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",
    "\n",
    "You may either submit your notebook through the workspace here, or you may work from your local machine and submit through the next page.  Either way assure that your code passes the project [RUBRIC](https://review.udacity.com/#!/rubrics/2322/view).  **Please save regularly.**\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. [Content Based Recommendations (EXTRA - NOT REQUIRED)](#Content-Recs)<br>\n",
    "V. [Matrix Factorization](#Matrix-Fact)<br>\n",
    "VI. [Extras & Concluding](#conclusions)\n",
    "\n",
    "At the end of the notebook, you will find directions for how to submit your work.  Let's get started by importing the necessary libraries and reading in the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[nltk_data] Downloading package punkt to /root/nltk_data...\n",
      "[nltk_data]   Package punkt is already up-to-date!\n",
      "[nltk_data] Downloading package stopwords to /root/nltk_data...\n",
      "[nltk_data]   Package stopwords is already up-to-date!\n"
     ]
    },
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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",
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       "      <td>healthcare python streaming application demo</td>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
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       "      <td>use deep learning for image classification</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",
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       "4      1276.0          deploy your python model as a restful api   \n",
       "\n",
       "                                      email  \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",
    "\n",
    "import re\n",
    "import nltk\n",
    "from nltk.corpus import stopwords\n",
    "from nltk.stem.porter import PorterStemmer\n",
    "from nltk.tokenize import word_tokenize\n",
    "\n",
    "nltk.download(['punkt', 'stopwords'])\n",
    "\n",
    "import pickle\n",
    "from sklearn.feature_extraction.text import TfidfVectorizer\n",
    "from sklearn.decomposition import NMF\n",
    "from sklearn.preprocessing import normalize\n",
    "from sklearn.metrics import precision_score, recall_score, 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": {},
   "outputs": [
    {
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       "0  Skip navigation Sign in SearchLoading...\\r\\n\\r...   \n",
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       "2  ☰ * Login\\r\\n * Sign Up\\r\\n\\r\\n * Learning Pat...   \n",
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       "\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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     "execution_count": 2,
     "metadata": {},
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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": {},
   "outputs": [],
   "source": [
    "user_article = df.groupby('email')['article_id'].count().values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4fc2536d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.style.use('ggplot')\n",
    "plt.figure(figsize=(6,4))\n",
    "plt.hist(user_article, bins=50)\n",
    "plt.xlabel('Number of articles', fontsize=12)\n",
    "plt.ylabel('User counts', fontsize=12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Fill in the median and maximum number of user_article interactios below\n",
    "\n",
    "median_val = np.median(user_article) # 50% of individuals interact with _3_ number of articles or fewer.\n",
    "max_views_by_user = np.max(user_article) # The maximum number of user-article interactions by any 1 user is _364_."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`2.` Explore and remove duplicate articles from the **df_content** dataframe.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\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>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>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>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>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",
       "    <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",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                              doc_body  \\\n",
       "365  Follow Sign in / Sign up Home About Insight Da...   \n",
       "692  Homepage Follow Sign in / Sign up Homepage * H...   \n",
       "761  Homepage Follow Sign in Get started Homepage *...   \n",
       "970  This video shows you how to construct queries ...   \n",
       "971  Homepage Follow Sign in Get started * Home\\r\\n...   \n",
       "\n",
       "                                       doc_description  \\\n",
       "365  During the seven-week Insight Data Engineering...   \n",
       "692  One of the earliest documented catalogs was co...   \n",
       "761  Today’s world of data science leverages data f...   \n",
       "970  This video shows you how to construct queries ...   \n",
       "971  If you are like most data scientists, you are ...   \n",
       "\n",
       "                                         doc_full_name doc_status  article_id  \n",
       "365                       Graph-based machine learning       Live          50  \n",
       "692  How smart catalogs can turn the big data flood...       Live         221  \n",
       "761  Using Apache Spark as a parallel processing fr...       Live         398  \n",
       "970                              Use the Primary Index       Live         577  \n",
       "971  Self-service data preparation with IBM Data Re...       Live         232  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Find and explore duplicate articles\n",
    "df_content[df_content.duplicated('article_id')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Remove any rows that have the same article_id - only keep the first\n",
    "df_content.drop_duplicates('article_id', inplace=True)"
   ]
  },
  {
   "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": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "714"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['article_id'].nunique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1051"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_content['article_id'].nunique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5148"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['email'].nunique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "45993"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "unique_articles = 714 # The number of unique articles that have at least one interaction\n",
    "total_articles = 1051 # The number of unique articles on the IBM platform\n",
    "unique_users = 5148 # The number of unique users\n",
    "user_article_interactions = 45993 # The number of 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": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1429.0    937\n",
       "Name: article_id, dtype: int64"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['article_id'].value_counts().head(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "most_viewed_article_id = '1429.0' # The most viewed article in the dataset as a string with one value following the decimal \n",
    "max_views = 937 # The most viewed article in the dataset was viewed how many times?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <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",
       "      <td>2</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>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1338.0</td>\n",
       "      <td>ml optimization using cognitive assistant</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1276.0</td>\n",
