Recommendations_with_IBM.ipynb

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   "cell_type": "markdown",
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   "source": [
    "# Recommendations with IBM\n",
    "\n",
    "In this notebook, you will be putting your recommendation skills to use on real data from the IBM Watson Studio platform. \n",
    "\n",
    "By following the table of contents, you will build out a number of different methods for making recommendations that can be used for different situations. \n",
    "\n",
    "\n",
    "## Table of Contents\n",
    "\n",
    "I. [Exploratory Data Analysis](#Exploratory-Data-Analysis)<br>\n",
    "II. [Rank Based Recommendations](#Rank)<br>\n",
    "III. [User-User Based Collaborative Filtering](#User-User)<br>\n",
    "IV. [Matrix Factorization](#Matrix-Fact)<br>\n",
    "V. [Extras & Conclusion](#conclusions)\n",
    "\n",
    "Let's get started by importing the necessary libraries and reading in the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
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       "      <th>0</th>\n",
       "      <td>1430.0</td>\n",
       "      <td>using pixiedust for fast, flexible, and easier...</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1314.0</td>\n",
       "      <td>healthcare python streaming application demo</td>\n",
       "      <td>083cbdfa93c8444beaa4c5f5e0f5f9198e4f9e0b</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1429.0</td>\n",
       "      <td>use deep learning for image classification</td>\n",
       "      <td>b96a4f2e92d8572034b1e9b28f9ac673765cd074</td>\n",
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       "    <tr>\n",
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       "      <td>deploy your python model as a restful api</td>\n",
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       "   article_id                                              title  \\\n",
       "0      1430.0  using pixiedust for fast, flexible, and easier...   \n",
       "1      1314.0       healthcare python streaming application demo   \n",
       "2      1429.0         use deep learning for image classification   \n",
       "3      1338.0          ml optimization using cognitive assistant   \n",
       "4      1276.0          deploy your python model as a restful api   \n",
       "\n",
       "                                      email  \n",
       "0  ef5f11f77ba020cd36e1105a00ab868bbdbf7fe7  \n",
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     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import project_tests as t\n",
    "import pickle\n",
    "from sklearn.metrics import f1_score\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "df = pd.read_csv('data/user-item-interactions.csv')\n",
    "df_content = pd.read_csv('data/articles_community.csv')\n",
    "del df['Unnamed: 0']\n",
    "del df_content['Unnamed: 0']\n",
    "\n",
    "# Show df to get an idea of the data\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
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       "      <td>Skip navigation Sign in SearchLoading...\\r\\n\\r...</td>\n",
       "      <td>Detect bad readings in real time using Python ...</td>\n",
       "      <td>Detect Malfunctioning IoT Sensors with Streami...</td>\n",
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       "      <td>This Week in Data Science (April 18, 2017)</td>\n",
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       "      <th>3</th>\n",
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       "      <td>This video demonstrates the power of IBM DataS...</td>\n",
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       "      <td>Live</td>\n",
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       "0  Skip navigation Sign in SearchLoading...\\r\\n\\r...   \n",
       "1  No Free Hunch Navigation * kaggle.com\\r\\n\\r\\n ...   \n",
       "2  ☰ * Login\\r\\n * Sign Up\\r\\n\\r\\n * Learning Pat...   \n",
       "3  DATALAYER: HIGH THROUGHPUT, LOW LATENCY AT SCA...   \n",
       "4  Skip navigation Sign in SearchLoading...\\r\\n\\r...   \n",
       "\n",
       "                                     doc_description  \\\n",
       "0  Detect bad readings in real time using Python ...   \n",
       "1  See the forest, see the trees. Here lies the c...   \n",
       "2  Here’s this week’s news in Data Science and Bi...   \n",
       "3  Learn how distributed DBs solve the problem of...   \n",
       "4  This video demonstrates the power of IBM DataS...   \n",
       "\n",
       "                                       doc_full_name doc_status  article_id  \n",
       "0  Detect Malfunctioning IoT Sensors with Streami...       Live           0  \n",
       "1  Communicating data science: A guide to present...       Live           1  \n",
       "2         This Week in Data Science (April 18, 2017)       Live           2  \n",
       "3  DataLayer Conference: Boost the performance of...       Live           3  \n",
       "4      Analyze NY Restaurant data using Spark in DSX       Live           4  "
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    }
   ],
   "source": [
    "# Show df_content to get an idea of the data\n",
    "df_content.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <a class=\"anchor\" id=\"Exploratory-Data-Analysis\">Part I : Exploratory Data Analysis</a>\n",
    "\n",
    "Use the dictionary and cells below to provide some insight into the descriptive statistics of the data.\n",
    "\n",
    "`1.` What is the distribution of how many articles a user interacts with in the dataset?  Provide a visual and descriptive statistics to assist with giving a look at the number of times each user interacts with an article.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "              count\n",
      "count  5148.000000\n",
      "mean      8.930847\n",
      "std      16.802267\n",
      "min       1.000000\n",
      "25%       1.000000\n",
      "50%       3.000000\n",
      "75%       9.000000\n",
      "max     364.000000\n"
     ]
    }
   ],
   "source": [
    "# df with number of articles interactions per user\n",
    "user_articles_count = df.groupby(\"email\")[\"article_id\"].count().sort_values().reset_index(name = 'count')\n",
    "\n",
    "# histogram with number of articles interactions per user\n",
    "plt.hist(user_articles_count[\"count\"], bins = 100)\n",
    "plt.title(\"Histogram - Number Article Interactions per Users\")\n",
    "plt.xlabel('Count Article Interactions per user')\n",
    "plt.ylabel('Number Users')\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "\n",
    "print(\"\\n\", user_articles_count.describe())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.0 median count of artilces per user\n",
      "364 max count of artilces by one user\n"
     ]
    }
   ],
   "source": [
    "# Fill in the median and maximum number of user_article interactios below\n",
    "median_val = user_articles_count[\"count\"].median() # 50% of individuals interact with ____ number of articles or fewer.\n",
    "print(\"{} median count of artilces per user\".format(median_val))\n",
    "\n",
    "max_views_by_user = user_articles_count[\"count\"].max() # The maximum number of user-article interactions by any 1 user is ______.\n",
    "print(\"{} max count of artilces by one user\".format(max_views_by_user))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`2.` Explore and remove duplicate articles from the **df_content** dataframe.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "        vertical-align: middle;\n",
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       "\n",
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       "        vertical-align: top;\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>doc_body</th>\n",
       "      <th>doc_description</th>\n",
       "      <th>doc_full_name</th>\n",
       "      <th>doc_status</th>\n",
       "      <th>article_id</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>Follow Sign in / Sign up Home About Insight Da...</td>\n",
       "      <td>Community Detection at Scale</td>\n",
       "      <td>Graph-based machine learning</td>\n",
       "      <td>Live</td>\n",
       "      <td>50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>365</th>\n",
       "      <td>Follow Sign in / Sign up Home About Insight Da...</td>\n",
       "      <td>During the seven-week Insight Data Engineering...</td>\n",
       "      <td>Graph-based machine learning</td>\n",
       "      <td>Live</td>\n",
       "      <td>50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>221</th>\n",
       "      <td>* United States\\r\\n\\r\\nIBM® * Site map\\r\\n\\r\\n...</td>\n",
       "      <td>When used to make sense of huge amounts of con...</td>\n",
       "      <td>How smart catalogs can turn the big data flood...</td>\n",
       "      <td>Live</td>\n",
       "      <td>221</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>692</th>\n",
       "      <td>Homepage Follow Sign in / Sign up Homepage * H...</td>\n",
       "      <td>One of the earliest documented catalogs was co...</td>\n",
       "      <td>How smart catalogs can turn the big data flood...</td>\n",
       "      <td>Live</td>\n",
       "      <td>221</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>232</th>\n",
       "      <td>Homepage Follow Sign in Get started Homepage *...</td>\n",
       "      <td>If you are like most data scientists, you are ...</td>\n",
       "      <td>Self-service data preparation with IBM Data Re...</td>\n",
       "      <td>Live</td>\n",
       "      <td>232</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>971</th>\n",
       "      <td>Homepage Follow Sign in Get started * Home\\r\\n...</td>\n",
       "      <td>If you are like most data scientists, you are ...</td>\n",
       "      <td>Self-service data preparation with IBM Data Re...</td>\n",
