLZoWfoW7Uuvar1YdWQVKVkpTNk1hYk7JlKuaDkSQxJpUroJRZ2KGh1VWBOzHYS30I8TO/QCbstU2DQJLLH6NGr5FmDnYHRSmyRbXgkhhLgve5M9cZY44ixxnL1ylnn755GSncLHGR/zWeZn1AqqRWJoIrUDa2Nvtjc6rrAmfuHQfCTUGwibftLvhZvZBVz9Ieo5fXstN3+DQ9oWKdyEEEI8ME8nT54u/zRPl3+avX/sJTU7ldnZs1mesxwvRy+alG5CYkgi5YqWQxXibZLEP+TsCdW7Q+xLkLVEH4VLGworh0F4S30UzhJTqLfWelSkcBNCCPFQwrzC6BPVh55Ve7L66GpSslKYtnsaP+38iTCvMBJDEmlauik+zj5GRxXWwmSCMg3043S2vgp14yTYNkO//y2mK1RsA/bORie1WoWv3bEQQogCZWeyo3ZQbT6L+4zl7ZbzduzbOJmd+DTzU+pNr0ePpT1YfHAx125eMzqqsCbeIdBoqL4atelwuHENUrrD8HBY/B6cPWR0QqskI25CCCEeGQ9HD5LKJZFULol9Z/eRkp3C7OzZrDi8Ag9HDxqXakzL0JaEe4fLVKrQObpCdBeIeh4O/ArrvobVo/WjbBN9FC64tkyj5pLCTQghRL4o7VmaXtV68UrkK6w9tpbUrFR+3vszybuTCfEIITE0kWalm+Hr4mt0VGENlNILtODacDYHMr+D9T/ArjngW07fGzWivV7oPcZkqlQIIUS+sjPZUTOwJp/U+YTlSct5t/q7uDq4Mnz9cOrNqMdLS15iwYEFXL151eiowlp4WvSVqL13QssxYOcEc/vA8PIwvx/8nmV0QsPIiJsQQogC4+7gTtsybWlbpi37z+1ndvZsUrNTeWPFG7g5uNG4VGMSQxOp5FNJplIF2DtBlaehcgc4nAnpX0PGd7BuLIQkQGw3CK2vL3p4TEjhJoQQwhDBHsG8WvVVulfpzrrj60jNTiUlO4Vpe6YR7BFMi5AWNC/dHL8ifkZHFUZTCizR+tFgMKz/HjLHw+R24FUKol+EyI7gXPj31ZXCTQghhKHMJjM1itegRvEa/Bn7J4sOLCI1O5VRG0bx+cbPqR5QncTQROpa6uJk52R0XGE0Nz+I6we1esPOVL2p76IBsHywvul9TFfwq2B0ynwjhZsQQgir4ebgRpsybWhTpg0Hzx8kNTuV1OxU+q7si5u9Gw2DG5IYkkhl38oylfq4M9vrPd8qtoFjm/UCbnOyPhpXsqa+mKFcM30LrkKkcL0bIYQQhUZJ95K8EvkK3at0J+N4BilZ+ob3M/bMoKR7SRJDEmke0hz/IrJl0mMvoDIkfgH1B8HGiXpj3+mdwT1Q31qr6rPgWjhWLz8+d/MJIYSwSSZlIjYgliG1hrC83XIG1RiEj7MPozeOpsGMBry46EXm7JvD5RuXjY4qjOZSFJ7sCa9ugvZTwCcMln0II8Lh525weL3RCf81GXETQghhM4rYF6FVWCtahbUi58+cv1elvvnrmxSxL0LDUvpUamSxSJlKfZyZzFCuiX6c2q2PwG2aDFuSIbCafh9chVZg52h00n9MRtyEEELYJIubhZervMy81vMY33A89UrUY/7++XRe0Jmms5oydvNYjl44anRMYTTfstBkmN4TrvEwuHIeZnXTt9Za+gGcO2J0wn9ECjchhBA2zaRMRPtH82HND0lrl8bgmoMJKBLAl5u+pOHMhnRZ2IXU7FQuXb9kdFRhJCd3iO0K3dOh0ywIioZfP4ORlWDaf+DAKvh/7d15dFXlvf/x95cQhhBAJBAmISSRakBACKjUKwQkRiA5tVWqyzor1euA+kOK19Z6ccCpy+E6e7VOt1q1bU4QuFGGiBYEEQUF1CaAEMWqVVEcGb6/P/aGe4wJCcPJyYHPa60s9tn72Wd/9nkIfNfz7H22e6JT1ktTpSIiss9IS02jJKeEkpwS3t/0PtOrphOtjHLVy1dxffPrGd1rNJHcCIMzB9PMNHaxX2rWDHJGBj+frQ2mUZc+DiujkNkvuBv1sJOgRZtEJ62V/taKiMg+qXt6d84fcD4zfz6TR4oeoah3EbPXzebs8rMZ89cx3PPGPaz/cn2iY0oidciCwuuCadTiO4N10ycGj9Yqvwo+XROsW/403NaP4RU/g9v6Ba8TRCNuIiKyTzMzBmcOZnDmYH4z5DfMWTeHsqoy7lt2H/cuu5f8zHxKckoozCqkTWrTHGWROGuRBoPPgEGnw7qFsPgBeOVeWHh3MAr3ybuw9TsMYON6mH5JsF//8Y0eVYWbiIjsN9JS0yjOKaY4p5gNmzYwfXVwV+rVC65m2uJpjO41mpKcEoZ0GaKp1P2RGfQaFvx88QEs+SO8dCv4th+22/wNzJmqwk1ERKSxdE3vyoT+EzjvsPNY9vEySitLKV9bTllVGV3bdKU4p5hIToSe7XomOqokQrtuMPIqmH9L7ds3VjdunpAKNxER2a+ZGQM7D2Rg54FMGTqFuevmEq2K8uDyB3lg+QMM6jyIkpwSjss6jvQW6YmOK42tfY9gerS29QmgcWAREZFQq+atGJM9hvtH38/zJz7PxEET+ey7z7hm4TUUPF3AlJemsOCDBWzdtjXRUaWxjLoaUlv/cF1q62B9AmjETUREpBZd2nTh3MPO5Zx+5/DmJ28