       "      <td>deploy your python model as a restful api</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   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": 15,
     "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": 16,
   "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": 17,
   "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 = df['title'].value_counts().index[:n].tolist()\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 = df['article_id'].value_counts().index[:n].tolist()\n",
    "    top_articles = [str(x) for x in top_articles]\n",
    " \n",
    "    return top_articles # Return the top article ids"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "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",
      "['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",
    "print(get_top_article_ids(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "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": 20,
   "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",
    "    # Create user item matrix\n",
    "    user_item = df.groupby(['user_id', 'article_id'])['title'].count().unstack()\n",
    "    \n",
    "    # Turn NAN into 0s and others into 1s\n",
    "    user_item = 1 - user_item.isna().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": 21,
   "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": "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": 22,
   "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",
    "    similarity = user_item.loc[user_id].dot(user_item.T)\n",
    "    \n",
    "    # sort by similarity\n",
    "    similarity = similarity.sort_values(ascending=False)\n",
    "    \n",
    "    # create list of just the ids\n",
    "    most_similar_users = similarity.index.tolist()\n",
    "            \n",
    "    # remove the own user's id\n",
    "    most_similar_users.remove(user_id)\n",
    "    \n",
    "    return most_similar_users # return a list of the users in order from most to least similar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The 10 most similar users to user 1 are: [3933, 23, 3782, 203, 4459, 131, 3870, 46, 4201, 5041]\n",
      "The 5 most similar users to user 3933 are: [1, 23, 3782, 4459, 203]\n",
      "The 3 most similar users to user 46 are: [4201, 23, 3782]\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": 24,
   "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 = df[df['article_id'].isin(article_ids)]['title'].drop_duplicates().tolist()\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][user_item.loc[user_id] == 1].index.tolist()\n",
    "    article_ids = [str(x) for x in article_ids]\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",
    "    # Find a list of the articles that have been seen by the user\n",
    "    article_ids, _ = get_user_articles(user_id)\n",
    "    \n",
    "    # Find similar users\n",
    "    similar_user_ids = find_similar_users(user_id)\n",
    "    \n",
    "    # Find recommendations\n",
    "    recs = []\n",
    "    for similar_user_id in similar_user_ids:\n",
    "        similar_user_article_ids, _ = get_user_articles(similar_user_id)\n",
    "        for article_id in similar_user_article_ids:\n",
    "            if article_id not in article_ids:\n",
    "                recs.append(article_id)\n",
    "            if len(recs) >= m:\n",
    "                break\n",
    "        if len(recs) >= m:\n",
    "            break\n",
    "       \n",
    "    return recs # return your recommendations for this user_id    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['got zip code data? prep it for analytics. – ibm watson data lab – medium',\n",
       " 'timeseries data analysis of iot events by using jupyter notebook',\n",
       " 'graph-based machine learning',\n",
       " 'using brunel in ipython/jupyter notebooks',\n",
       " 'experience iot with coursera',\n",
       " 'the 3 kinds of context: machine learning and the art of the frame',\n",
       " 'deep forest: towards an alternative to deep neural networks',\n",
       " 'this week in data science (april 18, 2017)',\n",
       " 'higher-order logistic regression for large datasets',\n",
       " 'using machine learning to predict parking difficulty']"
      ]
     },
     "execution_count": 25,
     "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": 26,
   "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": 27,
   "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",
    "    similar_user_ids = find_similar_users(user_id)\n",
    "    neighbors_dict = {'neighbor_id': [], 'similarity': [], 'num_interactions': []}\n",
    " \n",
    "    for similar_user_id in similar_user_ids:\n",
    "        neighbors_dict['neighbor_id'].append(similar_user_id)\n",
    "        neighbors_dict['similarity'].append(user_item.loc[user_id].dot(user_item.loc[similar_user_id]))\n",
    "        neighbors_dict['num_interactions'].append(user_item.loc[similar_user_id].sum())\n",
    "    \n",
    "    neighbors_df = pd.DataFrame(neighbors_dict).sort_values(['similarity', 'num_interactions'], ascending=[False, False])\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",
    "    # Find a list of the articles that have been seen by the user\n",
    "    article_ids, _ = get_user_articles(user_id)\n",
    "    \n",
    "    # Find similar users\n",
    "    similar_user_ids = get_top_sorted_users(user_id)['neighbor_id'].tolist()\n",
    "    \n",
    "    # Find recommendations\n",
    "    recs = []\n",
    "    for similar_user_id in similar_user_ids:\n",
    "        similar_user_article_ids, _ = get_user_articles(similar_user_id)\n",
    "        for article_id in similar_user_article_ids:\n",
    "            if article_id not in article_ids:\n",
    "                recs.append(article_id)\n",
    "            if len(recs) >= m:\n",
    "                break\n",
    "        if len(recs) >= m:\n",
    "            break\n",
    "            \n",
    "    rec_names = get_article_names(recs)\n",
    "    \n",
    "    return recs, rec_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The top 10 recommendations for user 20 are the following article ids:\n",
      "['12.0', '14.0', '29.0', '33.0', '43.0', '51.0', '109.0', '111.0', '130.0', '142.0']\n",
      "\n",
      "The top 10 recommendations for user 20 are the following article names:\n",
      "['got zip code data? prep it for analytics. – ibm watson data lab – medium', 'timeseries data analysis of iot events by using jupyter notebook', 'deep learning with tensorflow course by big data university', 'using brunel in ipython/jupyter notebooks', 'tidy up your jupyter notebooks with scripts', 'experience iot with coursera', 'tensorflow quick tips', 'neural networks for beginners: popular types and applications', 'modern machine learning algorithms', \"feature importance and why it's important\"]\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": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Tests with a dictionary of results\n",
    "user1_most_sim = get_top_sorted_users(1).iloc[0]['neighbor_id'] # Find the user that is most similar to user 1 \n",
    "user131_10th_sim = get_top_sorted_users(131).iloc[10]['neighbor_id'] # Find the 10th most similar user to user 131"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "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": [
    "**Collaborative flitering does not work for cold start problem. If given a new user, we can use get_top_article_ids( ) function to make recommendations, which means we will recommend the most popular articles to new users. It is reasonable to assume that a new user will like what everyone else like. Thus, rank based recommendations for new users makes sense.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`7.` Using your existing functions, provide the top 10 recommended articles you would provide for the a 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": 31,
