Recommendations_with_IBM.ipynb

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    "# Recommendations with IBM\n",
    "\n",
    "In this notebook, I will be putting my recommendation skills to use on real data from the IBM Watson Studio platform. \n",
    "\n",
    "\n",
    "## Table of Contents\n",
    "\n",
    "I. [Exploratory Data Analysis](#Exploratory-Data-Analysis)<br>\n",
    "II. [Rank Based Recommendations](#Rank)<br>\n",
    "III. [User-User Based Collaborative Filtering](#User-User)<br>\n",
    "IV. [Matrix Factorization](#Matrix-Fact)<br>\n",
    "\n",
    "Let's get started by importing the necessary libraries and reading in the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
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     "text": [
      "(45993, 3)\n"
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
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      "text/plain": [
       "   article_id                                              title  \\\n",
       "0      1430.0  using pixiedust for fast, flexible, and easier...   \n",
       "1      1314.0       healthcare python streaming application demo   \n",
       "2      1429.0         use deep learning for image classification   \n",
       "3      1338.0          ml optimization using cognitive assistant   \n",
       "4      1276.0          deploy your python model as a restful api   \n",
       "\n",
       "                                      email  \n",
       "0  ef5f11f77ba020cd36e1105a00ab868bbdbf7fe7  \n",
       "1  083cbdfa93c8444beaa4c5f5e0f5f9198e4f9e0b  \n",
       "2  b96a4f2e92d8572034b1e9b28f9ac673765cd074  \n",
       "3  06485706b34a5c9bf2a0ecdac41daf7e7654ceb7  \n",
       "4  f01220c46fc92c6e6b161b1849de11faacd7ccb2  "
      ]
     },
     "execution_count": 1,
     "metadata": {},
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    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import project_tests as t\n",
    "import pickle\n",
    "\n",
    "from sklearn.metrics import f1_score\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "df = pd.read_csv('data/user-item-interactions.csv')\n",
    "df_content = pd.read_csv('data/articles_community.csv')\n",
    "del df['Unnamed: 0']\n",
    "del df_content['Unnamed: 0']\n",
    "\n",
    "# Show df to get an idea of the data\n",
    "print(df.shape)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "article_id     714\n",
       "title          714\n",
       "email         5148\n",
       "dtype: int64"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.nunique()"
   ]
  },
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   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
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      "(1056, 5)\n"
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       "      <td>Skip navigation Sign in SearchLoading...\\r\\n\\r...</td>\n",
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       "      <td>Detect Malfunctioning IoT Sensors with Streami...</td>\n",
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       "3  DATALAYER: HIGH THROUGHPUT, LOW LATENCY AT SCA...   \n",
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       "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",
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   "source": [
    "# Show df_content to get an idea of the data\n",
    "print(df_content.shape)\n",
    "df_content.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "doc_body           1036\n",
       "doc_description    1022\n",
       "doc_full_name      1051\n",
       "doc_status            1\n",
       "article_id         1051\n",
       "dtype: int64"
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     "execution_count": 4,
     "metadata": {},
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   "source": [
    "df_content.nunique()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <a class=\"anchor\" id=\"Exploratory-Data-Analysis\">Part I : Exploratory Data Analysis</a>\n",
    "\n",
    "Let's get 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": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
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       "      <td>use deep learning for image classification</td>\n",
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      "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"
      ]
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     "execution_count": 5,
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   "source": [
    "# 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": 6,
   "metadata": {},
   "outputs": [
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       "3.0"
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     "execution_count": 6,
     "metadata": {},
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   ],
   "source": [
    "df.groupby('user_id')['article_id'].count().sort_values(ascending=False).median()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
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       "364"
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     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "df.groupby('user_id')['article_id'].count().sort_values(ascending=False).max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f186cfad0f0>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(15,4))\n",