SrYwya+0sZqyeQWZa5o6vHclqn5XoqBJP269jmzMV31iNte8RFG0JuL4NVLiJiIjslJnRv1N/+nfqz+Shk5m3fh7RyigPvfUQD775IAM6DSCSG+G4rONo16JdouNKPPQfD/3H82JFBSNGjEhoFBVuIiIiDdQypSVFWUUUZRXx0dcfMWP1DKKVUaYunMqNi25kVM9RRHIjHNn1SFKapSQ6ruyDVLiJiIjshs5pnTmr31mc2fdMVv5rJaWVpcxcM5NZa2fRuXVnxuWMI5ITIfuA7ERHlX2ICjcREZE9YGb0zehL34y+XDHkCl6sfpFoZZRHVzzKw289zGEZhxHJiVDUuyjRUWUfENe7Ss2syMzeMbNKM5tSy/ZeZjbHzJabWYWZ9YjZdrOZrTCzVWZ2p5lZjX3LzOyteOYXERHZFS1SWjC612juGnUXs0+azaT8SXyz5RuuW3QdBU8X8PDHDzO/ej5btm1JdFRJUnEbcTOzFOBuYDRQDbxqZmXuvjKm2a3AY+7+qJmNBKYBp5nZMOCnQP+w3cvAcKAifO+fA5vilV1ERGRPZbTO4Iy+Z3B63ums+nQVZVVllL5TyoVzLiSjdQbjssdRklPCwR0OTnRUSSLxnCodClS6+2oAM3sKiACxhVsecFm4PA8oDZcdaAW0AAxIBf4Zvk86cDkwAUjcU15FREQawMzI65hHXsc88r/Kx7KNaFWUJ1Y+wSMrHiGvYx6RnAhjeo/hgFYHJDquNHHxnCrtDsR+1XB1uC7WMuAX4fIJQFsz6+juCwkKuQ3hT7m7rwrbXQv8Afg6XsFFRETiobk1Z1SvUdw58k5mnzSb3wz5Ddt8G9MWT6PgmQIum3cZFesr2Lxtc6KjShMVzxE3q2Wd13g9CbjLzM4E5gPvA1vMLBc4FNh+zdsLZnYM8AWQ6+6XmVnWTg9uNoFgVI7MzEwqKip27yxkh02bNulzTGLqv+SnPkx+NfuwBz24sO2FVLesZvGmxbxS/Qqz182mbVOIgS8AABRMSURBVLO25LfJ54j0I+jeouaYhyRKU/gdNPeatdReemOzo4Br3P248PWVAO4+rY726cDb7t7DzK4AWrn7teG2q4FvgS+B3wHfExSdnYEF7j5iZ1ny8/N9yZIle+W89mcVTeCLB2X3qf+Sn/ow+dXXh5u3bebl6pcpqyqjorqCLdu2cOiBh1KSU8KY7DEc2OrAxgsrP9JYv4Nm9pq759e2LZ5Tpa8CB5tZbzNrAZwMlNUIlmFm2zNcCTwcLq8DhptZczNLJbgxYZW73+vu3dw9CzgaeLe+ok1ERCRZpDZLpaBnAbcV3Mbck+YyZegUzIybXr2JUU+PYuLcicxZN4fNWzWVur+K21Spu28xs4uAciAFeNjdV5jZVGCJu5cBI4BpZuYEU6UXhrs/C4wE3iSYXv1fd58er6wiIiJNTYdWHTj10FM59dBTefezdymrLOO51c8xd/1cOrTswNjssURyIxxy4CGJjiqNKK5fwOvuM4GZNdZdHbP8LEGRVnO/rcCv63nvtUC/vRJURESkCevToQ+Thkzi0sGXsuCDBZRWlvLnd/7ME6ueoE+HPkRyIozNHkvH1h0THVXiTE9OEBERSRLNmzXnmB7HcEyPY9j43UZmrZlFtDLKLUtu4bbXbuPo7kcTyY0wvMdwUlNSEx1X4kCFm4iISBJq37I9Jx9yMicfcjJVn1cRrYryXNVzVFRXcEDLAzi+9/FEciPkHZhHjYcPSRJT4SYiIpLkcg7I4fLBl3PJ4ZfwyoZXiFZG+cu7f+HJt58k94DcHVOpndI6JTqq7CEVbiIiIvuI5s2ac3T3ozm6+9Fs/G4j5WvLiVZF+cNrf+D2pbczrNswIrkRRhw0gpYpLRMdV3aDCjcREZF9UPuW7Rn/k/GM/8l41mxcQ1lVGWVVZUx6cRLtWrQLplJzIvTL6Kep1CSiwk1ERGQf17t9byYOmshFAy9i0YZFRKuiO+5MzW6fTUlOCeOyx5HZJjPRUaUeKtxERET2EynNUhjWfRjDug/jy++/pHxtOWVVZdy+9HbufP1Ojup2FJGcCAUHFdCqeatEx5VaqHATERHZD7Vt0ZYT+5zIiX1O5L0v3iNaGWX66ulMnj+ZtqltKepdRElOCQM6DdBUahOiwk1ERGQ/16tdLy4ZdAkXHX4Riz9cHBRxVdN55t1nyGqXRSQ3wrjscXRp0yXRUfd78XxWqYiIiCSRZtaMI7seybR/m8a88fOYOmwqHVt35I6ld1D4bCETnp/AjNUz+GbLN4mOut/SiJuIiIj8SHqLdE44+AROOPgE1n+xnrLVZUyvms6Ul6bQJrUNRVlFRHIjDOw0UFOpjUiFm4iIiOzUQe0O4sKBF3LBgAt47Z+vUVpZysw1M/nLP/5Cz7Y9KckpoTinmG7p3RIddZ+nwk1EREQapJk1Y0iXIQzpMoSrjriKF957gWhVlLveuIu73riLI7ocQSQ3wqieo0hLTUt03H2SCjcRERHZZWmpaURyI0RyI7y/6f3gC34ry/iPl/+DtOZpFGYVEsmJMChzEM1Ml9TvLSrcREREZI90T+/OBQMu4Pz+57P0o6VEK6OUry2ntLKU7undieREKM4ppkfbHomOmvRUuImIiMheYWYMzhzM4MzBTBk6hTnr5hCtinLvsnu5Z9k95GfmE8mNUNirUFOpu0mFm4iIiOx1aalpFOcUU5xTzIZNG5i+ejrRyii/+/vvuGHRDYzuNZpIToT8LvmaSt0FKtxEREQkrrqmd2VC/wmcd9h5vPHxGzumUsuqyujWphvFOcVEciIc1O6gREdt8lS4iYiISKMwMw7vfDiHdz6cKUOnMHfdXKJVUR5Y/gD3L7+fQZ0H7ZhKTW+Rnui4TZIKNxEREWl0rZq3Ykz2GMZkj+HDrz7kudXPEa2M8vsFv2faomkc2+tYSnJKOKLrEZpKjaHCTURERBKqS5sunHvYuZzT7xyWf7KcssoyZq2ZxXOrn6NLmy4UZxcTyY3Qq12vREdNOBVuIiIi0iSYGQM6DWBApwFMHjqZeevmEa2K8tBbD/Hgmw8ysNNASnJLKMoqom2LtomOmxAq3ERERKTJaZnSkqLeRRT1LuKjrz/aMZU6deFUblp8EyN7jiSSE+HIrkeS0iwl0XEbjQo3ERERadI6p3Xm7H5nc1bfs1jxrxWUVpYya80sZq2ZRee0zhRnF1OSW0J2++xER407FW4iIiKSFMyMfhn96JfRj8lDJlOxvoJoVZRHVjzCQ289RP+M/kRyIxyXdRztW7ZPdNy4UOEmIiIiSadFSgsKswopzCrkk28+YcbqGZRWlnLtK9dy0+KbKOhZQCQnwlHdjqJ5s32n3Nl3zkRERET2SxmtMzij7xmcnnc6qz5dRbQyysw1MylfW06n1p0Ylz2OkpwScjvkJjrqHlPhJiIiIvsEMyOvYx55HfOYlD+J+dXzKa0q5fGVj/PHFX+kX8d+lOSWMKb3mKSdSo3rN9qZWZGZvWNmlWY2pZbtvcxsjpktN7MKM+sRs+1mM1thZqvM7E4LpJnZDDN7O9x2Yzzzi4iISHJKTUllVK9R/NfI/2L2SbOZPGQym7dt5oZFN1DwdAGXV1zOi+tfZMu2LYmOukviNuJmZinA3cBooBp41czK3H1lTLNbgcfc/VEzGwlMA04zs2HAT4H+YbuXgeHAYuBWd59nZi2AOWZ2vLvPitd5iIiISHLr2Lojp+Wdxml5p/H2p28TrYwyY/UMXnjvBTq26sjY7LFEciP06dAn0VHrFc+p0qFApbuvBjCzp4AIEFu45QGXhcvzgNJw2YFWQAvAgFTgn+7+ddgOd//ezJYCPRARERFpgEMOPIRDhh7C5YMv56X3X6Ksqow/rfoTj618jEMPPJRIboQxvcfQoVWHREetVTynSrsD62NeV4frYi0DfhEunwC0NbOO7r6QoEDbEP6Uu/uq2B3N7ACgGJgTh+wiIiKyD0tNSWVkz5HcXnA7c8bPYcrQ4IquGxffyMhnRnLpvEuZu24um7dtZsbqGRQ+W8jF711M4bOFzFg9I2G5zd3j88ZmJwHHufu54evTgKHufnFMm27AXUBvYD5BEdcX6ATcAfwybPoC8Bt3nx/u1xyYTlDQ3V7H8ScAEwAyMzMHP/XUU3v9HPc3mzZtIj09PdExZDep/5Kf+jD5qQ+bvve/f59Fmxax5KslfLntS1rSks1sZhvbdrRJtVROOfAUhqQPiUuGgoKC19w9v7Zt8SzcjgKucffjwtdXArj7tDrapwNvu3sPM7sCaOXu14bbrga+dfebw9cPA5vc/ZKGZMnPz/clS5bs8Tnt7yoqKhgxYkSiY8huUv8lP/Vh8lMfJo/N2zaz4P0FTHpxEt9u/fZH27u26crzJz4fl2ObWZ2FWzynSl8FDjaz3uGNBCcDZTWCZZjZ9gxXAg+Hy+uA4WbW3MxSCW5MWBXucx3QHrg0jtlFRERkP5baLJXhBw3nu63f1br9w68+bOREgbgVbu6+BbgIKCcoup529xVmNtXMSsJmI4B3zOxdIBO4Plz/LFAFvElwHdwyd58efl3IVQQ3NSw1szfM7Nx4nYOIiIjs37q06bJL6+Mtrl/A6+4zgZk11l0ds/wsQZFWc7+twK9rWV9NcJepiIiISNxNHDSRaxZc84Pp0lYprZg4aGJC8ujJCSIiIiJ1GJs9FoA7lt7Bhq820LVNVyYOmrhjfWNT4SYiIiKyE2OzxzI2e2yTuLkkro+8EhEREZG9R4WbiIiISJJQ4SYiIiKSJFS4iYiIiCQJFW4iIiIiSUKFm4iIiEiSUOEmIiIikiRUuImIiIgkCRVuIiIiIklChZuIiIhIkjB3T3SGuDOzj4H3Ep1jH5ABfJLoELLb1H/JT32Y/NSHya2x+q+Xu3eqbcN+UbjJ3mFmS9w9P9E5ZPeo/5Kf+jD5qQ+TW1PoP02VioiIiCQJFW4iIiIiSUKFm+yKBxIdQPaI+i/5qQ+Tn/owuSW8/3SNm4iIiEiS0IibiIiISJJQ4SY/YGZFZvaOmVWa2ZRatl9uZivNbLmZzTGzXonIKXWrrw9j2p1oZm5musOtiWlIH5rZ+PB3cYWZ/amxM0rdGvDvaE8zm2dmr4f/lo5JRE6pm5k9bGYfmdlbdWw3M7sz7OPlZjaosbKpcJMdzCwFuBs4HsgDTjGzvBrNXgfy3b0/8Cxwc+OmlJ1pYB9iZm2BS4BFjZtQ6tOQPjSzg4ErgZ+6e1/g0kYPKrVq4O/gb4Gn3f1w4GTgnsZNKQ3wCFC0k+3HAweHPxOAexshE6DCTX5oKFDp7qvd/XvgKSAS28Dd57n71