       "      <td>Live</td>\n",
       "      <td>232</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>399</th>\n",
       "      <td>Homepage Follow Sign in Get started * Home\\r\\n...</td>\n",
       "      <td>Today’s world of data science leverages data f...</td>\n",
       "      <td>Using Apache Spark as a parallel processing fr...</td>\n",
       "      <td>Live</td>\n",
       "      <td>398</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>761</th>\n",
       "      <td>Homepage Follow Sign in Get started Homepage *...</td>\n",
       "      <td>Today’s world of data science leverages data f...</td>\n",
       "      <td>Using Apache Spark as a parallel processing fr...</td>\n",
       "      <td>Live</td>\n",
       "      <td>398</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>578</th>\n",
       "      <td>This video shows you how to construct queries ...</td>\n",
       "      <td>This video shows you how to construct queries ...</td>\n",
       "      <td>Use the Primary Index</td>\n",
       "      <td>Live</td>\n",
       "      <td>577</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>970</th>\n",
       "      <td>This video shows you how to construct queries ...</td>\n",
       "      <td>This video shows you how to construct queries ...</td>\n",
       "      <td>Use the Primary Index</td>\n",
       "      <td>Live</td>\n",
       "      <td>577</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                              doc_body  \\\n",
       "50   Follow Sign in / Sign up Home About Insight Da...   \n",
       "365  Follow Sign in / Sign up Home About Insight Da...   \n",
       "221  * United States\\r\\n\\r\\nIBM® * Site map\\r\\n\\r\\n...   \n",
       "692  Homepage Follow Sign in / Sign up Homepage * H...   \n",
       "232  Homepage Follow Sign in Get started Homepage *...   \n",
       "971  Homepage Follow Sign in Get started * Home\\r\\n...   \n",
       "399  Homepage Follow Sign in Get started * Home\\r\\n...   \n",
       "761  Homepage Follow Sign in Get started Homepage *...   \n",
       "578  This video shows you how to construct queries ...   \n",
       "970  This video shows you how to construct queries ...   \n",
       "\n",
       "                                       doc_description  \\\n",
       "50                        Community Detection at Scale   \n",
       "365  During the seven-week Insight Data Engineering...   \n",
       "221  When used to make sense of huge amounts of con...   \n",
       "692  One of the earliest documented catalogs was co...   \n",
       "232  If you are like most data scientists, you are ...   \n",
       "971  If you are like most data scientists, you are ...   \n",
       "399  Today’s world of data science leverages data f...   \n",
       "761  Today’s world of data science leverages data f...   \n",
       "578  This video shows you how to construct queries ...   \n",
       "970  This video shows you how to construct queries ...   \n",
       "\n",
       "                                         doc_full_name doc_status  article_id  \n",
       "50                        Graph-based machine learning       Live          50  \n",
       "365                       Graph-based machine learning       Live          50  \n",
       "221  How smart catalogs can turn the big data flood...       Live         221  \n",
       "692  How smart catalogs can turn the big data flood...       Live         221  \n",
       "232  Self-service data preparation with IBM Data Re...       Live         232  \n",
       "971  Self-service data preparation with IBM Data Re...       Live         232  \n",
       "399  Using Apache Spark as a parallel processing fr...       Live         398  \n",
       "761  Using Apache Spark as a parallel processing fr...       Live         398  \n",
       "578                              Use the Primary Index       Live         577  \n",
       "970                              Use the Primary Index       Live         577  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Find and explore duplicate articles\n",
    "df_content[df_content[\"article_id\"].duplicated(keep = False)].sort_values(by = \"article_id\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "df_content shape before duplicates removal: (1056, 5)\n",
      "df_content shape after duplicates removal: (1051, 5)\n"
     ]
    }
   ],
   "source": [
    "# df_content shape before dublicates removal\n",
    "print(\"df_content shape before duplicates removal: {}\".format(df_content.shape))\n",
    "\n",
    "# Remove any rows that have the same article_id - only keep the first\n",
    "df_content = df_content.drop_duplicates(subset = [\"article_id\"])\n",
    "\n",
    "# df_content shape after dublicates removal\n",
    "print(\"df_content shape after duplicates removal: {}\".format(df_content.shape))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`3.` Use the cells below to find:\n",
    "\n",
    "**a.** The number of unique articles that have an interaction with a user.  \n",
    "**b.** The number of unique articles in the dataset (whether they have any interactions or not).<br>\n",
    "**c.** The number of unique users in the dataset. (excluding null values) <br>\n",
    "**d.** The number of user-article interactions in the dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "714 unique articles\n",
      "1051 total articles\n",
      "5148 unique users\n",
      "45993 user article interactions\n"
     ]
    }
   ],
   "source": [
    "# The number of unique articles that have at least one interaction\n",
    "unique_articles = df[\"article_id\"].nunique()\n",
    "print(\"{} unique articles\".format(unique_articles))\n",
    "\n",
    "# The number of unique articles on the IBM platform\n",
    "total_articles = df_content[\"article_id\"].nunique()\n",
    "print(\"{} total articles\".format(total_articles))\n",
    "\n",
    "# The number of unique users\n",
    "unique_users = df[\"email\"].nunique() \n",
    "print(\"{} unique users\".format(unique_users))\n",
    "\n",
    "# The number of user-article interactions\n",
    "user_article_interactions = len(df) \n",
    "print(\"{} user article interactions\".format(user_article_interactions))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`4.` Use the cells below to find the most viewed **article_id**, as well as how often it was viewed.  After talking to the company leaders, the `email_mapper` function was deemed a reasonable way to map users to ids.  There were a small number of null values, and it was found that all of these null values likely belonged to a single user (which is how they are stored using the function below)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1429.0 most viewed article_id\n",
      "937 counted views of article 1429.0\n"
     ]
    }
   ],
   "source": [
    "most_viewed_article = df[\"article_id\"].value_counts().reset_index(name = \"count\")\n",
    "\n",
    "# The most viewed article in the dataset as a string with one value following the decimal \n",
    "most_viewed_article_id = str(most_viewed_article[\"index\"][0]) \n",
    "print(\"{} most viewed article_id\".format(most_viewed_article_id))\n",
    "\n",
    "# The most viewed article in the dataset was viewed how many times?\n",
    "max_views = most_viewed_article[\"count\"][0] \n",
    "print(\"{} counted views of article {}\".format(max_views, most_viewed_article_id))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>article_id</th>\n",
       "      <th>title</th>\n",
       "      <th>user_id</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1430.0</td>\n",
       "      <td>using pixiedust for fast, flexible, and easier...</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1314.0</td>\n",
       "      <td>healthcare python streaming application demo</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1429.0</td>\n",
       "      <td>use deep learning for image classification</td>\n",
       "      <td>3</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1338.0</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
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       "      <td>5</td>\n",
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       "</table>\n",
       "</div>"
      ],
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       "   article_id                                              title  user_id\n",
       "0      1430.0  using pixiedust for fast, flexible, and easier...        1\n",
       "1      1314.0       healthcare python streaming application demo        2\n",
       "2      1429.0         use deep learning for image classification        3\n",
       "3      1338.0          ml optimization using cognitive assistant        4\n",
       "4      1276.0          deploy your python model as a restful api        5"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## No need to change the code here - this will be helpful for later parts of the notebook\n",
    "# Run this cell to map the user email to a user_id column and remove the email column\n",
    "\n",
    "def email_mapper():\n",
    "    coded_dict = dict()\n",
    "    cter = 1\n",
    "    email_encoded = []\n",
    "    \n",
    "    for val in df[\"email\"]:\n",
    "        if val not in coded_dict:\n",
    "            coded_dict[val] = cter\n",
    "            cter+=1\n",
    "        \n",
    "        email_encoded.append(coded_dict[val])\n",
    "    return email_encoded\n",
    "\n",
    "email_encoded = email_mapper()\n",
    "del df[\"email\"]\n",
    "df[\"user_id\"] = email_encoded\n",
    "\n",
    "# show header\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "It looks like you have everything right here! Nice job!\n"
     ]
    }
   ],
   "source": [
    "## If you stored all your results in the variable names above, \n",
    "## you shouldn't need to change anything in this cell\n",