   "metadata": {},
   "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) # Your recommendations here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "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=\"Content-Recs\">Part IV: Content Based Recommendations</a>\n",
    "\n",
    "Another method we might use to make recommendations is to perform a ranking of the highest ranked articles associated with some term.  You might consider content to be the **doc_body**, **doc_description**, or **doc_full_name**.  There isn't one way to create a content based recommendation, especially considering that each of these columns hold content related information.  \n",
    "\n",
    "`1.` Use the function body below to create a content based recommender.  Since there isn't one right answer for this recommendation tactic, no test functions are provided.  Feel free to change the function inputs if you decide you want to try a method that requires more input values.  The input values are currently set with one idea in mind that you may use to make content based recommendations.  One additional idea is that you might want to choose the most popular recommendations that meet your 'content criteria', but again, there is a lot of flexibility in how you might make these recommendations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Combine the content "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<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",
       "      <th>doc</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <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>No Free Hunch Navigation * kaggle.com\\r\\n\\r\\n ...</td>\n",
       "      <td>See the forest, see the trees. Here lies the c...</td>\n",
       "      <td>Communicating data science: A guide to present...</td>\n",
       "      <td>Live</td>\n",
       "      <td>1</td>\n",
       "      <td>Communicating data science: A guide to present...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>☰ * Login\\r\\n * Sign Up\\r\\n\\r\\n * Learning Pat...</td>\n",
       "      <td>Here’s this week’s news in Data Science and Bi...</td>\n",
       "      <td>This Week in Data Science (April 18, 2017)</td>\n",
       "      <td>Live</td>\n",
       "      <td>2</td>\n",
       "      <td>This Week in Data Science (April 18, 2017) Thi...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>DATALAYER: HIGH THROUGHPUT, LOW LATENCY AT SCA...</td>\n",
       "      <td>Learn how distributed DBs solve the problem of...</td>\n",
       "      <td>DataLayer Conference: Boost the performance of...</td>\n",
       "      <td>Live</td>\n",
       "      <td>3</td>\n",
       "      <td>DataLayer Conference: Boost the performance of...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Skip navigation Sign in SearchLoading...\\r\\n\\r...</td>\n",
       "      <td>This video demonstrates the power of IBM DataS...</td>\n",
       "      <td>Analyze NY Restaurant data using Spark in DSX</td>\n",
       "      <td>Live</td>\n",
       "      <td>4</td>\n",
       "      <td>Analyze NY Restaurant data using Spark in DSX ...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                            doc_body  \\\n",
       "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   \n",
       "\n",
       "                                                 doc  \n",
       "0  Detect Malfunctioning IoT Sensors with Streami...  \n",
       "1  Communicating data science: A guide to present...  \n",
       "2  This Week in Data Science (April 18, 2017) Thi...  \n",
       "3  DataLayer Conference: Boost the performance of...  \n",
       "4  Analyze NY Restaurant data using Spark in DSX ...  "
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_content.fillna(\"\", inplace=True)\n",
    "# Give a higher weight on 'doc_full_name'\n",
    "df_content['doc'] = (df_content['doc_full_name'] + \" \") * 2 + \\\n",
    "                    df_content['doc_description'] + \" \" + df_content['doc_body']\n",
    "df_content.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Implement NMF\n",
    "\n",
    "For NMF (non-negative matrix factorization), we need to obtain a design matrix. Here, we apply TfidfVectorizer to the combined text content. The transformation will return a matrix of size (documents x features). To reduce the size of the matrix and speed up computation, we set the maximum feature size to 5000, which will take the top 5000 best features that can contribute to our model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "def tokenize(text):\n",
    "    '''      \n",
    "    INPUT:\n",
    "    text - (str) raw text data\n",
    "        \n",
    "    OUTPUT:\n",
    "    tokens - (list) a list of strings after tokenization\n",
    "        \n",
    "    Description:\n",
    "    Transform raw text data to a bag of words\n",
    "    '''\n",
    "    # Remove websites and email addresses\n",
    "    text = re.sub(\"((\\S+)?(http(s)?)(\\S+))|((\\S+)?(www)(\\S+))|((\\S+)?(\\@)(\\S+)?)\", \" \", text)\n",
    "    \n",
    "    # Normalize case and remove punctuation\n",
    "    text = re.sub(\"[^a-zA-Z]\", \" \", text.lower())\n",
    "\n",
    "    # Tokenize text\n",
    "    tokens = word_tokenize(text)\n",
    "    \n",
    "    # Stem and remove stop words\n",
    "    tokens = [PorterStemmer().stem(word)\n",
    "              for word in tokens if word not in stopwords.words(\"english\")] \n",
    "    \n",
    "    # Make sure there is no one letter words\n",
    "    tokens = [word for word in tokens if len(word) > 1] \n",
    "    \n",
    "    return tokens\n",
    "\n",
    "tfidf_vectorizer = TfidfVectorizer(tokenizer=tokenize, max_features=5000)\n",
    "tfidf = tfidf_vectorizer.fit_transform(df_content['doc'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Obtain a NMF model\n",
    "num_topics = 20\n",
    "nmf = NMF(n_components=num_topics, random_state=0)\n",
    "nmf_features = nmf.fit_transform(tfidf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Generate NMF topics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>Topic 11</th>\n",
       "      <th>Topic 12</th>\n",
       "      <th>Topic 13</th>\n",
       "      <th>Topic 14</th>\n",
       "      <th>Topic 15</th>\n",
       "      <th>Topic 16</th>\n",
       "      <th>Topic 17</th>\n",
       "      <th>Topic 18</th>\n",
       "      <th>Topic 19</th>\n",
       "      <th>Topic 20</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>data</td>\n",
       "      <td>durat</td>\n",
       "      <td>dashdb</td>\n",
       "      <td>compos</td>\n",
       "      <td>cloudant</td>\n",
       "      <td>scienc</td>\n",
       "      <td>deep</td>\n",
       "      <td>email</td>\n",
       "      <td>bluemix</td>\n",
       "      <td>spark</td>\n",
       "      <td>data</td>\n",
       "      <td>notebook</td>\n",
       "      <td>index</td>\n",
       "      <td>offlin</td>\n",
       "      <td>id</td>\n",
       "      <td>rstudio</td>\n",
       "      <td>graph</td>\n",
       "      <td>datalay</td>\n",
       "      <td>model</td>\n",
       "      <td>valu</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>watson</td>\n",
       "      <td>view</td>\n",
       "      <td>load</td>\n",
       "      <td>databas</td>\n",
       "      <td>replic</td>\n",
       "      <td>data</td>\n",
       "      <td>learn</td>\n",
       "      <td>window</td>\n",
       "      <td>servic</td>\n",
       "      <td>apach</td>\n",