+HLV4AejZxRdq7ePgxdS1B0f9uY4aRBGtKH5wF3u/tnAO7+USNnlLo1pP8caBcutwc+aMR80gDuPh/4dCdNIsBjHngFOMDMujZGNhVuEqs7sD7mdXW4ri7nALPimkh2Vb19aGaHAwe5+3ONGUwarCG/h32APmb2dzN7xcx2NjIgjash/XcN8CszqwZmAhc3TjTZi3b1/8u9pnljHESShtWyrtbbjs3sV0A+MDyuiWRX7bQPzawZcBtwZmMFkl3WkN/D5gRTNCMIRr1fMrN+7v55nLNJ/RrSf6cAj7j7H8zsKODxsP+2xT+e7CUN/v9yb9OIm8SqBg6Ked2DWobwzexY4CqgxN2/a6Rs0jD19WFboB9QYWZrgSOBMt2g0KQ05PewGoi6+2Z3XwO8Q1DISeI1pP/OAZ4GcPeFQCuCZ2BK8mjQ/5fxoMJNYr0KHGxmvc2sBcFFs2WxDcJptvsJijZdV9P07LQP3X2ju2e4e5a7ZxFcp1ji7ksSE1dqUe/vIVAKFACYWQbB1OnqRk0pdWlI/60DRgGY2aEEhdvHjZpS9lQZcHp4d+mRwEZ339AYB9ZUqezg7lvM7CKgHEgBHnb3FWY2FVji7mXALUA68IyZAaxz95KEhZYfaGAfShPWwD4sBwrNbCWwFbjC3f+VuNSyXQP77/8BD5rZZQTTa2e6vg2/STGzJwkuRcgIr0X8PZAK4O73EVybOAaoBL4Gzmq0bPq7IiIiIpIcNFUqIiIikiRUuImIiIgkCRVuIiIiIklChZuIiIhIklDhJiIiIpIkVLiJSFIxs4rtXxhsZjPN7IBEZ9qbzOxMM+vWCMdpbWYvmlmKmf3EzF4zs2XhN/ljZs3NbLaZpcXs81T4gHsRSRAVbiKStNx9TFN4zJOZpezFtzsTiHvhBpwN/NXdtwK/BqYAJwKTwu0XAI+7+9cx+9wLTG6EbCJSBxVuIrJHzKyNmc0IR2veMrNfhuuvNrNXw3UPWPiNzeGI2W1mNt/MVpnZEDP7q5n9w8yuC9tkmdnbZvaomS03s2djR35ijr3WzDLC9qvM7EEzW2Fmz5tZ67DNkPA9FprZLWb2Vi3vMyLM8zczW2lm94XPdcXMCsN9l5rZM2aWHnPsq83sZeAkM8sNR6iWhW1zwnZXhJ/DcjP7z5jz+1FeMzuR4BnA/2Nmb4Tr6vocaz2vcATtlphj/rqOrjsViIbLm4HWQBqwORzFLAYeq7HPS8CxZqYvbxdJEBVuIrKnioAP3H2Au/cD/jdcf5e7DwnXtQbGxezzvbsfA9xHUDxcSPAM1TPNrGPY5ifAA+7eH/gC+Pd6chwM3O3ufYHPgV+E6/8InO/uRxE8ZaAuQwm+0f4wIAf4uQWPk/otcKy7DwKWAJfH7POtux/t7k8B/xMefwAwDNhgZoVhrqHAQGCwmR1TV153fzY8xqnuPtDdv9nJ51jXeZ1D8PidIcAQ4Dwz6x17ohY8iinb3deGq+4Oz+s+4AbgauD6mt/mHz4EvRIYsJPPUUTiSIWbiOypNwlGYW4ys39z943h+gIzW2RmbwIjgb4x+5TF7LvC3Te4+3cEz9vc/uDm9e7+93D5CeDoenKscfc3wuXXgKxw5Kituy8I1/9pJ/svdvfV4dThk+HxjgTygL+b2RvAGUCvmH3+DGBmbYHu7v43AHf/NpxiLAx/XgeWAofwfw+D/1HeOnL96HOs57wKCZ6h+AawCOjIjx9An0FQLBLmXefuI8Ii8GuCqdq3zexxM/uzmfWJ2fcjGmcqV0RqoeFuEdkj7v6umQ0meG7fNDN7HrgZuAfId/f1ZnYNwYO0t/su/HNbzPL219v/Xar5PL76ns8X+z5bCUanrKHnUcfxDHjB3U+pY5+vwj/rOo4B09z9/h+sNMuqIy812rWi9s9xZ+dlwMXuXr6TNt/ww/6IdT3BKOMlBKOIawme03hquL1VuL+IJIBG3ERkj1hwB+TX7v4EcCswiP8rCj4Jrwk7cTfeuuf2OxyBU4CXd/UN3P0z4EszOzJcdfJOmg81s97htW2/DI/3CvBTM8sFMLO0GqNP24/zBVBtZj8L27UMr8krB86OuS6uu5l1rif2l0DbcLnWz7Ge8yoHLjCz1PCYfcysTY28nwEpYWG4g5kNB953938QXO+2jaCojL2+sA+wop5zEJE40YibiOypw4BbzGwbwUXuF7j752b2IMFU6Frg1d1431XAGWZ2P/APgjsad8c5wINm9hVQAWyso91C4EaC85kP/M3dt5nZmcCTZtYybPdb4N1a9j8NuN/MphJ8Die5+/NmdiiwMLynYBPwK3Z+rd0jwH1m9g1wFFDX51jXef03wbTr0vBGho+Bn9VynOcJpoNnA4RtfwuMD7c/QDDi1pzgDlPMLBP4xt037CS/iMSR1bj2VEQk4cKpxOfCC/L39L3S3X1TuDwF6OruE2u0GQFMcvdxtbxFk9SQ86pn/8OBy939tF3Y5zLgC3d/aJcDi8heoRE3EdnXjTWzKwn+vXuP4HvS9gV7dF7u/rqZzTOzlPCGjIb4HHh812KKyN6kETcRERGRJKGbE0RERESShAo3ERERkSShwk1EREQkSahwExEREUkSKtxEREREkoQKNxEREZEk8f8BA5wwnkYAkcsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "baseline_ndcgs, baseline_ndcgs_train\n",