    "\n",
    "sol_1_dict = {\n",
    "    '`50% of individuals have _____ or fewer interactions.`': median_val,\n",
    "    '`The total number of user-article interactions in the dataset is ______.`': user_article_interactions,\n",
    "    '`The maximum number of user-article interactions by any 1 user is ______.`': max_views_by_user,\n",
    "    '`The most viewed article in the dataset was viewed _____ times.`': max_views,\n",
    "    '`The article_id of the most viewed article is ______.`': most_viewed_article_id,\n",
    "    '`The number of unique articles that have at least 1 rating ______.`': unique_articles,\n",
    "    '`The number of unique users in the dataset is ______`': unique_users,\n",
    "    '`The number of unique articles on the IBM platform`': total_articles\n",
    "}\n",
    "\n",
    "# Test your dictionary against the solution\n",
    "t.sol_1_test(sol_1_dict)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <a class=\"anchor\" id=\"Rank\">Part II: Rank-Based Recommendations</a>\n",
    "\n",
    "Unlike in the earlier lessons, we don't actually have ratings for whether a user liked an article or not.  We only know that a user has interacted with an article.  In these cases, the popularity of an article can really only be based on how often an article was interacted with.\n",
    "\n",
    "`1.` Fill in the function below to return the **n** top articles ordered with most interactions as the top. Test your function using the tests below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_top_articles(n, df=df):\n",
    "    '''\n",
    "    INPUT:\n",
    "    n - (int) the number of top articles to return\n",
    "    df - (pandas dataframe) df as defined at the top of the notebook \n",
    "    \n",
    "    OUTPUT:\n",
    "    top_articles - (list) A list of the top 'n' article titles \n",
    "    \n",
    "    '''\n",
    "    top_articles = list(df[\"title\"].value_counts().head(n).index)\n",
    "    \n",
    "    return top_articles # Return the top article titles from df (not df_content)\n",
    "\n",
    "def get_top_article_ids(n, df=df):\n",
    "    '''\n",
    "    INPUT:\n",
    "    n - (int) the number of top articles to return\n",
    "    df - (pandas dataframe) df as defined at the top of the notebook \n",
    "    \n",
    "    OUTPUT:\n",
    "    top_articles - (list) A list of the top 'n' article titles \n",
    "    \n",
    "    '''\n",
    "    top_articles = list(df[\"article_id\"].value_counts().head(n).index)\n",
    " \n",
    "    return top_articles # Return the top article ids"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['use deep learning for image classification', 'insights from new york car accident reports', 'visualize car data with brunel', 'use xgboost, scikit-learn & ibm watson machine learning apis', 'predicting churn with the spss random tree algorithm', 'healthcare python streaming application demo', 'finding optimal locations of new store using decision optimization', 'apache spark lab, part 1: basic concepts', 'analyze energy consumption in buildings', 'gosales transactions for logistic regression model'] \n",
      "\n",
      "[1429.0, 1330.0, 1431.0, 1427.0, 1364.0, 1314.0, 1293.0, 1170.0, 1162.0, 1304.0]\n"
     ]
    }
   ],
   "source": [
    "print(get_top_articles(10),\"\\n\")\n",
    "print(get_top_article_ids(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your top_5 looks like the solution list! Nice job.\n",
      "Your top_10 looks like the solution list! Nice job.\n",
      "Your top_20 looks like the solution list! Nice job.\n"
     ]
    }
   ],
   "source": [
    "# Test your function by returning the top 5, 10, and 20 articles\n",
    "top_5 = get_top_articles(5)\n",
    "top_10 = get_top_articles(10)\n",
    "top_20 = get_top_articles(20)\n",
    "\n",
    "# Test each of your three lists from above\n",
    "t.sol_2_test(get_top_articles)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <a class=\"anchor\" id=\"User-User\">Part III: User-User Based Collaborative Filtering</a>\n",
    "\n",
    "\n",
    "`1.` Use the function below to reformat the **df** dataframe to be shaped with users as the rows and articles as the columns.  \n",
    "\n",
    "* Each **user** should only appear in each **row** once.\n",
    "\n",
    "\n",
    "* Each **article** should only show up in one **column**.  \n",
    "\n",
    "\n",
    "* **If a user has interacted with an article, then place a 1 where the user-row meets for that article-column**.  It does not matter how many times a user has interacted with the article, all entries where a user has interacted with an article should be a 1.  \n",
    "\n",
    "\n",
    "* **If a user has not interacted with an item, then place a zero where the user-row meets for that article-column**. \n",
    "\n",
    "Use the tests to make sure the basic structure of your matrix matches what is expected by the solution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create the user-article matrix with 1's and 0's\n",
    "\n",
    "def create_user_item_matrix(df):\n",
    "    '''\n",
    "    INPUT:\n",
    "    df - pandas dataframe with article_id, title, user_id columns\n",
    "    \n",
    "    OUTPUT:\n",
    "    user_item - user item matrix \n",
    "    \n",
    "    Description:\n",
    "    Return a matrix with user ids as rows and article ids on the columns with 1 values where a user interacted with \n",
    "    an article and a 0 otherwise\n",
    "    '''\n",
    "    user_item = df.groupby([\"user_id\", \"article_id\"])[\"title\"].max().unstack()\n",
    "    user_item = user_item.notnull().astype(int)\n",
    "    \n",
    "    return user_item # return the user_item matrix \n",
    "\n",
    "user_item = create_user_item_matrix(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "You have passed our quick tests!  Please proceed!\n"
     ]
    }
   ],
   "source": [
    "## Tests: You should just need to run this cell.  Don't change the code.\n",
    "assert user_item.shape[0] == 5149, \"Oops!  The number of users in the user-article matrix doesn't look right.\"\n",
    "assert user_item.shape[1] == 714, \"Oops!  The number of articles in the user-article matrix doesn't look right.\"\n",
    "assert user_item.sum(axis=1)[1] == 36, \"Oops!  The number of articles seen by user 1 doesn't look right.\"\n",
    "print(\"You have passed our quick tests!  Please proceed!\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Store data (serialize)\n",
    "with open(\"user_item_matrix.p\", \"wb\") as handle:\n",
    "    pickle.dump(user_item, handle, protocol = pickle.HIGHEST_PROTOCOL)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`2.` Complete the function below which should take a user_id and provide an ordered list of the most similar users to that user (from most similar to least similar).  The returned result should not contain the provided user_id, as we know that each user is similar to him/herself. Because the results for each user here are binary, it (perhaps) makes sense to compute similarity as the dot product of two users. \n",
    "\n",
    "Use the tests to test your function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def find_similar_users(user_id, user_item=user_item):\n",
    "    '''\n",
    "    INPUT:\n",
    "    user_id - (int) a user_id\n",
    "    user_item - (pandas dataframe) matrix of users by articles: \n",
    "                1's when a user has interacted with an article, 0 otherwise\n",
    "    \n",
    "    OUTPUT:\n",
    "    similar_users - (list) an ordered list where the closest users (largest dot product users)\n",
    "                    are listed first\n",
    "    \n",
    "    Description:\n",
    "    Computes the similarity of every pair of users based on the dot product\n",
    "    Returns an ordered\n",
    "    \n",
    "    '''\n",
    "    # compute similarity of each user to the provided user\n",
    "    user_row = user_item.iloc[user_id - 1] # subtract 1 from user_id, as user_id starts with 1 and index with 0\n",
    "    similarity = np.dot(user_row, user_item.T) # compute similarity with dot product from user_row and transversed user_item\n",
    "\n",
    "    # sort by similarity\n",
    "    sort_indices = np.argsort(-similarity) # sort array with similarity according user_id\n",
    "    sort_indices += 1 # add 1 from index, as index starts with 0 and user_id with 1\n",
    "   \n",
    "    # create list of just the ids and remove the own user's id\n",
    "    most_similar_users = list(sort_indices[1:])\n",
    "       \n",
    "    return most_similar_users # return a list of the users in order from most to least similar "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The 10 most similar users to user 1 are: [3933, 3782, 23, 203, 4459, 3870, 131, 46, 4201, 49]\n",
      "The 5 most similar users to user 3933 are: [3933, 23, 3782, 4459, 203]\n",
      "The 3 most similar users to user 46 are: [4201, 3782, 23]\n"
     ]
    }
   ],
   "source": [
    "# Do a spot check of your function\n",
    "print(\"The 10 most similar users to user 1 are: {}\".format(find_similar_users(1)[:10]))\n",
    "print(\"The 5 most similar users to user 3933 are: {}\".format(find_similar_users(3933)[:5]))\n",
    "print(\"The 3 most similar users to user 46 are: {}\".format(find_similar_users(46)[:3]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`3.` Now that you have a function that provides the most similar users to each user, you will want to use these users to find articles you can recommend.  Complete the functions below to return the articles you would recommend to each user. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_article_names(article_ids, df=df):\n",
    "    '''\n",
    "    INPUT:\n",
    "    article_ids - (list) a list of article ids\n",
    "    df - (pandas dataframe) df as defined at the top of the notebook\n",
    "    \n",
    "    OUTPUT:\n",