       "      <td>analyt</td>\n",
       "      <td>pixiedust</td>\n",
       "      <td>queri</td>\n",
       "      <td>pouchdb</td>\n",
       "      <td>node</td>\n",
       "      <td>shini</td>\n",
       "      <td>janusgraph</td>\n",
       "      <td>thom</td>\n",
       "      <td>machin</td>\n",
       "      <td>data</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>ibm</td>\n",
       "      <td>load</td>\n",
       "      <td>data</td>\n",
       "      <td>mongodb</td>\n",
       "      <td>databas</td>\n",
       "      <td>week</td>\n",
       "      <td>network</td>\n",
       "      <td>open</td>\n",
       "      <td>app</td>\n",
       "      <td>sql</td>\n",
       "      <td>blog</td>\n",
       "      <td>jupyt</td>\n",
       "      <td>search</td>\n",
       "      <td>app</td>\n",
       "      <td>use</td>\n",
       "      <td>june</td>\n",
       "      <td>node</td>\n",
       "      <td>crow</td>\n",
       "      <td>learn</td>\n",
       "      <td>order</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>catalog</td>\n",
       "      <td>tv</td>\n",
       "      <td>use</td>\n",
       "      <td>mysql</td>\n",
       "      <td>video</td>\n",
       "      <td>email</td>\n",
       "      <td>neural</td>\n",
       "      <td>click</td>\n",
       "      <td>applic</td>\n",
       "      <td>scala</td>\n",
       "      <td>big</td>\n",
       "      <td>cell</td>\n",
       "      <td>field</td>\n",
       "      <td>envoy</td>\n",
       "      <td>document</td>\n",
       "      <td>april</td>\n",
       "      <td>gremlin</td>\n",
       "      <td>confer</td>\n",
       "      <td>train</td>\n",
       "      <td>date</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>platform</td>\n",
       "      <td>video</td>\n",
       "      <td>datawork</td>\n",
       "      <td>postgresql</td>\n",
       "      <td>geospati</td>\n",
       "      <td>big</td>\n",
       "      <td>ai</td>\n",
       "      <td>new</td>\n",
       "      <td>ibm</td>\n",
       "      <td>systemml</td>\n",
       "      <td>podcast</td>\n",
       "      <td>python</td>\n",
       "      <td>type</td>\n",
       "      <td>sync</td>\n",
       "      <td>databas</td>\n",
       "      <td>packag</td>\n",
       "      <td>databas</td>\n",
       "      <td>talk</td>\n",
       "      <td>predict</td>\n",
       "      <td>averag</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>flow</td>\n",
       "      <td>queue</td>\n",
       "      <td>ibm</td>\n",
       "      <td>deploy</td>\n",
       "      <td>tutori</td>\n",
       "      <td>cours</td>\n",
       "      <td>machin</td>\n",
       "      <td>address</td>\n",
       "      <td>deploy</td>\n",
       "      <td>machin</td>\n",
       "      <td>video</td>\n",
       "      <td>dsx</td>\n",
       "      <td>cloudant</td>\n",
       "      <td>first</td>\n",
       "      <td>function</td>\n",
       "      <td>decemb</td>\n",
       "      <td>ibm</td>\n",
       "      <td>graphql</td>\n",
       "      <td>algorithm</td>\n",
       "      <td>df</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>scienc</td>\n",
       "      <td>developerwork</td>\n",
       "      <td>notebook</td>\n",
       "      <td>articl</td>\n",
       "      <td>queri</td>\n",
       "      <td>learn</td>\n",
       "      <td>research</td>\n",
       "      <td>share</td>\n",
       "      <td>stream</td>\n",
       "      <td>stream</td>\n",
       "      <td>infograph</td>\n",
       "      <td>scienc</td>\n",
       "      <td>doc</td>\n",
       "      <td>camp</td>\n",
       "      <td>connect</td>\n",
       "      <td>februari</td>\n",
       "      <td>edg</td>\n",
       "      <td>compos</td>\n",
       "      <td>regress</td>\n",
       "      <td>use</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>refineri</td>\n",
       "      <td>sign</td>\n",
       "      <td>cloud</td>\n",
       "      <td>redi</td>\n",
       "      <td>document</td>\n",
       "      <td>badg</td>\n",
       "      <td>human</td>\n",
       "      <td>pipe</td>\n",
       "      <td>click</td>\n",
       "      <td>datafram</td>\n",
       "      <td>govern</td>\n",
       "      <td>data</td>\n",
       "      <td>geo</td>\n",
       "      <td>web</td>\n",
       "      <td>key</td>\n",
       "      <td>januari</td>\n",
       "      <td>recip</td>\n",
       "      <td>articl</td>\n",
       "      <td>ml</td>\n",
       "      <td>count</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>clap</td>\n",
       "      <td>ibm</td>\n",
       "      <td>workbench</td>\n",
       "      <td>rethinkdb</td>\n",
       "      <td>couchdb</td>\n",
       "      <td>address</td>\n",
       "      <td>imag</td>\n",
       "      <td>data</td>\n",
       "      <td>js</td>\n",
       "      <td>val</td>\n",
       "      <td>busi</td>\n",
       "      <td>experi</td>\n",
       "      <td>document</td>\n",
       "      <td>mobil</td>\n",
       "      <td>command</td>\n",
       "      <td>octob</td>\n",
       "      <td>chatbot</td>\n",
       "      <td>expos</td>\n",
       "      <td>featur</td>\n",
       "      <td>row</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>experi</td>\n",
       "      <td>watch</td>\n",
       "      <td>bluemix</td>\n",
       "      <td>backup</td>\n",
       "      <td>account</td>\n",
       "      <td>post</td>\n",
       "      <td>artifici</td>\n",
       "      <td>couchdb</td>\n",
       "      <td>watson</td>\n",
       "      <td>learn</td>\n",
       "      <td>chat</td>\n",
       "      <td>scala</td>\n",
       "      <td>facet</td>\n",
       "      <td>user</td>\n",
       "      <td>file</td>\n",
       "      <td>septemb</td>\n",
       "      <td>queri</td>\n",
       "      <td>share</td>\n",
       "      <td>use</td>\n",
       "      <td>avg</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>asset</td>\n",
       "      <td>scienc</td>\n",
       "      <td>biginsight</td>\n",
       "      <td>share</td>\n",
       "      <td>center</td>\n",
       "      <td>news</td>\n",
       "      <td>algorithm</td>\n",
       "      <td>blog</td>\n",
       "      <td>search</td>\n",
       "      <td>use</td>\n",
       "      <td>stream</td>\n",
       "      <td>visual</td>\n",
       "      <td>array</td>\n",
       "      <td>devic</td>\n",
       "      <td>creat</td>\n",
       "      <td>email</td>\n",
       "      <td>vertex</td>\n",
       "      <td>present</td>\n",
       "      <td>test</td>\n",
       "      <td>calcul</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>unblock</td>\n",
       "      <td>transcript</td>\n",
       "      <td>analysi</td>\n",
       "      <td>enterpris</td>\n",
       "      <td>json</td>\n",
       "      <td>blog</td>\n",
       "      <td>layer</td>\n",
       "      <td>post</td>\n",
       "      <td>gateway</td>\n",
       "      <td>sparklyr</td>\n",
       "      <td>meetup</td>\n",
       "      <td>use</td>\n",
       "      <td>secondari</td>\n",
       "      <td>browser</td>\n",
       "      <td>api</td>\n",
       "      <td>august</td>\n",
       "      <td>slack</td>\n",
       "      <td>monday</td>\n",
       "      <td>tree</td>\n",
       "      <td>column</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>follow</td>\n",
       "      <td>experi</td>\n",
       "      <td>analyt</td>\n",
       "      <td>elasticsearch</td>\n",
       "      <td>use</td>\n",
       "      <td>machin</td>\n",
       "      <td>intellig</td>\n",
       "      <td>simpl</td>\n",
       "      <td>creat</td>\n",
       "      <td>run</td>\n",
       "      <td>hadoop</td>\n",
       "      <td>code</td>\n",
       "      <td>use</td>\n",