    "als_test_ndcgs, als_train_ndcgs\n",
    "\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(real_percetanges, baseline_ndcgs, marker='o')\n",
    "plt.plot(real_percetanges, knn_test_ndcgs, marker='o')\n",
    "plt.plot(real_percetanges, als_test_ndcgs, marker='o')\n",
    "\n",
    "plt.xlabel('sampling percentage (%)')\n",
    "plt.ylabel('NDCG')\n",
    "plt.title('NDCG Test vs Sample Size')\n",
    "plt.legend(['Baseline Model', 'KNN', 'ALS'])\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For NDCG, we get the highest values when the sample size is the smallest. This can be reasoned based on the fact that the smaller the data, it is likely that there aren't sufficient amount of data for each user/item (sparse). Therefore, we would be calculating NDCG based on the ranking of few items for each user. Despite having high NDCG (which is our goal), this would be an inaccurate evaluation of our model caused by sparsity of the samples. As the sample size increased, NDCG for all three models decreased, with the matrix factorization model having the lowest NDCG. If our sample size were larger with more dense data points, we would be more likely to obtain accurate evaluation of NDCG."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.2 Coverage <a class=\"anchor\" id=\"4-2\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Item Coverage"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 333,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(real_percetanges, baseline_test_item_coverages, marker='o')\n",
    "plt.plot(real_percetanges, knn_item_coverages_test, marker='o')\n",
    "plt.plot(real_percetanges, als_item_coverages_test,a marker='o')\n",
    "\n",
    "plt.xlabel('sampling percentage (%)')\n",
    "plt.ylabel('Item Coverage')\n",
    "plt.title('Item Coverage Test vs Sample Size')\n",
    "plt.legend(['Baseline Model', 'KNN', 'ALS'])\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Item coverage is the fraction of movies that we recommended well to at least k users. We defined 'well' as a movie having a rating greater than 3.0 and we used k=5. Therefore, we would want a higher coverage. For each model, as the sample size increased, the coverage increased. Our matrix factorization model had the lowest item coverage while the neighborhood based model had smilar item coverage as the baseline model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### User Coverage"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 334,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(real_percetanges, baseline_test_user_coverages, marker='o')\n",