    "ax = sns.boxplot(x=df.user_id.value_counts(ascending=False))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.0"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.user_id.value_counts(ascending=False).median()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "364"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.user_id.value_counts(ascending=False).max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 50% of individuals interact with this number of articles or fewer\n",
    "median_val = df.user_id.value_counts(ascending=False).median()\n",
    "\n",
    "# The maximum number of user-article interactions by any 1 user\n",
    "max_views_by_user = df.user_id.value_counts(ascending=False).max()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`2.` Explore and remove duplicate articles from the **df_content** dataframe.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\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",
       "    </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": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Find and explore duplicate articles\n",
    "df_content[df_content.duplicated(subset=['article_id'])]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "221    2\n",
       "232    2\n",
       "577    2\n",
       "398    2\n",
       "50     2\n",
       "356    1\n",
       "355    1\n",
       "Name: article_id, dtype: int64"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_content.article_id.value_counts().head(7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Remove any rows that have the same article_id - only keep the first\n",
    "df_content.drop_duplicates(subset=['article_id'], keep='first', inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <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",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Empty DataFrame\n",
       "Columns: [doc_body, doc_description, doc_full_name, doc_status, article_id]\n",
       "Index: []"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_content[df_content.duplicated(subset=['article_id'])]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`3.` Now let's 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": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "714"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.article_id.nunique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1051"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_content.article_id.nunique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5149"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.user_id.nunique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "45993"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "unique_articles = df.article_id.nunique() # The number of unique articles that have at least one interaction\n",
    "total_articles = df_content.article_id.nunique() # The number of unique articles on the IBM platform\n",
    "unique_users = df.user_id.nunique() # The number of unique users\n",
    "user_article_interactions = df.shape[0] # The number of user-article interactions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`4.` Let's find the most viewed **article_id**, as well as how often it was viewed.\n",
    "\n",
    "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": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1429.0"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.article_id.value_counts(ascending=False).head(1).index[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "937"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.article_id.value_counts(ascending=False).head(1).item()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The most viewed article in the dataset as a string\n",
    "most_viewed_article_id = str(df.article_id.value_counts(ascending=False).head(1).index[0]) \n",
    "\n",
    "# The most viewed article in the dataset was viewed how many times?\n",
    "max_views = df.article_id.value_counts(ascending=False).head(1).item()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Oops! It looks like the value associated with: `The number of unique users in the dataset is ______` wasn't right. Try again.  It might just be the datatype.  All of the values should be ints except the article_id should be a string.  Let each row be considered a separate user-article interaction.  If a user interacts with an article 3 times, these are considered 3 separate interactions.\n",
      "\n",
      "  Notice you may also find the number of unique users as 5149 if you count the null user.  However, this is hard to catch without mapping first!\n"
     ]
    }
   ],
   "source": [
    "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": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5149"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unique_users"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <a class=\"anchor\" id=\"Rank\">Part II: Rank-Based Recommendations</a>\n",
    "\n",
    "There's actually no 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.` The function below will return the **n** top articles ordered with most interactions as the top."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "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",
    "    df_ordered_articles_titles = df.title.value_counts()\n",
    "    top_articles_titles = list(df_ordered_articles_titles.head(n).index)\n",
    "    \n",
    "    return top_articles_titles # 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",
    "    df_ordered_articles_ids = df.article_id.value_counts()\n",