       "      <td>lab</td>\n",
       "      <td>json</td>\n",
       "      <td>sheet</td>\n",
       "      <td>vertic</td>\n",
       "      <td>wife</td>\n",
       "      <td>data</td>\n",
       "      <td>item</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>lab</td>\n",
       "      <td>count</td>\n",
       "      <td>start</td>\n",
       "      <td>dj</td>\n",
       "      <td>curl</td>\n",
       "      <td>event</td>\n",
       "      <td>comput</td>\n",
       "      <td>comment</td>\n",
       "      <td>vcap</td>\n",
       "      <td>rstudio</td>\n",
       "      <td>cyber</td>\n",
       "      <td>click</td>\n",
       "      <td>geometri</td>\n",
       "      <td>replic</td>\n",
       "      <td>var</td>\n",
       "      <td>cheat</td>\n",
       "      <td>travers</td>\n",
       "      <td>daughter</td>\n",
       "      <td>word</td>\n",
       "      <td>function</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>scientist</td>\n",
       "      <td>playlist</td>\n",
       "      <td>sampl</td>\n",
       "      <td>connect</td>\n",
       "      <td>show</td>\n",
       "      <td>bdu</td>\n",
       "      <td>problem</td>\n",
       "      <td>disqu</td>\n",
       "      <td>simpl</td>\n",
       "      <td>commun</td>\n",
       "      <td>industri</td>\n",
       "      <td>creat</td>\n",
       "      <td>elasticsearch</td>\n",
       "      <td>progress</td>\n",
       "      <td>server</td>\n",
       "      <td>march</td>\n",
       "      <td>relationship</td>\n",
       "      <td>beach</td>\n",
       "      <td>dataset</td>\n",
       "      <td>metric</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>sourc</td>\n",
       "      <td>data</td>\n",
       "      <td>get</td>\n",
       "      <td>walker</td>\n",
       "      <td>nosql</td>\n",
       "      <td>ibm</td>\n",
       "      <td>one</td>\n",
       "      <td>connector</td>\n",
       "      <td>cloud</td>\n",
       "      <td>ibm</td>\n",
       "      <td>visual</td>\n",
       "      <td>brunel</td>\n",
       "      <td>video</td>\n",
       "      <td>ibm</td>\n",
       "      <td>redi</td>\n",
       "      <td>juli</td>\n",
       "      <td>person</td>\n",
       "      <td>kukulinski</td>\n",
       "      <td>cluster</td>\n",
       "      <td>aggreg</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>stori</td>\n",
       "      <td>new</td>\n",
       "      <td>connect</td>\n",
       "      <td>morgan</td>\n",
       "      <td>job</td>\n",
       "      <td>repli</td>\n",
       "      <td>tensorflow</td>\n",
       "      <td>reddit</td>\n",
       "      <td>web</td>\n",
       "      <td>tpc</td>\n",
       "      <td>media</td>\n",
       "      <td>project</td>\n",
       "      <td>defin</td>\n",
       "      <td>hoodi</td>\n",
       "      <td>js</td>\n",
       "      <td>novemb</td>\n",
       "      <td>watson</td>\n",
       "      <td>ross</td>\n",
       "      <td>logist</td>\n",
       "      <td>median</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>miss</td>\n",
       "      <td>autoplay</td>\n",
       "      <td>oracl</td>\n",
       "      <td>rabbitmq</td>\n",
       "      <td>sign</td>\n",
       "      <td>program</td>\n",
       "      <td>gener</td>\n",
       "      <td>check</td>\n",
       "      <td>credenti</td>\n",
       "      <td>sqlcontext</td>\n",
       "      <td>ibm</td>\n",
       "      <td>follow</td>\n",
       "      <td>geospati</td>\n",
       "      <td>js</td>\n",
       "      <td>user</td>\n",
       "      <td>may</td>\n",
       "      <td>bot</td>\n",
       "      <td>tinker</td>\n",
       "      <td>linear</td>\n",
       "      <td>tabl</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>medium</td>\n",
       "      <td>analyt</td>\n",
       "      <td>analyz</td>\n",
       "      <td>support</td>\n",
       "      <td>sync</td>\n",
       "      <td>subscrib</td>\n",
       "      <td>inform</td>\n",
       "      <td>app</td>\n",
       "      <td>run</td>\n",
       "      <td>contribut</td>\n",
       "      <td>scienc</td>\n",
       "      <td>run</td>\n",
       "      <td>lucen</td>\n",
       "      <td>per</td>\n",
       "      <td>messag</td>\n",
       "      <td>dt</td>\n",
       "      <td>user</td>\n",
       "      <td>guy</td>\n",
       "      <td>random</td>\n",
       "      <td>id</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>block</td>\n",
       "      <td>youtub</td>\n",
       "      <td>desktop</td>\n",
       "      <td>scylladb</td>\n",
       "      <td>http</td>\n",
       "      <td>tensorflow</td>\n",
       "      <td>year</td>\n",
       "      <td>cloudant</td>\n",
       "      <td>use</td>\n",
       "      <td>command</td>\n",
       "      <td>manag</td>\n",
       "      <td>file</td>\n",
       "      <td>constitu</td>\n",
       "      <td>develop</td>\n",
       "      <td>set</td>\n",
       "      <td>ggplot</td>\n",
       "      <td>librari</td>\n",
       "      <td>chariti</td>\n",
       "      <td>classifi</td>\n",
       "      <td>plot</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Topic 01       Topic 02    Topic 03       Topic 04  Topic 05    Topic 06  \\\n",
       "0        data          durat      dashdb         compos  cloudant      scienc   \n",
       "1      watson           view        load        databas    replic        data   \n",
       "2         ibm           load        data        mongodb   databas        week   \n",
       "3     catalog             tv         use          mysql     video       email   \n",
       "4    platform          video    datawork     postgresql  geospati         big   \n",
       "5        flow          queue         ibm         deploy    tutori       cours   \n",
       "6      scienc  developerwork    notebook         articl     queri       learn   \n",
       "7    refineri           sign       cloud           redi  document        badg   \n",
       "8        clap            ibm   workbench      rethinkdb   couchdb     address   \n",
       "9      experi          watch     bluemix         backup   account        post   \n",
       "10      asset         scienc  biginsight          share    center        news   \n",
       "11    unblock     transcript     analysi      enterpris      json        blog   \n",
       "12     follow         experi      analyt  elasticsearch       use      machin   \n",
       "13        lab          count       start             dj      curl       event   \n",
       "14  scientist       playlist       sampl        connect      show         bdu   \n",
       "15      sourc           data         get         walker     nosql         ibm   \n",
       "16      stori            new     connect         morgan       job       repli   \n",
       "17       miss       autoplay       oracl       rabbitmq      sign     program   \n",
       "18     medium         analyt      analyz        support      sync    subscrib   \n",
       "19      block         youtub     desktop       scylladb      http  tensorflow   \n",
       "\n",
       "      Topic 07   Topic 08  Topic 09    Topic 10   Topic 11   Topic 12  \\\n",
       "0         deep      email   bluemix       spark       data   notebook   \n",
       "1        learn     window    servic       apach     analyt  pixiedust   \n",
       "2      network       open       app         sql       blog      jupyt   \n",
       "3       neural      click    applic       scala        big       cell   \n",
       "4           ai        new       ibm    systemml    podcast     python   \n",
       "5       machin    address    deploy      machin      video        dsx   \n",
       "6     research      share    stream      stream  infograph     scienc   \n",