    "plt.plot(real_percetanges, knn_user_coverages_test, marker='o')\n",
    "plt.plot(real_percetanges, als_user_coverages_test, marker='o')\n",
    "\n",
    "plt.xlabel('sampling percentage (%)')\n",
    "plt.ylabel('User Coverage')\n",
    "plt.title('User Coverage Test vs Sample Size')\n",
    "plt.legend(['Baseline Model', 'KNN', 'ALS'])\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "User coverage is the fraction of users who we recommend well at least k movies. We defined 'well' as a movie having a rating greater than 3.0 and we used k=3. For each model, as the sample size increased, the user coverage increased. The user coverage for each model is relatively the same."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Catalog Coverage"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 335,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(real_percetanges, baseline_catalog_coverages, marker='o')\n",
    "plt.plot(real_percetanges, knn_catalog_coverages, marker='o')\n",
    "plt.plot(real_percetanges, als_catalog_coverages, marker='o')\n",
    "\n",
    "plt.xlabel('sampling percentage (%)')\n",
    "plt.ylabel('Catalog Coverage')\n",
    "plt.title('Catalog Coverage Test vs Sample Size')\n",
    "plt.legend(['Baseline Model', 'KNN', 'ALS'])\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Catalog coverage is a measure of how many unique items appear in the top-k items over the total number of items. By maximizing coverage, we can assume that the model provides a good variety of items to users. For our largest sample, the matrix factorization model had the highest catalog coverage while the baseline model had the lowest catalog coverage. Similar to the issue we had with NDCG, we can attribute 100% catalog coverage for small sample data to sparsity. For a sparse sample data, it is likely that each user would have rated one to two items on average, so we would be recommending top one or two items out of one or two items they have rated. Although our initial objective was to recommend novel and diverse items to users, we would need to have more dense and larger dataset to have a more accurate measure of catalog coverage. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.3 User Distribution <a class=\"anchor\" id=\"4-3\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since our catalog coverages and NDCGs were unusually high, we wanted to see how our models would perform given different distribution of users. To observe the performance of our model based on different distribution of users, we have split our test data according to active and inactive users. For active users, we chose top-50 users who rated the most number of items. For inactive users, we chose bottom 10,000 users who rated 20 items or more. Both sets of users had similar number of ratings.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 363,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of movies rated by top 50 active users: 206590\n",