    "    article_names - (list) a list of article names associated with the list of article ids \n",
    "                    (this is identified by the title column)\n",
    "    '''\n",
    "    article_names = list(set(df[df[\"article_id\"].isin(article_ids)][\"title\"]))\n",
    "    \n",
    "    return article_names # Return the article names associated with list of article ids\n",
    "\n",
    "\n",
    "def get_user_articles(user_id, user_item=user_item):\n",
    "    '''\n",
    "    INPUT:\n",
    "    user_id - (int) a user id\n",
    "    user_item - (pandas dataframe) matrix of users by articles: \n",
    "                1's when a user has interacted with an article, 0 otherwise\n",
    "    \n",
    "    OUTPUT:\n",
    "    article_ids - (list) a list of the article ids seen by the user\n",
    "    article_names - (list) a list of article names associated with the list of article ids \n",
    "                    (this is identified by the doc_full_name column in df_content)\n",
    "    \n",
    "    Description:\n",
    "    Provides a list of the article_ids and article titles that have been seen by a user\n",
    "    '''\n",
    "    article_ids = user_item.loc[user_id]\n",
    "    article_ids = [str(a_id) for a_id in article_ids[article_ids == 1].index]\n",
    "    \n",
    "    article_names = get_article_names(article_ids)\n",
    "    \n",
    "    return article_ids, article_names # return the ids and names\n",
    "\n",
    "\n",
    "def user_user_recs(user_id, m=10):\n",
    "    '''\n",
    "    INPUT:\n",
    "    user_id - (int) a user id\n",
    "    m - (int) the number of recommendations you want for the user\n",
    "    \n",
    "    OUTPUT:\n",
    "    recs - (list) a list of recommendations for the user\n",
    "    \n",
    "    Description:\n",
    "    Loops through the users based on closeness to the input user_id\n",
    "    For each user - finds articles the user hasn't seen before and provides them as recs\n",
    "    Does this until m recommendations are found\n",
    "    \n",
    "    Notes:\n",
    "    Users who are the same closeness are chosen arbitrarily as the 'next' user\n",
    "    \n",
    "    For the user where the number of recommended articles starts below m \n",
    "    and ends exceeding m, the last items are chosen arbitrarily\n",
    "    \n",
    "    '''\n",
    "    user_ids = find_similar_users(user_id)    \n",
    "    recs = df[df[\"user_id\"].isin(user_ids)][\"article_id\"]\n",
    "    \n",
    "    recs = list(set(recs))[:m]\n",
    "    \n",
    "    return recs # return your recommendations for this user_id    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['apache spark™ 2.0: extend structured streaming for spark ml',\n",
       " 'timeseries data analysis of iot events by using jupyter notebook',\n",
       " 'detect malfunctioning iot sensors with streaming analytics',\n",
       " 'higher-order logistic regression for large datasets',\n",
       " 'data science bowl 2017',\n",
       " 'this week in data science (april 18, 2017)',\n",
       " 'analyze ny restaurant data using spark in dsx',\n",
       " 'got zip code data? prep it for analytics. – ibm watson data lab – medium',\n",
       " 'the greatest public datasets for ai – startup grind',\n",
       " '3992    using apache spark to predict attack vectors a...\\nName: title, dtype: object']"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Check Results\n",
    "get_article_names(user_user_recs(1, 10)) # Return 10 recommendations for user 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "If this is all you see, you passed all of our tests!  Nice job!\n"
     ]
    }
   ],
   "source": [
    "# Test your functions here - No need to change this code - just run this cell\n",
    "assert set(get_article_names(['1024.0', '1176.0', '1305.0', '1314.0', '1422.0', '1427.0'])) == set(['using deep learning to reconstruct high-resolution audio', 'build a python app on the streaming analytics service', 'gosales transactions for naive bayes model', 'healthcare python streaming application demo', 'use r dataframes & ibm watson natural language understanding', 'use xgboost, scikit-learn & ibm watson machine learning apis']), \"Oops! Your the get_article_names function doesn't work quite how we expect.\"\n",
    "assert set(get_article_names(['1320.0', '232.0', '844.0'])) == set(['housing (2015): united states demographic measures','self-service data preparation with ibm data refinery','use the cloudant-spark connector in python notebook']), \"Oops! Your the get_article_names function doesn't work quite how we expect.\"\n",
    "assert set(get_user_articles(20)[0]) == set(['1320.0', '232.0', '844.0'])\n",
    "assert set(get_user_articles(20)[1]) == set(['housing (2015): united states demographic measures', 'self-service data preparation with ibm data refinery','use the cloudant-spark connector in python notebook'])\n",
    "assert set(get_user_articles(2)[0]) == set(['1024.0', '1176.0', '1305.0', '1314.0', '1422.0', '1427.0'])\n",
    "assert set(get_user_articles(2)[1]) == set(['using deep learning to reconstruct high-resolution audio', 'build a python app on the streaming analytics service', 'gosales transactions for naive bayes model', 'healthcare python streaming application demo', 'use r dataframes & ibm watson natural language understanding', 'use xgboost, scikit-learn & ibm watson machine learning apis'])\n",
    "print(\"If this is all you see, you passed all of our tests!  Nice job!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`4.` Now we are going to improve the consistency of the **user_user_recs** function from above.  \n",
    "\n",
    "* Instead of arbitrarily choosing when we obtain users who are all the same closeness to a given user - choose the users that have the most total article interactions before choosing those with fewer article interactions.\n",
    "\n",
    "\n",
    "* Instead of arbitrarily choosing articles from the user where the number of recommended articles starts below m and ends exceeding m, choose articles with the articles with the most total interactions before choosing those with fewer total interactions. This ranking should be  what would be obtained from the **top_articles** function you wrote earlier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_top_sorted_users(user_id, df=df, user_item=user_item):\n",
    "    '''\n",
    "    INPUT:\n",
    "    user_id - (int)\n",
    "    df - (pandas dataframe) df as defined at the top of the notebook \n",
    "    user_item - (pandas dataframe) matrix of users by articles: \n",
    "            1's when a user has interacted with an article, 0 otherwise\n",
    "    \n",
    "            \n",
    "    OUTPUT:\n",
    "    neighbors_df - (pandas dataframe) a dataframe with:\n",
    "                    neighbor_id - is a neighbor user_id\n",
    "                    similarity - measure of the similarity of each user to the provided user_id\n",
    "                    num_interactions - the number of articles viewed by the user - if a u\n",
    "                    \n",
    "    Other Details - sort the neighbors_df by the similarity and then by number of interactions where \n",
    "                    highest of each is higher in the dataframe\n",
    "     \n",
    "    '''\n",
    "    user_articles_interactions = df.groupby([\"user_id\"])[\"article_id\"].count()\n",
    "    \n",
    "    # similarity of each user to selected user\n",
    "    n_users = user_item.shape[0]\n",
    "    \n",
    "    # columns\n",
    "    neighbor_id = [u_id for u_id in range(1, n_users) if u_id != user_id]\n",
    "    similarity = []\n",
    "    num_interactions = []\n",
    "    \n",
    "    # set similarity and num_interactions\n",
    "    for u_id in neighbor_id:\n",
    "        similarity.append(np.dot(user_item.loc[user_id], user_item.loc[u_id]))\n",
    "        num_interactions.append(user_articles_interactions.loc[u_id])\n",
    "    \n",
    "    # create dataframe\n",
    "    neighbors_df = pd.DataFrame({\"neighbor_id\": neighbor_id,\n",
    "                                \"similarity\": similarity,\n",
    "                                \"num_interactions\": num_interactions\n",
    "                                })\n",
    "    \n",
    "    # sort dataframe by similarity\n",
    "    neighbors_df.sort_values(by = [\"similarity\", \"num_interactions\"], ascending = False, inplace = True)\n",
    "    \n",
    "    return neighbors_df # Return the dataframe specified in the doc_string\n",
    "\n",
    "\n",
    "def user_user_recs_part2(user_id, m=10):\n",
    "    '''\n",
    "    INPUT:\n",
    "    user_id - (int) a user id\n",
    "    m - (int) the number of recommendations you want for the user\n",
    "    \n",
    "    OUTPUT:\n",
    "    recs - (list) a list of recommendations for the user by article id\n",
    "    rec_names - (list) a list of recommendations for the user by article title\n",
    "    \n",
    "    Description:\n",
    "    Loops through the users based on closeness to the input user_id\n",
    "    For each user - finds articles the user hasn't seen before and provides them as recs\n",
    "    Does this until m recommendations are found\n",
    "    \n",
    "    Notes:\n",
    "    * Choose the users that have the most total article interactions \n",
    "    before choosing those with fewer article interactions.\n",
    "\n",
    "    * Choose articles with the articles with the most total interactions \n",
    "    before choosing those with fewer total interactions. \n",
    "   \n",
    "    '''\n",
    "    neighbors_df = get_top_sorted_users(user_id)\n",
    "    \n",
    "    # set top-m neighbor_id\n",
    "    top_m_neighbors = list(neighbors_df[:m][\"neighbor_id\"])\n",
    "    \n",
    "    # set article_ids seen by top-m neighbors\n",
    "    recs = []\n",
    "    for u_id in top_m_neighbors:\n",