       "7        human       pipe     click    datafram     govern       data   \n",
       "8         imag       data        js         val       busi     experi   \n",
       "9     artifici    couchdb    watson       learn       chat      scala   \n",
       "10   algorithm       blog    search         use     stream     visual   \n",
       "11       layer       post   gateway    sparklyr     meetup        use   \n",
       "12    intellig      simpl     creat         run     hadoop       code   \n",
       "13      comput    comment      vcap     rstudio      cyber      click   \n",
       "14     problem      disqu     simpl      commun   industri      creat   \n",
       "15         one  connector     cloud         ibm     visual     brunel   \n",
       "16  tensorflow     reddit       web         tpc      media    project   \n",
       "17       gener      check  credenti  sqlcontext        ibm     follow   \n",
       "18      inform        app       run   contribut     scienc        run   \n",
       "19        year   cloudant       use     command      manag       file   \n",
       "\n",
       "         Topic 13  Topic 14  Topic 15  Topic 16      Topic 17    Topic 18  \\\n",
       "0           index    offlin        id   rstudio         graph     datalay   \n",
       "1           queri   pouchdb      node     shini    janusgraph        thom   \n",
       "2          search       app       use      june          node        crow   \n",
       "3           field     envoy  document     april       gremlin      confer   \n",
       "4            type      sync   databas    packag       databas        talk   \n",
       "5        cloudant     first  function    decemb           ibm     graphql   \n",
       "6             doc      camp   connect  februari           edg      compos   \n",
       "7             geo       web       key   januari         recip      articl   \n",
       "8        document     mobil   command     octob       chatbot       expos   \n",
       "9           facet      user      file   septemb         queri       share   \n",
       "10          array     devic     creat     email        vertex     present   \n",
       "11      secondari   browser       api    august         slack      monday   \n",
       "12            use       lab      json     sheet        vertic        wife   \n",
       "13       geometri    replic       var     cheat       travers    daughter   \n",
       "14  elasticsearch  progress    server     march  relationship       beach   \n",
       "15          video       ibm      redi      juli        person  kukulinski   \n",
       "16          defin     hoodi        js    novemb        watson        ross   \n",
       "17       geospati        js      user       may           bot      tinker   \n",
       "18          lucen       per    messag        dt          user         guy   \n",
       "19       constitu   develop       set    ggplot       librari     chariti   \n",
       "\n",
       "     Topic 19  Topic 20  \n",
       "0       model      valu  \n",
       "1      machin      data  \n",
       "2       learn     order  \n",
       "3       train      date  \n",
       "4     predict    averag  \n",
       "5   algorithm        df  \n",
       "6     regress       use  \n",
       "7          ml     count  \n",
       "8      featur       row  \n",
       "9         use       avg  \n",
       "10       test    calcul  \n",
       "11       tree    column  \n",
       "12       data      item  \n",
       "13       word  function  \n",
       "14    dataset    metric  \n",
       "15    cluster    aggreg  \n",
       "16     logist    median  \n",
       "17     linear      tabl  \n",
       "18     random        id  \n",
       "19   classifi      plot  "
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def get_nmf_topics(vectorizer=tfidf_vectorizer, model=nmf, n_top_words=20):\n",
    "    '''\n",
    "    INPUT:\n",
    "    vectorizer - (object) an object that vectorize documents\n",
    "    model - (object) a model built for topic extraction\n",
    "    n_top_words - (int) the number of top words in each topic\n",
    "    \n",
    "    OUTPUT:\n",
    "    word_df - (pandas datafram) top words for each topic\n",
    "    \n",
    "    Description:\n",
    "    Display the latent article topics using NMF\n",
    "    '''\n",
    "    feat_names = vectorizer.get_feature_names()\n",
    "    \n",
    "    word_dict = {};\n",
    "    for i in range(num_topics):\n",
    "        # Obtain the largest values for each topic, and add the words they map to into the dictionary\n",
    "        words_ids = model.components_[i].argsort()[:-n_top_words-1:-1]\n",
    "        words = [feat_names[key] for key in words_ids]\n",
    "        word_dict['Topic ' + '{:02d}'.format(i+1)] = words;\n",
    "        \n",
    "    word_df = pd.DataFrame(word_dict)\n",
    "    \n",
    "    return word_df\n",
    "\n",
    "get_nmf_topics()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Compute document similarity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "norm_features = normalize(nmf_features) \n",
    "nmf_feat_df = pd.DataFrame(norm_features, index=df_content['doc_full_name'].apply(lambda x: x.lower()).tolist())\n",
    "\n",
    "def get_similar_articles(article_name, n_top, vectorizer=tfidf_vectorizer, model=nmf, feat_df=nmf_feat_df):\n",
    "    '''\n",
    "    INPUT: \n",
    "    article_name - (int) an article name to query\n",
    "    n_top - (int) the number of similar articles to return\n",
    "    vectorizer - (object) an object that vectorize documents\n",
    "    model - (object) a model built for topic extraction\n",
    "    feat_df - (pandas dataframe) similarity matrix of documents by topics\n",
    "    \n",
    "    OUTPUT:\n",
    "    similar_articles - (list) top n_top similar articles \n",
    "    \n",
    "    Description:\n",
    "    Find top similar articles for a given article\n",
    "    '''\n",
    "    # For any article that is not included in 'df_content'\n",
    "    if article_name not in feat_df.index: \n",
    "        test_feature_mat = vectorizer.transform([article_name])\n",
    "        test_output = model.transform(test_feature_mat)\n",
    "        # Calculate the cosine similarities\n",
    "        similarities = feat_df.dot(normalize(test_output).T)\n",
    "        similar_articles = similarities.squeeze().sort_values(ascending=False).iloc[:n_top]\n",
    "    else:\n",
    "        similarities = feat_df.dot(feat_df.loc[article_name])\n",
    "        similar_articles = similarities.sort_values(ascending=False).iloc[1:n_top+1]\n",
    "    \n",
    "    return similar_articles"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Make recommendations "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_content_recs(user_id=None, \n",
    "                      article_list=None, \n",
    "                      n_recs=10, \n",
    "                      user_item=user_item, \n",
    "                      df=df, \n",
    "                      vectorizer=tfidf_vectorizer, \n",
    "                      model=nmf,\n",
    "                      feat_df=nmf_feat_df):\n",
    "    '''\n",
    "    INPUT:\n",
    "    user_id - (int) a user id\n",
    "    article_list - (list) a list of article ids (from df)\n",
    "    n_recs - (int) the number of recommendations to make\n",
    "    user_item - (pandas dataframe) matrix of users by articles: \n",
    "                1's when a user has interacted with an article, 0 otherwise\n",
    "    vectorizer - (object) an object that vectorize documents\n",
    "    model - (object) a model built for topic extraction\n",
    "    \n",
    "    OUTPUT:\n",