    "    top_articles_ids = list(df_ordered_articles_ids.head(n).index)\n",
    " \n",
    "    return top_articles_ids"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "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": 28,
   "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 the 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 the 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.` Let's 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**. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create the user-article matrix with 1's and 0's\n",
    "\n",
    "def create_user_item_matrix(df):\n",
    "    '''\n",
    "    INPUT:\n",
    "    df - pandas dataframe with article_id, title, user_id columns\n",
    "    \n",
    "    OUTPUT:\n",
    "    user_item - user item matrix \n",
    "    \n",
    "    Description:\n",
    "    Return a matrix with user ids as rows and article ids on the columns with 1 values where a user interacted with \n",
    "    an article and a 0 otherwise\n",
    "    '''\n",
    "    user_item = df.groupby(['user_id', 'article_id'])['user_id'].nunique().unstack()\n",
    "    user_item.fillna(0, inplace=True)\n",
    "    user_item = user_item.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": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5149, 714)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "user_item.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "You have passed our quick tests!  Please proceed!\n"
     ]
    }
   ],
   "source": [
    "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.` The function below will 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 makes sense to compute similarity as the dot product of two users."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "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_dict = {}\n",
    "    n_users = user_item.shape[0]\n",
    "    \n",
    "    for i in range(1, n_users):\n",
    "        similarity_dict[i] = np.dot(user_item.loc[user_id], user_item.loc[i])\n",
    "\n",
    "    # sort by similarity\n",
    "    similarity_dict = dict(sorted(similarity_dict.items(), key=lambda item: item[1], reverse=True))\n",
    "\n",
    "    # create list of just the ids\n",
    "    most_similar_users = [key for key in similarity_dict.keys()]\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": 33,
   "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, 49]\n",
      "The 5 most similar users to user 3933 are: [1, 23, 3782, 203, 4459]\n",
      "The 3 most similar users to user 46 are: [4201, 23, 3782]\n"
     ]
    }
   ],
   "source": [
    "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 we have a function that provides the most similar users to each user, we will want to use these users to find articles we can recommend.  The functions below will return the articles we would recommend to each user. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_article_names(article_ids, df=df):\n",
    "    '''\n",
    "    INPUT:\n",
    "    article_ids - (list) a list of article ids\n",
    "    df - (pandas dataframe) df as defined at the top of the notebook\n",
    "    \n",
    "    OUTPUT:\n",
    "    article_names - (list) a list of article names associated with the list of article ids \n",
    "                    (this is identified by the title column)\n",
    "    '''\n",
    "    article_names = list(df[df.article_id.isin(article_ids)].title.unique())\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",
    "    \n",
    "    article_ids = [str(ids) for ids in list(df[df.user_id == user_id]['article_id'])]\n",
    "    article_names = list(df[df.user_id == user_id]['title'])\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 most similar users to the user\n",
    "    most_similar_users = find_similar_users(user_id)\n",
    "    \n",
    "    # get a list of articles the user has interacted with (to exclude from recs)\n",
    "    seen_article_ids, seen_article_names = get_user_articles(user_id)\n",
    "    \n",
    "    # get a list of articles unseen by the user that most similar users have interacted with\n",
    "    recs_ids = []\n",
    "    for similar_user in most_similar_users:\n",
    "        # get articles from similar user\n",
    "        recs_article_ids, recs_article_names = get_user_articles(similar_user)\n",
    "        \n",
    "        # get the difference between two arrays (articles the similar user has seen and articles the user has seen)\n",
    "        unseen_article_ids = np.setdiff1d(recs_article_ids, seen_article_ids, assume_unique=True)\n",
    "        \n",
    "        # concatenate the new recommendations found with the previous recommendations and getting only the unique values\n",
    "        recs_ids = np.unique(np.concatenate([unseen_article_ids, recs_ids], axis=0))\n",
    "        \n",
    "        # break if reaches the number of recs requested\n",
    "        if len(recs_ids) >= m:\n",
    "            recs_ids = recs_ids[:m]\n",
    "            break\n",
    "        \n",
    "    \n",
    "    return recs_ids # return recommendations for this user_id    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['analyze energy consumption in buildings',\n",
       " 'analyze accident reports on amazon emr spark',\n",
       " '520    using notebooks with pixiedust for fast, flexi...\\nName: title, dtype: object',\n",
       " '1448    i ranked every intro to data science course on...\\nName: title, dtype: object',\n",
       " 'data tidying in data science experience',\n",