      "number of movies rated by bottom 10000 inactive users: 207926\n"
     ]
    }
   ],
   "source": [
    "df = ratings_df.copy()\n",
    "df_ratings_cnt = pd.DataFrame(df.groupby('userId').size(), columns=['count']).sort_values('count', ascending=False).sort_values(by=['count'], ascending=False).reset_index()\n",
    "print('number of movies rated by top 50 active users:',df_ratings_cnt[:50]['count'].sum())\n",
    "print('number of movies rated by bottom 10000 inactive users:',df_ratings_cnt[-10000:]['count'].sum())\n",
    "\n",
    "active_userId = df_ratings_cnt[:50]['userId'].values.tolist()\n",
    "inactive_userId = df_ratings_cnt[-10000:]['userId'].values.tolist()\n",
    "active_user_df = df[df['userId'].isin(active_userId)]\n",
    "inactive_user_df = df[df['userId'].isin(inactive_userId)]\n",
    "\n",
    "dfs = {}\n",
    "dfs['active'] = active_user_df\n",
    "dfs['inactive'] = inactive_user_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 366,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "active\n",
      "RMSE: 1.0331\n",
      "ndcg testing: 0.41272006070946715\n",
      "Catalog Coverage: 1.0395910941696265%\n",
      "\n",
      "\n",
      "inactive\n",
      "RMSE: 1.1734\n",
      "ndcg testing: 0.8916193680878496\n",
      "Catalog Coverage: 91.92812321734169%\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "cols = ['userId','movieId','rating','predicted']\n",
    "test_data = []\n",
    "\n",
    "for item in dfs.keys():\n",
    "    \n",
    "    print(item)\n",
    "    data = Dataset.load_from_df(dfs[item][['userId', 'movieId', 'rating']], reader)\n",
    "    trainset, testset = s_train_test_split(data, test_size=.15)\n",
    "\n",
    "    test_pred = algo.test(testset)\n",
    "    accuracy.rmse(test_pred, verbose=True)\n",
    "    for i in range(len(test_pred)):\n",
    "        test_data.append([test_pred[i][0],test_pred[i][1],test_pred[i][2],test_pred[i][3]])\n",
    "        \n",
    "    testDF = pd.DataFrame(test_data, columns = cols).sort_values(by=['userId', 'predicted'])\n",
    "    test_ratings_dictionary = dict(testDF.set_index('userId').groupby(level = 0).apply(lambda x : x.to_dict(orient= 'records')))\n",
    "    \n",
    "    ndcg_test = ndcg_score(testDF)\n",
    "    print('ndcg testing:', ndcg_test)\n",