    "    rec_names - (list) a list of recommended article names \n",
    "    \n",
    "    Description:\n",
    "    Recommend a user n_recs articles similar to the ones he/she has already seen\n",
    "    '''       \n",
    "    if not article_list:\n",
    "        # Recommend top articles for a new user\n",
    "        if user_id not in user_item.index:\n",
    "            rec_names = get_top_articles(n_recs) \n",
    "            return rec_names\n",
    "        else:\n",
    "            # Get the articles the user has interacted with\n",
    "            _, seen_article_names = get_user_articles(user_id)   \n",
    "    else:\n",
    "        seen_article_ids = article_list\n",
    "        seen_article_names = get_article_names(seen_article_ids)\n",
    "    \n",
    "    # Find n_recs similar articles in df_content for each article the user has seen\n",
    "    similar_articles = pd.Series([])\n",
    "    for article_name in seen_article_names:\n",
    "        sims = get_similar_articles(article_name, n_recs)\n",
    "        similar_articles = similar_articles.append(sims)\n",
    "    \n",
    "    rec_names = similar_articles.sort_values(ascending=False).drop_duplicates().index.tolist()[:n_recs]\n",
    "                \n",
    "    return rec_names"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`2.` Now that you have put together your content-based recommendation system, use the cell below to write a summary explaining how your content based recommender works.  Do you see any possible improvements that could be made to your function?  Is there anything novel about your content based recommender?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Our content based recommender is designed based on the assumption that similar articles should have similar topics. To compute the similarities between ariticles, we perform the followeing steps:**\n",
    "1. Combine **doc_body**, **doc_description**, or **doc_full_name** into a single document for each article. A higher weight is given to **doc_full_name** to emphasizes the key words in the article name by increasing their frequency.\n",
    "2. Convert the combined raw documents to a matrix of TF-IDF features using a self-defined tokenize function.\n",
    "3. Apply non-negative matrix factorization (NMF) to find latent topics for the collection of articles. This step will generate an article-topic matrix.\n",
    "4. Calculate the cosine similarities between articles from the article-topic matrix as the article similarties.\n",
    "\n",
    "**Our strategy to recommend a user n articles can be summarized as:**\n",
    "1. Get a list of articles the user has already seen.\n",
    "2. For each seen article, find n most similar articles.\n",
    "3. Assemble all these articles in a list and sort them in descending order by their similarity values.\n",
    "4. Select the top n articles from this list as the recommendations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`3.` Use your content-recommendation system to make recommendations for the below scenarios based on the comments.  Again no tests are provided here, because there isn't one right answer that could be used to find these content based recommendations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The top 10 recommendations for a new user are the following article names:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "['use deep learning for image classification',\n",
       " 'insights from new york car accident reports',\n",
       " 'visualize car data with brunel',\n",
       " 'use xgboost, scikit-learn & ibm watson machine learning apis',\n",
       " 'predicting churn with the spss random tree algorithm',\n",
       " 'healthcare python streaming application demo',\n",
       " 'finding optimal locations of new store using decision optimization',\n",
       " 'apache spark lab, part 1: basic concepts',\n",
       " 'analyze energy consumption in buildings',\n",
       " 'gosales transactions for logistic regression model']"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# make recommendations for a brand new user\n",
    "print(\"The top 10 recommendations for a new user are the following article names:\")\n",
    "make_content_recs(user_id=0) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The top 10 recommendations for a user who only has interacted with article ['use xgboost, scikit-learn & ibm watson machine learning apis'] are the following article names:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "['best practices for custom models in watson visual recognition',\n",
       " 'machine learning for everyone',\n",
       " 'lifelong (machine) learning: how automation can help your models get smarter over time',\n",
       " '3 scenarios for machine learning on multicloud',\n",
       " 'modern machine learning algorithms',\n",
       " 'the 3 kinds of context: machine learning and the art of the frame',\n",
       " 'which one to choose for your problem',\n",
       " 'top 10 machine learning use cases: part 1',\n",
       " 'the machine learning database',\n",
       " 'apple, ibm add machine learning to partnership with watson-core ml coupling']"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# make a recommendations for a user who only has interacted with article id '1427.0'\n",
    "print(\"The top 10 recommendations for a user who only has interacted with article {} are the following article names:\".format(get_article_names(article_ids=['1427.0'])))\n",
    "make_content_recs(article_list=['1427.0'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <a class=\"anchor\" id=\"Matrix-Fact\">Part V: Matrix Factorization</a>\n",
    "\n",
    "In this part of the notebook, you will build 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 V** of the notebook. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load the matrix here\n",
    "user_item_matrix = pd.read_pickle('user_item_matrix.p')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
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      ],
      "text/plain": [
       "article_id  0.0  100.0  1000.0  1004.0  1006.0  1008.0  101.0  1014.0  1015.0  \\\n",
       "user_id                                                                         \n",
       "1           0.0    0.0     0.0     0.0     0.0     0.0    0.0     0.0     0.0   \n",
       "2           0.0    0.0     0.0     0.0     0.0     0.0    0.0     0.0     0.0   \n",
       "3           0.0    0.0     0.0     0.0     0.0     0.0    0.0     0.0     0.0   \n",
       "4           0.0    0.0     0.0     0.0     0.0     0.0    0.0     0.0     0.0   \n",
       "5           0.0    0.0     0.0     0.0     0.0     0.0    0.0     0.0     0.0   \n",
       "\n",
       "article_id  1016.0  ...    977.0  98.0  981.0  984.0  985.0  986.0  990.0  \\\n",
       "user_id             ...                                                     \n",
       "1              0.0  ...      0.0   0.0    1.0    0.0    0.0    0.0    0.0   \n",
       "2              0.0  ...      0.0   0.0    0.0    0.0    0.0    0.0    0.0   \n",
       "3              0.0  ...      1.0   0.0    0.0    0.0    0.0    0.0    0.0   \n",
       "4              0.0  ...      0.0   0.0    0.0    0.0    0.0    0.0    0.0   \n",
       "5              0.0  ...      0.0   0.0    0.0    0.0    0.0    0.0    0.0   \n",
       "\n",
       "article_id  993.0  996.0  997.0  \n",
       "user_id                          \n",
       "1             0.0    0.0    0.0  \n",
       "2             0.0    0.0    0.0  \n",
       "3             0.0    0.0    0.0  \n",
       "4             0.0    0.0    0.0  \n",
       "5             0.0    0.0    0.0  \n",
       "\n",