       " 'airbnb data for analytics: vancouver listings',\n",
       " 'recommender systems: approaches & algorithms',\n",
       " 'airbnb data for analytics: mallorca reviews',\n",
       " 'analyze facebook data using ibm watson and watson studio',\n",
       " 'a tensorflow regression model to predict house values']"
      ]
     },
     "execution_count": 37,
     "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": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "If this is all you see, you passed all of our tests!  Nice job!\n"
     ]
    }
   ],
   "source": [
    "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, we'll 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, we'll 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 we wrote earlier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "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",
    "    n_users = user_item.shape[0]\n",
    "    \n",
    "    neighbors_ids = []\n",
    "    similarities = []\n",
    "    interactions = []\n",
    "\n",
    "    for i in range(1, n_users):\n",
    "        neighbors_ids.append(i)\n",
    "        similarities.append(np.dot(user_item.loc[user_id], user_item.loc[i]))\n",
    "        interactions.append(df[df['user_id'] == i].user_id.value_counts().item())\n",
    "\n",
    "    neighbors_data = {'neighbor_id': neighbors_ids, 'similarity': similarities, 'num_interactions': interactions}\n",
    "    \n",
    "    neighbors_df = pd.DataFrame.from_dict(neighbors_data)\n",
    "    \n",
    "    neighbors_df.drop(neighbors_df[neighbors_df.neighbor_id == user_id].index[0], inplace=True)\n",
    "    neighbors_df.sort_values(by=['similarity', 'num_interactions'], ascending=False, inplace=True)\n",
    "    \n",
    "    return neighbors_df # Return the dataframe specified in the doc_string\n",
    "\n",
    "\n",
    "def get_user_top_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 that have been seen by a user\n",
    "    '''\n",
    "    ordered_articles = user_item.sum().sort_values(ascending=False)\n",
    "    \n",
    "    user_articles_list = list(user_item.loc[user_id][user_item.loc[user_id]==1].index)\n",
    "    articles_ids = []\n",
    "    popularity = []\n",
    "\n",
    "    for article in user_articles_list:\n",
    "        articles_ids.append(article)\n",
    "        popularity.append(ordered_articles.loc[article])\n",
    "\n",
    "    articles_data = {'articles_ids': articles_ids, 'popularity': popularity}\n",
    "    articles_df = pd.DataFrame.from_dict(articles_data)\n",
    "    articles_df.sort_values(by='popularity', ascending=False, inplace=True)\n",
    "    \n",
    "    return articles_df # return the ordered articles ids\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 most similar users to the user using the new function\n",
    "    neighbors_df = get_top_sorted_users(user_id)\n",
    "    better_similar_users = list(neighbors_df.neighbor_id)\n",
    "    \n",
    "    # get a list of articles the user has interacted with (to exclude from recs)\n",
    "    seen_article_ids, seen_article_names = get_user_articles(user_id)\n",
    "    \n",
    "    # get a list of articles unseen by the user that most similar users have interacted with\n",
    "    better_recs_ids = []\n",
    "    for similar_user in better_similar_users:\n",
    "        # get articles from similar user\n",
    "        articles_df = get_user_top_articles(similar_user)\n",
    "        top_recs_article_ids = [str(ids) for ids in list(articles_df.articles_ids)]\n",
    "        \n",
    "        # get the difference between two arrays (articles the similar user has seen and articles the user has seen)\n",
    "        unseen_article_ids = np.setdiff1d(top_recs_article_ids, seen_article_ids, assume_unique=True)\n",
    "        \n",
    "        # concatenate the new recommendations found with the previous recommendations and getting only the unique values\n",
    "        better_recs_ids = pd.unique(np.concatenate([unseen_article_ids, better_recs_ids], axis=0))\n",
    "        \n",
    "        # break if reaches the number of recs requested\n",
    "        if len(better_recs_ids) >= m:\n",
    "            better_recs_ids = better_recs_ids[:m]\n",
    "            break\n",
    "    \n",
    "    rec_names = get_article_names(better_recs_ids)\n",
    "    \n",
    "    return better_recs_ids, rec_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The top 10 recommendations for user 20 are the following article ids:\n",
      "['1330.0' '1364.0' '1427.0' '1160.0' '1351.0' '1336.0' '1304.0' '1368.0'\n",
      " '1170.0' '1338.0']\n",
      "\n",
      "The top 10 recommendations for user 20 are the following article names:\n",
      "['ml optimization using cognitive assistant', 'apache spark lab, part 1: basic concepts', 'predicting churn with the spss random tree algorithm', 'use xgboost, scikit-learn & ibm watson machine learning apis', 'putting a human face on machine learning', 'gosales transactions for logistic regression model', 'insights from new york car accident reports', 'model bike sharing data with spss', 'analyze accident reports on amazon emr spark', 'learn basics about notebooks and apache spark']\n"
     ]
    }
   ],
   "source": [
    "# Quick spot check\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": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The top 5 recommendations for user 9 are the following article ids:\n",
      "['1330.0' '1429.0' '1364.0' '1427.0' '43.0']\n",