    "        article_ids = user_item.loc[u_id]\n",
    "        recs.extend([str(a_id) for a_id in article_ids[article_ids == 1].index])\n",
    "    \n",
    "    recs = list(set(recs))[:m]\n",
    "    \n",
    "    # set article names and remove dublicates\n",
    "    rec_names = list(set(df[df[\"article_id\"].isin(recs)][\"title\"]))\n",
    "    \n",
    "    return recs, rec_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The top 10 recommendations for user 20 are the following article ids:\n",
      "['256.0', '1314.0', '112.0', '1298.0', '761.0', '1184.0', '465.0', '981.0', '1152.0', '1330.0']\n",
      "\n",
      "The top 10 recommendations for user 20 are the following article names:\n",
      "['airbnb data for analytics: venice reviews', 'healthcare python streaming application demo', 'variational auto-encoder for \"frey faces\" using keras', 'super fast string matching in python', 'xml2 1.0.0', 'introduction to neural networks, advantages and applications', 'from scikit-learn model to cloud with wml client', 'building custom machine learning algorithms with apache systemml', 'insights from new york car accident reports', 'city population by sex, city and city type']\n"
     ]
    }
   ],
   "source": [
    "# Quick spot check - don't change this code - just use it to test your functions\n",
    "rec_ids, rec_names = user_user_recs_part2(20, 10)\n",
    "print(\"The top 10 recommendations for user 20 are the following article ids:\")\n",
    "print(rec_ids)\n",
    "print()\n",
    "print(\"The top 10 recommendations for user 20 are the following article names:\")\n",
    "print(rec_names)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`5.` Use your functions from above to correctly fill in the solutions to the dictionary below.  Then test your dictionary against the solution.  Provide the code you need to answer each following the comments below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1st user which is most similar to user 1: 3933\n",
      "\n",
      "10th user which is most similar to user 131: 242\n"
     ]
    }
   ],
   "source": [
    "### Tests with a dictionary of results\n",
    "\n",
    "# Find the user that is most similar to user 1 \n",
    "user1_most_sim = get_top_sorted_users(1).iloc[0].neighbor_id \n",
    "print(\"1st user which is most similar to user 1: {}\\n\".format(user1_most_sim))\n",
    "\n",
    "# Find the 10th most similar user to user 131\n",
    "user131_10th_sim = get_top_sorted_users(131).iloc[9].neighbor_id \n",
    "print(\"10th user which is most similar to user 131: {}\".format(user131_10th_sim))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This all looks good!  Nice job!\n"
     ]
    }
   ],
   "source": [
    "## Dictionary Test Here\n",
    "sol_5_dict = {\n",
    "    'The user that is most similar to user 1.': user1_most_sim, \n",
    "    'The user that is the 10th most similar to user 131': user131_10th_sim,\n",
    "}\n",
    "\n",
    "t.sol_5_test(sol_5_dict)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`6.` If we were given a new user, which of the above functions would you be able to use to make recommendations?  Explain.  Can you think of a better way we might make recommendations?  Use the cell below to explain a better method for new users."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Response:**\n",
    "\n",
    "The User-Based Collaborative Filtering Method is not applicable due to the cold start problem. We don't have data of interactions with articles from the new user and therefore calculation of similarities is not possible (because row in user_item matrix for new user has no values).\n",
    "For new users we can only recommend articles using the Ranked-Based Filtering method with the function \"get_top_articles\".\n",
    "\n",
    "A better way of making recommedations to new users could be with the Knowledge Based Filtering Method. Here we would need selected input informations from the user as preferences of article topics. We could use also the Content Based Filtering Method.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`7.` Using your existing functions, provide the top 10 recommended articles you would provide for the new user below.  You can test your function against our thoughts to make sure we are all on the same page with how we might make a recommendation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "new_user = '0.0'\n",
    "\n",
    "# What would your recommendations be for this new user '0.0'?  As a new user, they have no observed articles.\n",
    "# Provide a list of the top 10 article ids you would give to \n",
    "new_user_recs = get_top_article_ids(10)\n",
    "new_user_recs = [str(id) for id in new_user_recs]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "That's right!  Nice job!\n"
     ]
    }
   ],
   "source": [
    "assert set(new_user_recs) == set(['1314.0','1429.0','1293.0','1427.0','1162.0','1364.0','1304.0','1170.0','1431.0','1330.0']), \"Oops!  It makes sense that in this case we would want to recommend the most popular articles, because we don't know anything about these users.\"\n",
    "\n",
    "print(\"That's right!  Nice job!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <a class=\"anchor\" id=\"Matrix-Fact\">Part IV: Matrix Factorization</a>\n",
    "\n",
    "In this part of the notebook, you will use matrix factorization to make article recommendations to the users on the IBM Watson Studio platform.\n",
    "\n",
    "`1.` You should have already created a **user_item** matrix above in **question 1** of **Part III** above.  This first question here will just require that you run the cells to get things set up for the rest of **Part IV** of the notebook. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 714 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "article_id  0.0     2.0     4.0     8.0     9.0     12.0    14.0    15.0    \\\n",
       "user_id                                                                      \n",
       "1                0       0       0       0       0       0       0       0   \n",
       "2                0       0       0       0       0       0       0       0   \n",
       "3                0       0       0       0       0       1       0       0   \n",
       "4                0       0       0       0       0       0       0       0   \n",
       "5                0       0       0       0       0       0       0       0   \n",
       "\n",
       "article_id  16.0    18.0    ...  1434.0  1435.0  1436.0  1437.0  1439.0  \\\n",
       "user_id                     ...                                           \n",
       "1                0       0  ...       0       0       1       0       1   \n",
       "2                0       0  ...       0       0       0       0       0   \n",
       "3                0       0  ...       0       0       1       0       0   \n",
       "4                0       0  ...       0       0       0       0       0   \n",
       "5                0       0  ...       0       0       0       0       0   \n",
       "\n",
       "article_id  1440.0  1441.0  1442.0  1443.0  1444.0  \n",
       "user_id                                             \n",
       "1                0       0       0       0       0  \n",
       "2                0       0       0       0       0  \n",
       "3                0       0       0       0       0  \n",
       "4                0       0       0       0       0  \n",
       "5                0       0       0       0       0  \n",
       "\n",
       "[5 rows x 714 columns]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Load the matrix here\n",
    "user_item_matrix = pd.read_pickle('user_item_matrix.p')\n",
    "\n",
    "# quick look at the matrix\n",
    "user_item_matrix.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`2.` In this situation, you can use Singular Value Decomposition from [numpy](https://docs.scipy.org/doc/numpy-1.14.0/reference/generated/numpy.linalg.svd.html) on the user-item matrix.  Use the cell to perform SVD, and explain why this is different than in the lesson."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Perform SVD on the User-Item Matrix Here\n",
    "u, s, vt = np.linalg.svd(user_item_matrix, full_matrices = False) # use the built in to get the three matrices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((5149, 714), (714,), (714, 714))"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u.shape, s.shape, vt.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Response:**\n",
    "\n",
    "We can use SVD method because the user-item matrix is completely filled with values (0 and 1). In case of one or more missing values in the matrix (None or NaN), as in the example from the lesson, SVD couldn't decomposit user-item matrix into the 3 matrices u, s, vt. Then we would need to use FunkSVD."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`3.` Now for the tricky part, how do we choose the number of latent features to use?  Running the below cell, you can see that as the number of latent features increases, we obtain a lower error rate on making predictions for the 1 and 0 values in the user-item matrix.  Run the cell below to get an idea of how the accuracy improves as we increase the number of latent features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_latent_feats = np.arange(10,700+10,20)\n",
    "sum_errs = []\n",
    "\n",
    "for k in num_latent_feats:\n",
    "    # restructure with k latent features\n",
    "    s_new, u_new, vt_new = np.diag(s[:k]), u[:, :k], vt[:k, :]\n",
    "    \n",
    "    # take dot product\n",
    "    user_item_est = np.around(np.dot(np.dot(u_new, s_new), vt_new))\n",
    "    \n",
    "    # compute error for each prediction to actual value\n",
    "    diffs = np.subtract(user_item_matrix, user_item_est)\n",
    "    \n",
    "    # total errors and keep track of them\n",
    "    err = np.sum(np.sum(np.abs(diffs)))\n",