       "[5 rows x 714 columns]"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 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": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Perform SVD on the User-Item Matrix Here\n",
    "u, s, vt = np.linalg.svd(user_item_matrix) # use the built in to get the three matrices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**In this case, we have a matrix without missing values, which makes it feasible to perform SVD. If the matrix includes missing values, then we have to use FunkSVD instead.**"
   ]
  },
  {
   "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": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4fc045f2b0>"
      ]
     },
     "metadata": {},
     "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 of 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": 45,
   "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",
    "    # Create user-item matrices with 1's and 0's for the training and testing dataframe\n",
    "    user_item_train = create_user_item_matrix(df_train)\n",
    "    user_item_test = create_user_item_matrix(df_test)\n",
    "    \n",
    "    train_idx = set(user_item_train.index.tolist())\n",
    "    test_idx = set(user_item_test.index.tolist())\n",
    "    match_idx = list(train_idx.intersection(test_idx))\n",
    "    \n",
    "    train_arts = set(user_item_train.columns.tolist())\n",
    "    test_arts = set(user_item_test.columns.tolist())\n",
    "    match_cols = list(test_arts.intersection(train_arts))\n",
    "    \n",
    "    user_item_test = user_item_test.loc[match_idx, match_cols]\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": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Find the number of users we can make predictions for in the test set\n",
    "user_item_test.shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "662"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Find the number of users in the test set we are unable to make predictions for because of the cold start problem\n",
    "len(test_idx) - user_item_test.shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "574"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Find the number of movies we can make predictions for in the test set\n",
    "user_item_test.shape[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Find the number of movies in the test set we are unable to make predictions for because of the cold start problem\n",
    "len(test_arts) - user_item_test.shape[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Awesome job!  That's right!  All of the test movies 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?': c, \n",
    "    'How many users in the test set are we not able to make predictions for because of the cold start problem?': a, \n",
    "    'How many movies can we make predictions for in the test set?': b,\n",
    "    'How many movies in the test set are we not able to make predictions for because of the cold start problem?': d\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": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "# fit SVD on the user_item_train matrix\n",
    "u_train, s_train, vt_train = np.linalg.svd(user_item_train) # fit svd similar to above then use the cells below"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Find row and column indices for test user ids and article ids in the training set\n",
    "row_idx = user_item_train.index.isin(test_idx)\n",
    "col_idx = user_item_train.columns.isin(test_arts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get u_test and vt_test\n",
    "u_test = u_train[row_idx, :]\n",
    "vt_test = vt_train[:, col_idx]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_latent_feats = np.arange(10,700+10,20)\n",
    "\n",
    "accuracy_train = []\n",
    "accuracy_test = []\n",
    "\n",
    "precision_train = []\n",
    "precision_test = []\n",
    "\n",
    "recall_train = []\n",
    "recall_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_k, u_train_k, vt_train_k = np.diag(s_train[:k]), u_train[:, :k], vt_train[:k, :]\n",
    "    u_test_k, vt_test_k = u_test[:, :k], vt_test[:k, :]\n",
    "    \n",
    "    # take dot product\n",
    "    user_item_train_pred = np.clip(np.around(u_train_k.dot(s_train_k).dot(vt_train_k)), 0, 1)\n",
    "    user_item_test_pred = np.clip(np.around(u_test_k.dot(s_train_k).dot(vt_test_k)), 0, 1)\n",
    "    \n",
    "    # compute precision values\n",
    "    precision_train.append(precision_score(np.array(user_item_train).reshape(-1,), user_item_train_pred.reshape(-1,)))\n",
    "    precision_test.append(precision_score(np.array(user_item_test).reshape(-1,), user_item_test_pred.reshape(-1,)))\n",
    "    \n",
    "    # compute recall values\n",
    "    recall_train.append(recall_score(np.array(user_item_train).reshape(-1,), user_item_train_pred.reshape(-1,)))\n",
    "    recall_test.append(recall_score(np.array(user_item_test).reshape(-1,), user_item_test_pred.reshape(-1,)))\n",
    "    \n",
    "    # compute f1 score\n",
    "    f1_train.append(f1_score(np.array(user_item_train).reshape(-1,), user_item_train_pred.reshape(-1,)))\n",
    "    f1_test.append(f1_score(np.array(user_item_test).reshape(-1,), user_item_test_pred.reshape(-1,)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4fc00b4358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(num_latent_feats, precision_train, label='Train')\n",
    "plt.plot(num_latent_feats, precision_test, label='Test')\n",
    "plt.xlabel('Number of latent features');\n",
    "plt.ylabel('Precision');\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4fc04cac50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(num_latent_feats, recall_train, label='Train')\n",
    "plt.plot(num_latent_feats, recall_test, label='Test')\n",
    "plt.xlabel('Number of latent features');\n",
    "plt.ylabel('Recall');\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4fbfcd65f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(num_latent_feats, f1_train, label='Train')\n",
    "plt.plot(num_latent_feats, f1_test, label='Test')\n",
    "plt.xlabel('Number of latent features');\n",
    "plt.ylabel('F1');\n",
    "plt.legend();"
   ]
  },
  {
   "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": [
    "**Due to the class imbalance of 0's and 1's in the training and testing datasets, we use precision, recall and f1 score to demonstrate prediction performance instead of accuracy. It can be seen that the f1 score of the test set peaks at a low value with ~70 latent features. The low precision and recall values of the test set further show that SVD performs poorly towards making predictions for recommendations.**\n",
    "\n",
    "**On the other hand, our test set only consists of 20 users. The fact that we can only evaluate an extremely small subset of users implies that our work might not generalize well to the population that we want to use our recommendation system on. A better way to evaluate recommendation systems is to set up an A/B test, where account-based users will be randomly assigned to a control group that receives recommendations using the current system, and an experimental group that receives recommendations using a new system. The number of users in each group should not be significantly different. After the experiment size is estimated, we then measure the average number of interactions by users in each group. We conduct a hypothesis test of whether there is difference in number of user interactions between the two systems. The new system will be deployed if the results are both statistically and practically significant.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 58,
     "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": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}