      "\n",
      "The top 5 recommendations for user 9 are the following article names:\n",
      "['use deep learning for image classification', 'predicting churn with the spss random tree algorithm', 'use xgboost, scikit-learn & ibm watson machine learning apis', 'insights from new york car accident reports', 'deep learning with tensorflow course by big data university']\n"
     ]
    }
   ],
   "source": [
    "# Quick spot check\n",
    "rec_ids, rec_names = user_user_recs_part2(9, 5)\n",
    "print(\"The top 5 recommendations for user 9 are the following article ids:\")\n",
    "print(rec_ids)\n",
    "print()\n",
    "print(\"The top 5 recommendations for user 9 are the following article names:\")\n",
    "print(rec_names)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`5.` Let's use our functions from above to correctly fill in the solutions to the dictionary below.  Then test our dictionary against the solution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Tests with a dictionary of results\n",
    "\n",
    "user1_most_sim = get_top_sorted_users(1).iloc[0, :1].neighbor_id # Find the user that is most similar to user 1 \n",
    "user131_10th_sim = get_top_sorted_users(131).iloc[9, :10].neighbor_id # Find the 10th most similar user to user 131"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3933"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "user1_most_sim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "242"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "user131_10th_sim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "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.` Let's give this some thought...\n",
    "\n",
    "If we were given a new user, which of the above functions would we be able to use to make recommendations?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Facing the issue of not having any user history to make predictions based on that (the cold start problem), recommending some overall top articles could be a good way to start.**\n",
    "\n",
    "**That can be done using the `get_top_articles` function from the Ranked-Based Recommendation part.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Is there a better way we might make recommendations?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A more personalized method to make recommendations could be content-based recommendations. Recommendations based on the content of the articles."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`7.` Let's provide the top 10 recommended articles we would recommend for a new user below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "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 = [str(id) for id in get_top_article_ids(10)] # Your recommendations here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "That's right!  Nice job!\n"
     ]
    }
   ],
   "source": [
    "assert set(new_user_recs) == set(['1314.0','1429.0','1293.0','1427.0','1162.0','1364.0','1304.0','1170.0','1431.0','1330.0']), \"Oops!  It makes sense that in this case we would want to recommend the most popular articles, because we don't know anything about these users.\"\n",
    "\n",
    "print(\"That's right!  Nice job!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <a class=\"anchor\" id=\"Matrix-Fact\">Part IV: Matrix Factorization</a>\n",
    "\n",
    "In this part of the notebook, we will build use matrix factorization to make article recommendations to the users on the IBM Watson Studio platform.\n",
    "\n",
    "`1.` Let' get thing set up as we've already created a **user_item** matrix above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load the matrix here\n",
    "user_item_matrix = pd.read_pickle('user_item_matrix.p')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
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       "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": 65,
     "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, we 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.  Let's perform SVD."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((5149, 5149), (714,), (714, 714))"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Perform SVD on the User-Item Matrix\n",
    "\n",
    "u, s, vt = np.linalg.svd(user_item_matrix) # use the built in to get the three matrices\n",
    "\n",
    "u.shape, s.shape, vt.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((5149, 5149), (714,), (714, 714))"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u_, s_, vt_ = np.linalg.svd(user_item) # use the built in to get the three matrices\n",
    "\n",
    "u_.shape, s_.shape, vt_.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There was no problem performing the SVD on the user-item matrix because it's a matrix composed of dummy values, which means it's all 1's or 0's to represent whether the user interacted with an article or not.\n",
    "\n",
    "The lack of null values is due to the fact that we're not getting to the detail of if the user liked it or not, just if there was an interaction or not."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`3.` Now for the tricky part, how do we choose the number of latent features to use?  As shown below, we 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.  Below we will get an idea of how the accuracy improves as we increase the number of latent features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f186aaade10>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_latent_feats = np.arange(10,700+10,20)\n",