    "    sum_errs.append(err)\n",
    "    \n",
    "    \n",
    "plt.plot(num_latent_feats, 1 - np.array(sum_errs)/df.shape[0]);\n",
    "plt.xlabel('Number of Latent Features');\n",
    "plt.ylabel('Accuracy');\n",
    "plt.title('Accuracy vs. Number of Latent Features');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`4.` From the above, we can't really be sure how many features to use, because simply having a better way to predict the 1's and 0's of the matrix doesn't exactly give us an indication if we are able to make good recommendations.  Instead, we might split our dataset into a training and test set of data, as shown in the cell below.  \n",
    "\n",
    "Use the code from question 3 to understand the impact on accuracy of the training and test sets of data with different numbers of latent features. Using the split below: \n",
    "\n",
    "* How many users can we make predictions for in the test set?  \n",
    "* How many users are we not able to make predictions for because of the cold start problem?\n",
    "* How many articles can we make predictions for in the test set?  \n",
    "* How many articles are we not able to make predictions for because of the cold start problem?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_train = df.head(40000)\n",
    "df_test = df.tail(5993)\n",
    "\n",
    "def create_test_and_train_user_item(df_train, df_test):\n",
    "    '''\n",
    "    INPUT:\n",
    "    df_train - training dataframe\n",
    "    df_test - test dataframe\n",
    "    \n",
    "    OUTPUT:\n",
    "    user_item_train - a user-item matrix of the training dataframe \n",
    "                      (unique users for each row and unique articles for each column)\n",
    "    user_item_test - a user-item matrix of the testing dataframe \n",
    "                    (unique users for each row and unique articles for each column)\n",
    "    test_idx - all of the test user ids\n",
    "    test_arts - all of the test article ids\n",
    "    \n",
    "    '''\n",
    "    user_item_train = create_user_item_matrix(df_train)\n",
    "    user_item_test = create_user_item_matrix(df_test)\n",
    "    \n",
    "    test_idx = list(set(user_item_test.index))\n",
    "    test_arts = list(set(user_item_test.columns))\n",
    "    \n",
    "    return user_item_train, user_item_test, test_idx, test_arts\n",
    "\n",
    "user_item_train, user_item_test, test_idx, test_arts = create_test_and_train_user_item(df_train, df_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "20 number of users in test set we can make predictions for\n",
      "662 number of users in test set we can NOT make predictions for (cold start problem)\n",
      "574 number of articles in test set we can make predictions for\n",
      "0 number of articles in test set we can NOT make predictions for (cold start problem)\n"
     ]
    }
   ],
   "source": [
    "# How many users can we make predictions for the test set?\n",
    "answer_1 = len(np.intersect1d(user_item_test.index, user_item_train.index))\n",
    "print(\"{} number of users in test set we can make predictions for\".format(answer_1))\n",
    "\n",
    "# How many users in the test set are we not able to make predictions for because of the cold start problem?\n",
    "answer_2 = len(set(user_item_test.index) - set(user_item_train.index))\n",
    "print(\"{} number of users in test set we can NOT make predictions for (cold start problem)\".format(answer_2))\n",
    "\n",
    "# How many articles can we make predictions for in the test set?\n",
    "answer_3 = len(np.intersect1d(user_item_test.columns, user_item_train.columns))\n",
    "print(\"{} number of articles in test set we can make predictions for\".format(answer_3))\n",
    "\n",
    "# How many articles in the test set are we not able to make predictions for because of the cold start problem?\n",
    "answer_4 = len(set(user_item_test.columns) - set(user_item_train.columns))\n",
    "print(\"{} number of articles in test set we can NOT make predictions for (cold start problem)\".format(answer_4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Awesome job!  That's right!  All of the test articles are in the training data, but there are only 20 test users that were also in the training set.  All of the other users that are in the test set we have no data on.  Therefore, we cannot make predictions for these users using SVD.\n"
     ]
    }
   ],
   "source": [
    "# Replace the values in the dictionary below\n",
    "a = 662 \n",
    "b = 574 \n",
    "c = 20 \n",
    "d = 0 \n",
    "\n",
    "\n",
    "sol_4_dict = {\n",
    "    'How many users can we make predictions for in the test set?': answer_1, \n",
    "    'How many users in the test set are we not able to make predictions for because of the cold start problem?': answer_2, \n",
    "    'How many articles can we make predictions for in the test set?': answer_3,\n",
    "    'How many articles in the test set are we not able to make predictions for because of the cold start problem?': answer_4\n",
    "}\n",
    "\n",
    "t.sol_4_test(sol_4_dict)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`5.` Now use the **user_item_train** dataset from above to find U, S, and V transpose using SVD. Then find the subset of rows in the **user_item_test** dataset that you can predict using this matrix decomposition with different numbers of latent features to see how many features makes sense to keep based on the accuracy on the test data. This will require combining what was done in questions `2` - `4`.\n",
    "\n",
    "Use the cells below to explore how well SVD works towards making predictions for recommendations on the test data.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((4487, 714), (714,), (714, 714))"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# fit SVD on the user_item_train matrix\n",
    "u_train, s_train, vt_train = np.linalg.svd(user_item_train, full_matrices = False) # fit svd similar to above then use the cells below\n",
    "\n",
    "u_train.shape, s_train.shape, vt_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((20, 714), (714, 574))"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# find subset of user and article matrices which could be calculated with dot product\n",
    "u_test = u_train[user_item_train.index.isin(test_idx), :]\n",
    "vt_test = vt_train[:, user_item_train.columns.isin(test_arts)]\n",
    "\n",
    "u_test.shape, vt_test.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "# find the subset of users and articles from user_item_test that be could predict.\n",
    "test_users = np.intersect1d(user_item_train.index, user_item_test.index)\n",
    "test_articles = np.intersect1d(user_item_train.columns, user_item_test.columns)\n",
    "user_item_test_pred = user_item_test.loc[test_users, test_articles]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_latent_feats = np.arange(10,700+10,20)\n",
    "\n",
    "sum_errs_train = []\n",
    "sum_errs_test = []\n",
    "\n",
    "f1_train = []\n",
    "f1_test = []\n",
    "\n",
    "for k in num_latent_feats:\n",
    "    # restructure with k latent features\n",
    "    s_train_new, u_train_new, vt_train_new = np.diag(s_train[:k]), u_train[:, :k], vt_train[:k, :]\n",
    "    u_test_new, vt_test_new = u_test[:, :k], vt_test[:k, :]\n",
    "    \n",
    "    # take dot product\n",
    "    user_item_train_est = np.around(np.dot(np.dot(u_train_new, s_train_new), vt_train_new))\n",
    "    user_item_test_est = np.around(np.dot(np.dot(u_test_new, s_train_new), vt_test_new))\n",
    "    \n",
    "    # compute error for each prediction to actual value\n",
    "    diffs_train = np.subtract(user_item_train, user_item_train_est)\n",
    "    diffs_test = np.subtract(user_item_test_pred, user_item_test_est)\n",
    "    \n",
    "    # total errors and keep track of them\n",
    "    errs_train = np.sum(np.sum(np.abs(diffs_train)))\n",
    "    sum_errs_train.append(errs_train)\n",
    "    errs_test = np.sum(np.sum(np.abs(diffs_test)))\n",
    "    sum_errs_test.append(errs_test)\n",
    "    \n",
    "    # compute denominators for accuracy score\n",
    "    denom_acc_train = user_item_train_est.shape[0] * user_item_train_est.shape[1]\n",
    "    denom_acc_test = user_item_test_est.shape[0] * user_item_test_est.shape[1]\n",
    "    \n",
    "    # compute f1 score (macro) for each prediction\n",
    "    f1_train.append(f1_score(np.array(user_item_train).flatten(), user_item_train_est.flatten(), labels=[1.0], average='macro'))\n",