    "\n",
    "    totalMovies = []\n",
    "    for i in testset:\n",
    "        totalMovies.append(i[1])\n",
    "    totalMovies = set(totalMovies)\n",
    "    \n",
    "    calculate_catalog_coverage(test_ratings_dictionary, len(totalMovies))\n",
    "    \n",
    "    print('\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For active users, having a significantly low catalog coverage is reasonable given the dense dataset. While we would have a large number of items, we are only recommending top-k movies for 50 users. The number of items in top-k would not be as diverse due to the small number of users. Low coverage value can also be attributed to the fact that these top 50 active users were provided with similar items. One of the reasons for low ndcg values can be attributed to the fact that we excluded ubiquitous items from training data set.\n",
    "\n",
    "For inactive users, we see similar results to the model performance on our initial test set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 5. Conclusion <a class=\"anchor\" id=\"5\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While both of our models scaled relatively well for our sample datasets, they might require offline and online phases to make it more scalable for real datasets. For example, if we were to use item-based CF to recommend items to users, it would be reasonable to calculate the similarity matrix (model training process) offline, and provide rating predictions offline. \n",
    "Overall, vanilla matrix factorization and k-nearest neighbor item-based collaborative filtering achieved our initial objective to a certain extent. We were able to recommend items to users with reasonable ndcg and coverage. The performance metrics (NDCG, and coverage) were not as high as we expected (in cases when those metrics were high, e.g. high item coverage, this was partly caused by the sparsity of the data). Even though real-world datasets are extremely sparse and face cold start problems, by having a more scalable model with larger training and test sets would improve both of our models significantly.\n",
    "\n",
    "Based on our evaluation, several improvements would be required in order for our models to be production ready.\n",
    "To improve our model, we could try to implement models that take other factors (e.g. latent) into account. One way to do that is to use content information as additional source of data. In addition, we could also consider implementing different model-based frameworks, such as deep-learning based models (e.g. autoencoders)."
   ]
  }
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