    "sum_errs = []\n",
    "\n",
    "for k in num_latent_feats:\n",
    "    # restructure with k latent features\n",
    "    s_new, u_new, vt_new = np.diag(s[:k]), u[:, :k], vt[:k, :]\n",
    "    \n",
    "    # take dot product\n",
    "    user_item_est = np.around(np.dot(np.dot(u_new, s_new), vt_new))\n",
    "    \n",
    "    # compute error for each prediction to actual value\n",
    "    diffs = np.subtract(user_item_matrix, user_item_est)\n",
    "    \n",
    "    # total errors and keep track of them\n",
    "    err = np.sum(np.sum(np.abs(diffs)))\n",
    "    sum_errs.append(err)\n",
    "    \n",
    "    \n",
    "plt.plot(num_latent_feats, 1 - np.array(sum_errs)/df.shape[0]);\n",
    "plt.xlabel('Number of Latent Features');\n",
    "plt.ylabel('Accuracy');\n",
    "plt.title('Accuracy vs. Number of Latent Features');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`4.` From the above, we can't really be sure how many features to use, because simply having a better way to predict the 1's and 0's of the matrix doesn't exactly give us an indication of if we are able to make good recommendations.  Instead, we might split our dataset into a training and test set of data.  \n",
    "\n",
    "Let's use the code from earlier (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": 69,
   "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>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": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_train = df.head(40000)\n",
    "df_test = df.tail(5993)\n",
    "\n",
    "def create_test_and_train_user_item(df_train, df_test):\n",
    "    '''\n",
    "    INPUT:\n",
    "    df_train - training dataframe\n",
    "    df_test - test dataframe\n",
    "    \n",
    "    OUTPUT:\n",
    "    user_item_train - a user-item matrix of the training dataframe \n",
    "                      (unique users for each row and unique articles for each column)\n",
    "    user_item_test - a user-item matrix of the testing dataframe \n",
    "                    (unique users for each row and unique articles for each column)\n",
    "    test_idx - all of the test user ids\n",
    "    test_arts - all of the test article ids\n",
    "    \n",
    "    '''\n",
    "    user_item_train = create_user_item_matrix(df_train)\n",
    "    user_item_test = create_user_item_matrix(df_test)\n",
    "    \n",
    "    train_idx = list(user_item_train.index)\n",
    "    test_idx = list(user_item_test.index)\n",
    "    common_idx = np.intersect1d(test_idx, train_idx)\n",
    "    \n",
    "    train_arts = list(user_item_train.columns)\n",
    "    test_arts = list(user_item_test.columns)\n",
    "    common_arts = np.intersect1d(test_arts, train_arts)\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": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "common_idx = np.intersect1d(test_idx, list(user_item_train.index))\n",
    "common_arts = np.intersect1d(test_arts, list(user_item_train.columns))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(np.intersect1d(test_idx, list(user_item_train.index)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "662"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(np.setdiff1d(test_idx, list(user_item_train.index)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "574"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(np.intersect1d(test_arts, list(user_item_train.columns)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(np.setdiff1d(test_arts, list(user_item_train.columns)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "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": [
    "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 let's use the **user_item_train** dataset from above to find U, S, and V transpose using SVD. Then we'll find the subset of rows in the **user_item_test** dataset that we 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.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4487, 714)"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "user_item_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((4487, 4487), (714,), (714, 714))"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# fit SVD on the user_item_train matrix\n",
    "u_train, s_train, vt_train = np.linalg.svd(user_item_train) # fit svd similar to above then use the cells below\n",
    "\n",
    "u_train.shape, s_train.shape, vt_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((20, 4487), (714,), (714, 574))"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "common_rows = user_item_train.index.isin(test_idx)\n",
    "common_cols = user_item_train.columns.isin(test_arts)\n",
    "\n",
    "u_test = u_train[common_rows, :]\n",
    "s_test = s_train\n",
    "vt_test = vt_train[:, common_cols]\n",
    "\n",
    "u_test.shape, s_test.shape, vt_test.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((4487, 714), (714, 714), (714, 714))"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u_train_2 = u_train[:,:len(s_train)]\n",
    "s_train_2 = np.diag(s_train)\n",
    "vt_train_2 = vt_train\n",
    "\n",
    "u_train_2.shape, s_train_2.shape, vt_train_2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(np.dot(np.dot(u_train_2, s_train_2), vt_train_2), user_item_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((4487, 400), (400, 400), (400, 714))"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# using 400 latent features\n",
    "\n",
    "u_train_400 = u_train[:,:400]\n",