    "    f1_test.append(f1_score(np.array(user_item_test_pred).flatten(), user_item_test_est.flatten(), labels=[1.0], average='macro'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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tYM89oUcP2GOPMLRtGz5btw5XEs656uGJw6XM+vUwZw7MmxeSRHGimDv356xbt7VcTk5IAO3bw/HHh8/4kJe3fVcJzrnU8MThdlhRUbhimDkTZswInzNnhiuJ4oeWpJAcOnSA/v2X0a9fazp0CNPt24c7fpxz2cETh0vKxo0hKUydCtOmwUcfwezZocEaQoLYe2/o2hXOOgu6dIGOHcO83NxQZtKk+fTt2zp9B+Gc2yGeOFy5iopCVdO0aSUTxcaNYXmLFpCfD0OHhkTRpQt06hRuNXXO1VyeONwWGzfCe+/BG2/AxIkhWaxfH5Y1bhwapi+/HHr2hAMPDA3W3vbg3M7HE8dOrKgIPvwwJIo33oC33gqJQoLu3WHIkJAgevaEfffN7KeOnXPVxxPHTubLL+HZZ+GVV2DSpNB1BkDnznDBBXD44XDYYeEhOOecK4snjp3A4sXw9NMwfjxMmRLudGrfHk47LSSKfv3Cw3HOOZcITxw11Pz5IVGMHx8atQG6dYObboKBA0MjtnPObQ9PHDXI4sXwr3/BE0+E5ykgtFHcdltIFvvsk974nHM1gyeOLLduXQ5jx8JDD4U2C4CDD4ZRo+CUU8JDd845V5U8cWShoiJ47bWQLMaP78OPP4YnsG+5Bc45J9wm65xzqeKJI4vMmwf33w+PPAJffRXufPrFL77m+utb07u3P1PhnKsefmd+FvjoI/jlL8O7I+64I7RbjB8fkseVV87noIM8aTjnqo9fcWSwqVPhj3+ECRPC2+ZuuAEuuwx22y3dkTnndmaeODLQf/8bEsbLL4f+oG6+GS69NLyRzjnn0s0TR4YwC91+3HILvPlmuKr485/hootCP1HOOZcpPHFkgDlz4OKLw+20u+8e2jEuvBAaNEh3ZM45t62UNo5LOlrSPEkLJA0vY3lzSc9ImiHpfUn7x5ZdLmmWpNmSrojNHyHpC0kF0XBsKo8hldavh+uvD090z5gB99wTXoh0+eWeNJxzmStlVxyScoB7gSOBpcBUSRPMbE6s2A1AgZkNkNQxKt8/SiAXAr2AjcB/JL1gZvOj9UaZ2e2pir06/Pvfod1i8WI4//xQLbXrrumOyjnnKpfKK45ewAIz+8zMNgLjgJNKlekEvA5gZh8D7STlAfsB75rZejMrBN4EBqQw1mrz+edw8slw4onQqBFMngxjxnjScM5lD1nxS6GresPSqcDRZjYkmh4E9DazS2Jl/gTkmtlVknoBU4DewHrgOeBnwA+E5DLNzC6VNAIYDKwGpgFXm9n3Zex/KDAUIC8vr8e4ceMSinvt2rU0atRou465IoWF4skn2/DQQ+0AOO+8RZx66lJq196x85+qeFPJY64e2RZztsULNT/mfv36TTezntssMLOUDMBpwP2x6UHA3aXKNAHGAgXAw8BUoFu07ALgA2AyMJpQPQWQB+QQrpZuBcZUFkuPHj0sURMnTky4bKLeftusc2czMDv5ZLPFi6tu26mIN9U85uqRbTFnW7xmNT9mwg/2bb5TU1lVtRRoG5tuA3wZL2Bmq83sfDPLB84FdgUWRsv+aWbdzexQ4DtgfjR/mZkVmdlm4B+EKrGMtHFjaPz++c9h7drwIN8zz3jHg8657JbKxDEV6CCpvaS6wBnAhHgBSc2iZQBDgMlmtjpatlv0uQdwCvBYNN0qtokBwKwUHsN2mzULevUKXZoPGQIzZ8IJJ6Q7Kuec23Epu6vKzAolXQK8TKhaGmNmsyUNi5aPJjSCPySpCJhDqJ4qNl5SS2ATcLFtbccYKSkfMGAR8OtUHcP22Lw5dGl+ww3hSe8JEzxhOOdqlpQ+AGhmLwIvlpo3Ojb+DtChnHUPKWf+oKqMsSotXgznnRee/D75ZLjvPr9byjlX83jvuFXADB58ELp2hQ8+gLFjwzu+PWk452oiTxw76Ntv4dRTYfDgrU+ADx7s3Zw752ou76tqB3z3HfTtC/Pnw8iRcNVVkJOT7qiccy61PHFsp/XrQ6P3/Pnw0ktw+OHpjsg556qHJ47tsGlTeCPfO+/Ak0960nDO7Vw8cSTJLHR5/sILMHo0DByY7oicc656eeN4kq67LtxBddNN8OuMeoLEOeeqhyeOJNx+O/zlL+GlS7//fbqjcc659PDEkaAHH4Tf/ja0bdx5p99u65zbeXniSMDzz8MFF0D//vDQQ37LrXNu5+aJoxJTpoSrjPz80LNtvXrpjsg559LLE0cFZs2C446DNm3CsxqNG6c7IuecSz9PHBUYNQrq14dXXvF+p5xzrpg/x1GB0aNh6VJo1y7dkTjnXObwK44K1KkD7dunOwrnnMssnjicc84lxROHc865pHjicM45lxRPHM4555KS0sQh6WhJ8yQtkDS8jOXNJT0jaYak9yXtH1t2uaRZkmZLuiI2v4WkVyXNjz6bp/IYnHPOlZSyxCEpB7gXOAboBJwpqVOpYjcABWbWFTgXuDNad3/gQqAX0A04XlKHaJ3hwOtm1gF4PZp2zjlXTVJ5xdELWGBmn5nZRmAccFKpMp0IX/6Y2cdAO0l5wH7Au2a23swKgTeBAdE6JwEPRuMPAien8Bicc86VIjNLzYalU4GjzWxIND0I6G1ml8TK/AnINbOrJPUCpgC9gfXAc8DPgB8IyWWamV0qaaWZNYtt43sz26a6StJQYChAXl5ej3HjxiUU99q1a2nUqNH2HHJaZFu84DFXl2yLOdvihZofc79+/aabWc/S81P55HhZHY+XzlK3AXdKKgBmAh8ChWY2V9KfgVeBtcBHQGEyOzez+4D7AHr27Gl9+/ZNaL1JkyaRaNlMkG3xgsdcXbIt5myLF3bemFOZOJYCbWPTbYAv4wXMbDVwPoAkAQujATP7J/DPaNmfou0BLJPUysy+ktQK+CaFx+Ccc66UVLZxTAU6SGovqS5wBjAhXkBSs2gZwBBgcpRMkLRb9LkHcArwWFRuAnBeNH4eoUrLOedcNUnZFYeZFUq6BHgZyAHGmNlsScOi5aMJjeAPSSoC5gAXxDYxXlJLYBNwsZl9H82/DXhC0gXA58BpqToG55xz20pp77hm9iLwYql5o2Pj7wAdSq8XLTuknPkrgP5VGKZzzrkk+JPjzjnnkuKJwznnXFI8cTjnnEuKJw7nnHNJ8cThnHMuKZ44nHPOJcUTh3POuaR44nDOOZcUTxzOOeeS4onDOedcUjxxOOecS4onDuecc0nxxOGccy4pnjicc84lxROHc865pHjicM45lxRPHM4555JSaeKQdLwkTzDOOeeAxK44zgDmSxopab9UB+Sccy6zVZo4zOwc4ADgU2CspHckDZXUuLJ1JR0taZ6kBZKGl7G8uaRnJM2Q9L6k/WPLrpQ0W9IsSY9Jyo3mj5D0haSCaDg2qSN2zjm3QxKqgjKz1cB4YBzQChgAfCDp0vLWkZQD3AscA3QCzpTUqVSxG4ACM+sKnAvcGa3bGrgM6Glm+wM5hCufYqPMLD8aXkzkGJxzzlWN2pUVkHQC8Ctgb+BhoJeZfSOpATAXuLucVXsBC8zss2g744CTgDmxMp2A/wUws48ltZOUF4utvqRNQAPgy2QPzjmXPps2bWLp0qVs2LAhofJNmzZl7ty5KY6qatWUmHNzc2nTpg116tRJaBuVJg7gNMIv/MnxmWa2XtKvKlivNbAkNr0U6F2qzEfAKcB/JfUC9gTamNl0SbcDnwM/AK+Y2Sux9S6RdC4wDbjazL4vvXNJQ4GhAHl5eUyaNKnyIwXWrl2bcNlMkG3xgsdcXdIdc6NGjcjLy6N169ZIqrR8UVEROTk51RBZ1akJMZsZq1at4qOPPmLt2rWJbcTMKhyA9kBubLo+0C6B9U4D7o9NDwLuLlWmCTAWKCBczUwFugHNgTeAXYE6wLPAOdE6eYSqq1rArcCYymLp0aOHJWrixIkJl80E2RavmcdcXdId85w5c2zz5s0Jl1+9enUKo0mNmhLz5s2bbc6cOdvMB6ZZGd+pibRxPAlsjiesaF5llgJtY9NtKFXdZGarzex8M8sntHHsCiwEjgAWmtlyM9sEPA30idZZZmZFZrYZ+AehSsw5l4ESudJw6Zfsv1MiiaO2mW0snojG6yaw3lSgg6T2kuoSGrcnxAtIahYtAxgCTLbQEP85cJCkBgpH1J/QnoKkVrFNDABmJRCLc24nsmLFCvLz88nPz+cnP/kJrVu33jK9cePGCtedNm0al112WTVFmp0SaeNYLulEM5sAIOkk4NvKVjKzQkmXAC8TqpbGmNlsScOi5aOB/YCHJBURGs0viJa9J+kp4AOgEPgQuC/a9EhJ+YABi4BfJ3iszrmdRMuWLSkoKABgxIgRNGrUiGuuuWbL8sLCQmrXLvvrr2fPnvTs2bM6wkxaRXFXp0SuOIYBN0j6XNIS4DoS/LI2sxfNbF8z29vMbo3mjY6SBmb2jpl1MLOOZnaKxRq5zezGaP7+ZjbIzH6M5g8ysy5m1tXMTjSzr5I9aOfczmfw4MFcddVV9OvXj+uuu47333+fPn36cMABB9CnTx/mzZsHwKRJkzj++OOBkHR+9atf0bdvX/baay/uuuuuMrd90UUX0bNnTzp37syNN964Zf7UqVPp06cP3bp1o1evXqxZs4aioiKuueYaunTpQteuXbn77nBjart27fj22/CbfNq0afTt23dLDEOHDuWoo47i3HPPZdGiRRxyyCF0796d7t27M2XKlC37GzlyJF26dKFbt24MHz6cTz/9lO7du29ZPn/+fA499NAdPpeVpi4z+5RQbdQIkJmt2eG9Oud2KldcAdEFQLmKiuqTzA1K+flwxx3JxfHJJ5/w2muvkZOTw+rVq5k8eTK1a9fmtdde44YbbmD8+PHbrPPxxx8zceJE1qxZw09/+lMuuuiibW5bvfXWW2nRogVFRUX079+fGTNm0LFjR04//XQef/xxDjzwQFavXk39+vW57777WLhwIR9++CG1a9fmu+++qzTu6dOn89///pf69euzfv16Xn31VXJzc5k/fz5nnnkm06ZN46WXXuLZZ5/lvffeo0GDBnz33Xe0aNGCpk2bUlBQQH5+PmPHjuWss85K7qSVIaFrHknHAZ2B3OJGFDO7eYf37pxz1ei0007bcivqqlWrOO+885g/fz6S2LRpU5nrHHfccdSrV4969eqx2267sWzZMtq0aVOizBNPPMF9991HYWEhX331FXPmzEESrVq14sADDwSgSZMmALz22msMGzZsS5VTixYtKo37xBNPpH79+kB4PuaSSy6hoKCAnJwcPvnkky3bPf/882nQoEGJ7Q4ZMoSxY8fyt7/9jccff5zXX389qXNWlkQeABxNeACvH3A/cCrw/g7v2Tm300jkymDNmh9o3LjSnox2SMOGDbeM//73v6dfv34888wzLFq0aEvVUGn16tXbMp6Tk0NhYWGJ5QsXLuT2229n6tSpNG/enMGDB7NhwwbMrMy7lcqbX7t2bTZvDjewln5oMh73qFGjyMvL46OPPmLz5s3k5uZWuN2BAwdy0003cfjhh9OjRw9atmxZ5nEmI5E2jj5mdi7wvZndBPyMkrfZOudc1lm1ahWtW7cG4IEHHtju7axevZqGDRvStGlTli1bxksvvQRAx44d+fLLL5k6dSoAa9asobCwkKOOOorRo0dvSUDFVVXt2rVj+vTpAGVWmcXjbtWqFbVq1eLhhx+mqKgIgKOOOooxY8awfv36EtvNzc3lF7/4BRdddBHnn3/+dh9nXCKJozj1rZe0O7CJ8FCgc85lrWuvvZbrr7+egw8+eMuX7/bo1q0bBxxwAJ07d+ZXv/oVBx98MAB169bl8ccf59JLL6Vbt24ceeSRbNiwgSFDhrDHHnvQtWtXunXrxqOPPgrAjTfeyOWXX84hhxxS4dPov/nNb3jwwQc56KCD+OSTT7ZcjRx99NGceOKJ9OzZk/z8fG6//fYt65x99tlI4qijjtru4yyhrKcCreTT3b8HmgEDga+Br4CbK1svkwZ/cjyzeMzVI90xl/UkckVqylPYmegvf/mL/c///I+ZlR9zMk+OV9jGEb3A6XUzWwmMl/Q8ofuRVVWTtpxzzqXSgAED+PTTT3njjTeqbJsVJg4z2yzpr4R2DSw8S/Fjle3dOedcSj3zzDNVvs1E2jhekTRQ3umMc845EnuO4yqgIVAoaQMgwMysSUojc845l5ESeXI8tTdWO+ecyyqJPABYZscmVurFTs4553YOiVRV/TY2nkt4/8V04PCUROSccztoxYoV9O/fH4Cvv/6anJwcdt11VwDef/996tat+M0QkyZNom7duvTp0yflsWajRKqqTohPS2oLjExZRM45t4Mq61a9MpMmTaJRo0ZpTxyZ+mraRO6qKm0psH9VB+Kcc6k0ffp0DjvsMHr06MEvfvELvvoqvJHhrrvuolOnTnTt2pUzzjiDRYsWMXr0aEaNGkV+fj5vvfVWie3Eu2M/4ogjtnTHXl536WV1rf7AAw9wySWXbNnm8ccfv+X98I0aNeIPf/gDvXv35p133uHmm2/mwAMPZP/992fo0KHFD2azYMECjjjiCLp160b37t359NNPGTRoEM8999yW7Z599tlMmFDi/XlVIpE2jrsJL02CkGjygY+qPBLnXM2VQL/q9YuKSFW/6mbGpZdeynPPPceuu+7K448/zu9+9zvGjBnDbbfdxsKFC6lXrx4rV66kWbNmDBs2rNyrlI4dO27pjn3ChAlbumMvq7v0jRs3ltm1ekXWrVvH/vvvz803hw7IO3XqxB/+8AcABg0axPPPP88JJ5zA2WefzfDhwxkwYAAbNmxg8+bNDBkyhFGjRnHSSSexatUqpkyZwoMPPpj4OU1QIm0c02LjhcBjZvZ2lUfinHMp8uOPPzJr1iyOPPJIIFwdtGoV3kLdtWtXzj77bE4++WROPvnkSrcV747dzLb0c1VWd+kzZ84ss2v1iuTk5DBw4MAt0xMnTmTkyJGsX7+e7777js6dO9O3b1+++OILBgwYALClh9zDDjuMiy++mG+++Yann36agQMHpuSNgYls8Slgg5kVAUjKkdTAzNZXeTTOuZopgSuDH9asSVm36mZG586deeedd7ZZ9sILLzB58mQmTJjALbfcwuzZsyvcVrw79lmzZm15W6CV0a15WfOgZBfqULIb9dzc3C3tGhs2bOA3v/kN06ZNo23btowYMWJLl+3lGTRoEI888gjjxo1jzJgxFR7L9kqkjeN1IH5tVR94LZGNSzpa0jxJCyQNL2N5c0nPSJoh6X1J+8eWXSlptqRZkh6TlBvNbyHpVUnzo8/micTinNt51atXj+XLl29JHJs2bWL27Nls3ryZJUuW0K9fP0aOHMnKlStZu3YtjRs3Zs2asl92Gu+O/ZFHHtkyv6zu0svrWr1du3YUFBRs2f/775f9iqPihLLLLruwdu1annrqKSBcubRp04Znn30WCFdUxd2pDx48mDuiRN25c+ftPWUVSiRx5JrZ2uKJaLxBZStJygHuBY4BOgFnSupUqtgNQIGZdQXOBe6M1m0NXAb0NLP9gRzgjGid4YSOFzsQkto2Cck55+Jq1arFU089xXXXXUe3bt3Iz89nypQpFBUVcc4559ClSxcOOOAArrzySpo1a8YJJ5zAM888U2bjeHndsZfVXXp5XasffPDBtG/fni5dunDNNdeUeC94XLNmzbjwwgvp0qULJ5988pYqL4CHH36Yu+66i65du9KnTx++/vprAPLy8thvv/2q7N0bZSqry9z4ALwNdI9N9wDeSWC9nwEvx6avB64vVeYF4Oex6U+BPKA1sARoQahOex44KiozD2gVjbcC5lUWi3ernlk85uqR7pi9W/X0WLdune211162cuXKMpenvFv1yBXAk5K+jKZbAacnsF7xl3+xpUDvUmU+Ak4B/iupF7An0MbMpku6Hfgc+AF4xcxeidbJM7OvAMzsK0m7lbVzSUOBoRAycPGtbpVZu3ZtwmUzQbbFCx5zdUl3zE2bNi23uqcsRUVFSZXPBJkW88SJE7n44ou5+OKLqVWrVpmxlRfzhg0bEv97KSublB6AOoRnN7oAdRJc5zTg/tj0IODuUmWaAGOBAuBhYCrQDWgOvAHsGu37WeCcaJ2VpbbxfWWx+BVHZvGYq0e6Y/YrjsxUFVcclbZxSLoYaGhms8xsJtBI0m8SyElLKflu8jbAl/ECZrbazM43s3xCG8euwELgCGChmS03s03A00DxI5zLJLWKYmsFfJNALM4556pIIo3jF1p4AyAAZvY9cGEC600FOkhqL6kuoXG7xCOMkppFywCGAJPNbDWhiuogSQ2i94D0B+ZG5SYA50Xj5wHP4ZzLSFbBbaMucyT775RI4qgVf4lTdLdUxT2EhUAKgUuAlwlf+k+Y2WxJwyQNi4rtB8yW9DHh7qvLo3XfIzw/8gEwM4rzvmid24AjJc0HjoymnXMZJjc3lxUrVnjyyHBmxooVK7Y8RJiIRBrHXwaekDSa0PXIMOClBAN6EXix1LzRsfF3gA7lrHsjcGMZ81cQrkCccxmsTZs2LF26lOXLlydUfsOGDUl9eWWCmhJzbm4ubdq0SXgbiSSO6wh3J11EePvfh4Q7q5xzrlx16tShffv2CZefNGkSBxxwQAojqno7a8yVVlWZ2WbgXeAzoCcl2xucc87tZMq94pC0L6FB+0xgBfA4gJn1q57QMsDixTBtGsQ6HHPOuZ1dRVccHxOuLk4ws5+b2d1AUQXla57f/x7OOANefjndkTjnXMaoKHEMBL4GJkr6h6T+hDaOncc990DnznDqqfDhh+mOxjnnMkK5icPMnjGz04GOwCTgSiBP0v9JOqqa4kuvJk3gxReheXM47jj4/PN0R+Scc2mXSOP4OjN7xMyOJzz9XcDO1CPt7rvDSy/B+vVwzDHw/ffpjsg559IqqXeOm9l3ZvZ3Mzs8VQFlpM6d4dlnYcECGDAAfvwx3RE551zaJJU4dmp9+8IDD8Cbb8LgwRB7e5dzzu1Mqv5ltDXZmWeGdo7hw2GPPeDPf053RM45V+08cSTr2mtD8hg5MiSPiy9Od0TOOVetPHEkS4K77oKlS+Gyy6BNGzjppHRH5Zxz1cbbOLZHTg489hj07Bmqr957L90ROedctfHEsb0aNIB//zvcrnvkkfDUU+mOyDnnqoUnjh2x224wcSJ06gSnnQaXXw4bN6Y7KuecSylPHDuqbVuYPBmuuCK0fRxySOgc0TnnaihPHFWhbl0YNQrGj4ePP4YDDoDnn093VM45lxKeOKrSKafABx9Au3Zwwglw3XWwaVO6o3LOuSrliaOq7b03TJkCw4aFZz0OPxy++CLdUTnnXJVJaeKQdLSkeZIWSNqmY0RJzSU9I2mGpPcl7R/N/6mkgtiwWtIV0bIRkr6ILTs2lcewXXJz4f/+Dx55JHTHnp8Pr7+e7qicc65KpCxxSMoB7gWOAToBZ0rqVKrYDUCBmXUFzgXuBDCzeWaWb2b5QA9gPfBMbL1RxcvN7MVUHcMOO+us8AbBvDw49thwB5ZzzmW5VF5x9AIWmNlnZrYRGAeUfsS6E/A6gJl9DLSTlFeqTH/gUzPLzluVOnYMd1116AAnnhgSiXPOZTGZWWo2LJ0KHG1mQ6LpQUBvM7skVuZPQK6ZXSWpFzAlKjM9VmYM8IGZ3RNNjwAGA6uBacDVZrbNSzIkDQWGAuTl5fUYN25cQnGvXbuWRo0aJX/Alaj77bcccOml5PzwAwV33cX6Pfaoku2mKt5U8pirR7bFnG3xQs2PuV+/ftPNrOc2C8wsJQNwGnB/bHoQcHepMk2AsYSXQz0MTAW6xZbXBb4F8mLz8oAcwtXSrcCYymLp0aOHJWrixIkJl03a/Plmu+1m1rat2eLFVbLJlMabIh5z9ci2mLMtXrOaHzMwzcr4Tk1lVdVSoG1sug3wZbyAma02s/MttGWcC+wKLIwVOYZwtbEsts4yMysys83APwhVYtlhn33g5Zdh1So46ihYvjzdETnnXNJSmTimAh0ktZdUFzgDmBAvIKlZtAxgCDDZzFbHipwJPFZqnVaxyQHArCqPPJXy88PDgYsXh1fRrlmT7oiccy4pKUscZlYIXAK8DMwFnjCz2ZKGSRoWFdsPmC3pY8LVxeXF60tqABwJPF1q0yMlzZQ0A+gHXJmqY0iZQw6BJ5+EgoLQJfuGDemOyDnnEpbS93FYuFX2xVLzRsfG3wE6lLPueqBlGfMHVXGY6XH88eFVtIMGha7Zn3wSavvrUZxzmc+fHE+nc86BO++EZ5+FX/8aUnSHm3POVSX/iZtul10GK1bAzTeHd3zccUd4UZRzzmUoTxyZYMSI0Eg+ahQsWACPPgrNm6c7KuecK5NXVWUCCf72Nxg9Gl57DXr3hrlz0x2Vc86VyRNHJvn1r+GNN2DlypA8/J0ezrkM5Ikj0xxySOjPqrhvqz/9yRvNnXMZxRNHJtpjD3jrrXCb7u9+B6efDuvWpTsq55wDPHFkrgYN4F//Ci+DeuopOPhgWLQo3VE555wnjowmwW9/Cy+8EJLGgQeGLtqdcy6NPHFkg2OOgfffh5Yt4bjjwlsFnXMuTTxxZIt99w13XDVvHt4muDg732vlnMt+njiyye67w0svwQ8/hKuQ77d5f5VzzqWcJ45s07lz6Nvq00/h5JPRxo3pjsg5t5PxLkeyUd++oWfds85iv5wcOOIIqOW/AZxz1cO/bbLVmWfCbbex28SJMHx4uqNxzu1EPHFks2uv5YuTToK//AXuuSfd0TjndhJeVZXNJOZfeimtzUL37G3awMknpzsq51wN51cc2S4nBx57LDwceOaZ8O676Y7IOVfDeeKoCRo0gH//G1q3hhNOgE8+SXdEzrkaLKWJQ9LRkuZJWiBpmxZcSc0lPSNphqT3Je0fzf+ppILYsFrSFdGyFpJelTQ/+vQ3HgHstlt4xgOgRw+4/XbYtCm9MTnnaqSUJQ5JOcC9wDFAJ+BMSZ1KFbsBKDCzrsC5wJ0AZjbPzPLNLB/oAawHnonWGQ68bmYdgNejaQehK/b33gu36/72t9CtG7z+erqjcs7VMKm84ugFLDCzz8xsIzAOOKlUmU6EL3/M7GOgnaS8UmX6A5+aWXEfGycBD0bjDwInpyD27LXXXqHa6t//hh9/DM94/PKXsGRJuiNzztUQshS9JEjSqcDRZjYkmh4E9DazS2Jl/gTkmtlVknoBU6Iy02NlxgAfmNk90fRKM2sWW/69mW1TXSVpKDAUIC8vr8e4ceMSinvt2rU0atQo6eNNl4rirbVxI20ff5w9HnkEJBaffTZLfvlLrG7dao6ypGw7x+AxV4dsixdqfsz9+vWbbmY9t1lgZikZgNOA+2PTg4C7S5VpAowFCoCHgalAt9jyusC3QF5s3spS2/i+slh69OhhiZo4cWLCZTNBQvEuWmR2yilmYNahg9lLL6U8ropk2zk285irQ7bFa1bzYwamWRnfqamsqloKtI1NtwG+jBcws9Vmdr6FtoxzgV2BhbEixxCuNpbF5i2T1Aog+vwmBbHXLHvuCePHw8svh65JjjkGjj4a3n473ZE557JQKhPHVKCDpPaS6gJnABPiBSQ1i5YBDAEmm9nqWJEzgcdKbXcCcF40fh7wXJVHXlMddRTMmBGeNP/gA/j5z+Hww0N37f5ec+dcglKWOMysELgEeBmYCzxhZrMlDZM0LCq2HzBb0seEq4vLi9eX1AA4Eni61KZvA46UND9afluqjqFGqlsXrrkGFi6Ev/0NPv4Y+vcPSeQ///EE4pyrVEqf4zCzF81sXzPb28xujeaNNrPR0fg7ZtbBzDqa2Slm9n1s3fVm1tLMVpXa5goz6x+t19/MvkvlMdRYDRvClVfCZ5/BvfeGu66OOQZ69YLnnvME4pwrlz85vrPLzYXf/AYWLIB//AO++y70d5WfD488Av6+D+dcKZ44XFC3LgwZAvPmwUMPhYRxzjnQrh3ccgt84/cgOOcCTxyupNq1YdAgmD0bXnwRunaFP/wB9tgDzj8fCgrSHaFzLs08cbiyFd+2+5//wNy5cMEF8MQTcMABcOih4fbewsJ0R+mcSwNPHK5yHTuGBvQvvgidJy5ZAqeeCnvvDSNHhnYR59xOwxOHS1yzZnD11aEh/emnoX17uO46aNsWhg2DOXPSHaFzrhp44nDJy8mBAQNg0iT48EM4/XR44AHo3Dk8ZPjCC7B5c7qjdM6liCcOt2Py82HMmFB99cc/hkb1448P1Vt33w1r1qQ7QudcFfPE4arGrrvC734HixbBo49CixbhPeitW8MVV8Cnn6Y7QudcFfHE4apWnTpb333+7rvhVbb33hteMnXiieHFUv5UunNZzROHS53evcPT54sXh6uRd9+FI46g5wUXhKfU169Pd4TOue3gicOl3u67h6fPP/8cxo7FcnJg6NBwN9bw4f52QueyTO10B+B2Irm5MHgw0/fck745OXDnnaGL99tvDw8WHnRQuEo56KDwjIiU7oidc2XwxOGqnxSePj/00FCN9c9/wltvwdixcM89oUzLliGJFA+9ekHzbd4Q7JxLA08cLr323BNuvjmMFxWF23nfe29r4/pLL21tTO/TBwYODMOee6YvZud2ct7G4TJHTk7oVPHCC8NVyOzZ8P338OqrcOONsG5deHK9XTvo2RNuuw3mz0931M7tdDxxuMzWtCkccQSMGBF65p0/H/7855Bkrr8e9t03JJubboJZs/xWX+eqgScOl1322QeuvTZUZy1eDKNGheRy003QpQvsthscd1y4i+uVV2DlynRH7FyN420cLnvtsUd4Kv2KK+Drr+H55+Gdd0JSibeNdOy49W6t3r1hv/3CHV7Oue2S0sQh6WjgTiAHuN/Mbiu1vDkwBtgb2AD8ysxmRcuaAfcD+wMWLXtH0gjgQmB5tJkbzOzFVB6HywI/+Ul4g+GQIWF61SqYNi00sL/3Xngp1YMPhmW1asFee4UE0qlTGPbbLySYxo3TdwzOZYmUJQ5JOcC9wJHAUmCqpAlmFu97+wagwMwGSOoYle8fLbsT+I+ZnSqpLtAgtt4oM7s9VbG7GqBpU+jfPwwQrj4WLYKpU0P378XDf/4DmzZtXa9t29DLb8+eW69QdtklLYfgXKZK5RVHL2CBmX0GIGkccBIQTxydgP8FMLOPJbWTlAf8ABwKDI6WbQQ2pjBWV9NJ4f0h7duXnF9YGDpgnDs3JJK5c2HmTPjf/w23BwPstRf7tW8PM2aERJKfD/XqVfshOJcpZCm6C0XSqcDRZjYkmh4E9DazS2Jl/gTkmtlVknoBU4DeQBFwHyHJdAOmA5eb2bqoqmowsBqYBlxtZt+Xsf+hwFCAvLy8HuPGjUso7rVr19KoUaPtOuZ0yLZ4ITtirvXDDzT+5BOazJ1Lk7lzaTR7NvVXrABgc506rGvXjs1161a4DcvJYWPLlvy4yy78uOuuW4dddmFjy5ZY7dQ2MWbDeY7Ltnih5sfcr1+/6WbWs/T8VCaO04BflEocvczs0liZJoQqqQOAmUBHYAhQB3gXONjM3pN0J7DazH4fXZF8S2j3uAVoZWa/qiiWnj172rRp0xKKe9KkSfTt2zepY02nbIsXsjjmffYJ7SXvvReuSoqvSMqzcSN89RUsXbpth45SaJfZbbdwa3FF6tQJ/X21abN1aN1662c5Df3Zdp6zLV6o+TFLKjNxpPInz1KgbWy6DfBlvICZrQbOjwIUsDAaGgBLzey9qOhTwPBonWXF60v6B/B8iuJ3rqTiL+2BA5NbzyzcFvzFFyGJFA9ffAHLllX+7MmGDTBvXuiSfvXqbZe3bBneh1Kr5N31B65bBw0bJhdrGmVbvJAlMf/97/Dzn1fpJlOZOKYCHSS1B74AzgDOiheI7pxaH7VhDAEmR8lktaQlkn5qZvMIDeZzonVamdlX0SYGALNSeAzO7Tgp9LPVvDnsv/+ObWvNmpBw4knoiy9g+fJtiq5bvpyGu+66Y/urRtkWL2RJzClIbClLHGZWKOkS4GXC7bhjzGy2pGHR8tHAfsBDkooIieGC2CYuBR6J7qj6jOjKBBgpKZ9QVbUI+HWqjsG5jNO4cbhtuGPHSovOmTSJ3bKoGiXb4oXsjLkqpLR1Lnq+4sVS80bHxt8BOpSzbgGwTd2amQ2q2iidc84lw7sccc45lxRPHM4555LiicM551xSPHE455xLiicO55xzSfHE4ZxzLimeOJxzziUlZX1VZRJJy4HFCRbfhdAXVrbItnjBY64u2RZztsULNT/mPc1sm0fjd4rEkQxJ08rq1CtTZVu84DFXl2yLOdvihZ03Zq+qcs45lxRPHM4555LiiWNb96U7gCRlW7zgMVeXbIs52+KFnTRmb+NwzjmXFL/icM45lxRPHM4555LiiSMi6WhJ8yQtkDQ83fEUkzRG0jeSZsXmtZD0qqT50Wfz2LLro2OYJ+kXaYi3raSJkuZKmi3p8iyIOVfS+5I+imK+KdNjjsWRI+lDSc9nQ8ySFkmaKalA0rRMj1lSM0lPSfo4+pv+WYbH+9Po3BYPqyVdUeUxm9lOPxDeUPgpsBdQF/gI6JTuuKLYDgW6A7Ni80YCw6Px4cCfo/FOUez1gPbRMeVUc7ytgO7ReGPgkyiuTI5ZQKNovA7wHnBQJscci/0q4FHg+Uz/24jiWATsUmpexsYMPAgMicbrAs0yOd5SsecAXwN7VnXMaTmgTBuAnwEvx6avB65Pd1yxeNpRMnHMA1pF462AeWXFTXht78/SHPtzwJHZEjPQAPgA6J3pMQNtgNeBw2OJI9NjLitxZGTMQBNgIdFNRJkebxnxHwW8nYqYvaoqaA0siU0vjeZlqjwz+wog+twtmp9RxyGpHXAA4Rd8RsccVfkUAN8Ar5pZxscM3AFcC2yOzcv0mA14RdJ0SUOjeZka817AcmBsVB14v6SGGRxvaWcAj0XjVRqzJ45AZczLxvuUM+Y4JDUCxgNXmNnqioqWMa/aYzazIjPLJ/yK7yVp/wqKpz1mSccD35jZ9ERXKWNeOv42Djaz7sAxwMWSDq2gbLpjrk2oJv4/MzsAWEeo5ilPuuPdQlJd4ETgycqKljGv0pg9cQRLgbax6TbAl2mKJRHLJLUCiD6/ieZnxHFIqkNIGo+Y2dPR7IyOuZiZrQQmAUeT2TEfDJwoaREwDjhc0r/I7Jgxsy+jz2+AZ4BeZG7MS4Gl0dUnwFOERJKp8cYdA3xgZsui6SqN2RNHMBXoIKl9lKnPACakOaaKTADOi8bPI7QjFM8/Q1I9Se2BDsD71RmYJAH/BOaa2d9iizI55l0lNYvG6wNHAB9ncsxmdr2ZtTGzdoS/1zfM7JxMjllSQ0mNi8cJdfCzMjVmM/saWCLpp9Gs/sCcTI23lDPZWk0FVR1zuhpuMm0AjiXcAfQp8Lt0xxOL6zHgK2AT4dfBBUBLQqPo/OizRaz876JjmAcck4Z4f0641J0BFETDsRkec1fgwyjmWcAfovkZG3Op+PuytXE8Y2MmtBl8FA2zi/+fZXjM+cC06G/jWaB5JscbxdAAWAE0jc2r0pi9yxHnnHNJ8aoq55xzSfHE4ZxzLimeOJxzziXFE4dzzrmkeOJwzjmXFE8cLuNIMkl/jU1fI2lEFW37AUmnVsW2ou0tkrRLgmXzJR27g/u7oZJYinueLZDUZzu233d71nM7F08cLhP9CJyS6BdydZGUs4ObyCc807Ijyk0ckX5mlh8NU7Zj+32BpBJHFZwXl2U8cbhMVEh4L/KVpReUvmKQtDb67CvpTUlPSPpE0m2SzlZ4z8ZMSXvHNnOEpLeicsdH6+dI+oukqZJmSPp1bLsTJT0KzEwkeEm9JE2JOsabEr0joS5wM3B6dDVwevQk9Zhonx9KOilaf7CkpyX9J3p/wsho/m1A/Wj9RxKMZe9oO9OjY+4YzT9B0nvRfl+TlKfQKeUw4MpoH4dUcr63nJcKzl8rSZOj7c2SdEgicbsMl44nG33woaIBWEvo0noR0BS4BhgRLXsAODVeNvrsC6wkdBldD/gCuCladjlwR2z9/xB+NHUgPI2fCwwF/icqU4/wtHD7aLvrgPblxLqIbbsJbwLUjsaPAMZH44OBe2Ll/gScE403I/Rc0DAq91l07LnAYqBt/HgriGUm4Wn996J5rwMdovHehK5JIDwBXfwA8BDgr9H4COCa2DYrOt9bzksF5+9qtj4hngM0Tvfflw87PtTGuQxkZqslPQRcBvyQ4GpTLeo6WtKnwCvR/JlAv1i5J8xsMzBf0mdAR0K/SV1jv66bEhLLRuB9M1uYRPhNgQcldSB0v1KnnHJHEToqvCaazgX2iMZfN7NV0bHMIbyMZ8m2m9hGPzP7NlqvEaHa6cnQhRgQvtQhdGb3uEKHd3UJ751IVvy8lHf+pgJjFDq+fNbMCrZjPy7DeOJwmewOwkuVxsbmFRJVsSp8G9aNLfsxNr45Nr2Zkn/rpfvZMUL30pea2cvxBZL6En5ZJ+MWYKKZDYiqfyaVU07AQDObV2qfvSl5LEVs3//VWsBKC93Fl3Y38DczmxAd44hytlHR+Y6flzLPX7TeocBxwMOS/mJmDyV3GC7TeBuHy1hm9h3wBKFjx2KLgB7R+EmU/2u+IqdJqhW1e+xF6NztZeCi6JcxkvZV6MF1ezQlVJVBqHYqtobwOt1iLwOXRl/ISDoggW1vKo6xMhbeg7JQ0mnR9iWpWxkxnhdbrXSMi0jsfJd5/iTtSXhvyD8IvSZ3TyR2l9k8cbhM91cgfnfVP4DDJL1PqLNP9moAQqJ4E3gJGGZmG4D7CV1mfyBpFvB3Ev+VP0PS0mj4G+H9zv8r6W1CvX6xiUCn4sZxwpVJnWj9WdF0Ze6LyifUOA6cDVwgqbhH2pOi+SMIVVhvAd/Gyv8bGFDcOE7i57u889cXKJD0ITAQuDPBuF0G895xnXPOJcWvOJxzziXFE4dzzrmkeOJwzjmXFE8czjnnkuKJwznnXFI8cTjnnEuKJw7nnHNJ+f+Pnk0f5zcZ1QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(num_latent_feats, 1 - np.array(sum_errs_train)/denom_acc_train, c = \"b\", label = \"Train accuracy\")\n",
    "plt.plot(num_latent_feats, 1 - np.array(sum_errs_test)/denom_acc_test, c = \"r\", label = \"Test accuracy\")\n",
    "plt.title('Accuracy vs. Number of Latent Features')\n",
    "plt.xlabel('Number Latent Features')\n",
    "plt.ylabel('Accuracy')\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax_train = plt.subplots()\n",
    "ax_test = ax_train.twinx()\n",
    "\n",
    "f1_train_plot, = ax_train.plot(num_latent_feats, f1_train, c = \"b\", label = \"Train f1 score\")\n",
    "f1_test_plot, = ax_test.plot(num_latent_feats, f1_test, c = \"r\", label = \"Test f1 score\")\n",
    "ax_train.set_title(\"f1 score vs. Number of Latent Features\")\n",
    "ax_train.set_xlabel(\"Number Latent Features\")\n",
    "ax_train.set_ylabel(\"Train f1 score\")\n",
    "ax_test.set_ylabel(\"Test f1 score\")\n",
    "ax_train.grid(True)\n",
    "\n",
    "lines = [f1_train_plot, f1_test_plot]\n",
    "ax_train.legend(lines, [l.get_label() for l in lines])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "`6.` Use the cell below to comment on the results you found in the previous question. Given the circumstances of your results, discuss what you might do to determine if the recommendations you make with any of the above recommendation systems are an improvement to how users currently find articles? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Response:**\n",
    "\n",
    "Train accuracy is increasing with higher number of latent features while test accuracy is decreasing.\n",
    "\n",
    "In the data set we have only 20 users in train and test set we can make predictions for. Furthermore there are many zeros in the user-item matrix showing that users were not active in many times. In short we have an imbalanced distribution with few interactions and the accuracy is not a good metric to evaluate the performance of the recommendations. In this case the f1 score is a better evaluation metric.\n",
    "\n",
    "The f1 score for the test set increases to a maximum peak at appr. 100 latent features and then decreases. The decline after the peak indicates that the model gets more and more overfitted with higher number of latent features when performing matrix factorization.\n",
    "\n",
    "One possible evaluation metric for our recommender system would be an A/B test. We would split users into two groups (control & experiment). In the control group we would recommend articles with the Ranked-Based Recommendation method while in the experiment group we would recommend articles using the Matrix Factorization method. Thus we could check if we could increase user engagement on IBM Watson Studio platform with this metric."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### <a class=\"anchor\" id=\"conclusions\">Part V: Extras & Conclusion</a>\n",
    "\n",
    "### Extras\n",
    "Using your workbook, you could now save your recommendations for each user, develop a class to make new predictions and update your results, and make a flask app to deploy your results.  These tasks are beyond what is required for this project.  However, from what you learned in the lessons, you certainly capable of taking these tasks on to improve upon your work here!\n",
    "\n",
    "\n",
    "## Conclusion\n",
    "\n",
    "> Congratulations!  You have reached the end of the Recommendations with IBM project! \n",
    "\n",
    "\n",
    "## Directions to Submit\n",
    "\n",
    "> Before you submit your project, you need to create a .html or .pdf version of this notebook in the workspace here. To do that, run the code cell below. If it worked correctly, you should get a return code of 0, and you should see the generated .html file in the workspace directory (click on the orange Jupyter icon in the upper left)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from subprocess import call\n",
    "call(['python', '-m', 'nbconvert', 'Recommendations_with_IBM.ipynb'])"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}