    "s_train_400 = np.diag(s_train[:400])\n",
    "vt_train_400 = vt_train[:400,:]\n",
    "\n",
    "u_train_400.shape, s_train_400.shape, vt_train_400.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "985.42657381869196"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Make predictions\n",
    "pred_400 = np.dot(np.dot(u_train_400, s_train_400), vt_train_400)\n",
    "\n",
    "# Compute the squared error for each predicted vs. actual rating\n",
    "sse_400 = np.sum(np.sum((user_item_train - pred_400)**2))\n",
    "sse_400"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((4487, 200), (200, 200), (200, 714))"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# using 200 latent features\n",
    "\n",
    "u_train_200 = u_train[:,:200]\n",
    "s_train_200 = np.diag(s_train[:200])\n",
    "vt_train_200 = vt_train[:200,:]\n",
    "\n",
    "u_train_200.shape, s_train_200.shape, vt_train_200.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4934.2829225572359"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Make predictions\n",
    "pred_200 = np.dot(np.dot(u_train_200, s_train_200), vt_train_200)\n",
    "\n",
    "# Compute the squared error for each predicted vs. actual rating\n",
    "sse_200 = np.sum(np.sum((user_item_train - pred_200)**2))\n",
    "sse_200"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [],
   "source": [
    "user_item_test = user_item_test.loc[common_idx, common_arts]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.6/site-packages/sklearn/metrics/classification.py:1137: UndefinedMetricWarning: F-score is ill-defined and being set to 0.0 in labels with no true samples.\n",
      "  'recall', 'true', average, warn_for)\n"
     ]
    }
   ],
   "source": [
    "num_latent_feats = np.arange(10,700+10,20)\n",
    "sum_errs_train = []\n",
    "sum_errs_test = []\n",
    "\n",
    "f1_train = []\n",
    "f1_test = []\n",
    "\n",
    "for k in num_latent_feats:\n",
    "    # restructure with k latent features\n",
    "    s_new_train, u_new_train, vt_new_train = np.diag(s_train[:k]), u_train[:, :k], vt_train[:k, :]\n",
    "    s_new_test, u_new_test, vt_new_test = np.diag(s_test[:k]), u_test[:, :k], vt_test[:k, :]\n",
    "    \n",
    "    # take dot product\n",
    "    user_item_est_train = np.around(np.dot(np.dot(u_new_train, s_new_train), vt_new_train))\n",
    "    user_item_est_test = np.around(np.dot(np.dot(u_new_test, s_new_test), vt_new_test))\n",
    "    \n",
    "    # compute error for each prediction to actual value\n",
    "    diffs_train = np.subtract(user_item_train, user_item_est_train)\n",
    "    diffs_test = np.subtract(user_item_test, user_item_est_test)\n",
    "    \n",
    "    # total errors and keep track of them\n",
    "    err_train = np.sum(np.sum(np.abs(diffs_train)))\n",
    "    sum_errs_train.append(err_train)\n",
    "    \n",
    "    err_test = np.sum(np.sum(np.abs(diffs_test)))\n",
    "    sum_errs_test.append(err_test)\n",
    "    \n",
    "    # f1 score\n",
    "    f1_train.append(f1_score(np.array(user_item_train).flatten(), user_item_est_train.flatten(), average='macro'))\n",
    "    f1_test.append(f1_score(np.array(user_item_test).flatten(), user_item_est_test.flatten(), average='macro'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1847704438>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(num_latent_feats, 1 - np.array(sum_errs_train)/(user_item_train.shape[0] * user_item_train.shape[1]), label='train')\n",
    "plt.plot(num_latent_feats, 1 - np.array(sum_errs_test)/(user_item_test.shape[0] * user_item_test.shape[1]), label='test')\n",
    "plt.xlabel('Number of Latent Features')\n",
    "plt.ylabel('Accuracy')\n",
    "plt.title('Accuracy vs. Number of Latent Features')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1847705f28>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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 Score')\n",
    "plt.title('F1 Score vs. Number of Latent Features')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "`6.` Conclusions:\n",
    "\n",
    "Let's think about what we might do to determine if the recommendations we make with any of the above recommendation systems are an improvement to how users currently find articles?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It's pretty clear the difference in performance between train and test sets, not only regarding **accuracy** but also **F1 score**.\n",
    "\n",
    "The accuracy metric isn't the best to evaluate in this case because it can't really show us how good the predictions are. The F1 score is somewhat more appropriate as it takes in consideration precision and recall.\n",
    "\n",
    "There is too much brand new users to make recommendations for (cold start problem) as opposed to users that have some history already. That leads us to believe that the model is overfitting due to the imbalanced proportion and can't generalize well enough.\n",
    "\n",
    "For new users, I would recommend articles based on their rank (Rank-Based Recommendations developed in PartII of this notebook) and from there, the user will then begin to show it's interests and preferences so I can then make more personalized recommendations.\n",
    "\n",
    "Another approach is applying A/B testing on new users. The control group would receive the rank-based recommendations and the experimental group would receive matrix-factorization recommendations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 90,
     "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
}