courswork/si671/hw1/hw1.ipynb

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   "source": [
    "# SI 671/721 (Fall 2021) Data Mining: Methods and Applications"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d8f0f20-cb21-49be-8f9a-09002d9d83de",
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   "source": [
    "Summary: For this assignment, we sampled ~10 thousand Tweets with two or more food/drink emojis. You\n",
    "will represent this dataset as a collection of itemsets and practice what we learned in class --\n",
    "mining and evaluating frequent itemsets, and calculating the similarity of itemsets.\n",
    "\n",
    "Disclaimer: The data are collected from the real world. As you step into the wild, things might\n",
    "not always be nice and clean. Although we, the instructing team, have tried our best effort to\n",
    "filter out Tweets containing poisonous vocabularies and links, it is still possible that you will\n",
    "encounter offensive contents."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "0c8b2802-b62b-4269-ab30-36cc573218b6",
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   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import sklearn\n",
    "import matplotlib.pyplot as plt\n",
    "import mlxtend\n",
    "from mlxtend.frequent_patterns import association_rules, apriori\n",
    "from tqdm.auto import tqdm\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8949fe22-f127-4511-859d-8acb18bc3c21",
   "metadata": {},
   "source": [
    "## 1.1 Load & transform the Twitter emoji dataset [11 points]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a1d571c-62b7-410a-9896-c57f8fc6341e",
   "metadata": {},
   "source": [
    "a) [3 points] First, read in the itemsets_data/food_drink_emoji_tweets.txt file and create a pandas DataFrame with the contents. You should find that every line of the data is a Tweet.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "36b9b984-2b95-49a1-93b8-cf66ca538944",
   "metadata": {},
   "outputs": [],
   "source": [
    "tweets_df = pd.read_csv(\"itemsets_data/food_drink_emoji_tweets.txt\", sep=\"\\t\", header=None).rename({0: 'Tweet'}, axis=1)\n",
    "emoji_set = {'🍫', '🍡', '🍏', '🍈', '🍯', '🥠', '🍪', '🌰', '🥯', '🍐', '🌯', '🍧', '🥮', '🥚', '🍎', '🍍', '🍠', '🍨', '🥣', '🍊', '🍘', '🍆', '🥓', '🌽', '🥐', '🌮', '🍬', '🍛', '🥘', '🥔', '🍿', '🍉', '🥞', '🍄', '🎂', '🧀', '🥩', '🍺', '🦀', '🥦', '🥭', '🍒', '🍤', '🦐', '🥝', '🥙', '🍖', '🥜', '🍥', '🍷', '🍾', '🍲', '🧂', '🥪', '🍚', '🥬', '🥑', '🍙', '🍞', '🥃', '🥗', '🍕', '🍔', '🥕', '🧁', '🍋', '🍰', '🥫', '🍗', '🥧', '🥛', '🍮', '🥡', '🍟', '🍅', '🥂', '🍸', '🥥', '🍢', '🍌', '🍝', '🍵', '🍼', '🍦', '🍭', '🍑', '🍹', '🍇', '🥨', '🍱', '🦞', '☕', '🌶', '🍻', '🍳', '🥒', '🍣', '🥟', '🥖', '🍶', '🍜', '🍓', '🦑', '🍩', '🌭'} "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "de00ce76-672d-4a79-bdd0-1ffe36df0145",
   "metadata": {},
   "source": [
    "b) [3 points] Using this DataFrame, extract the emojis that appear in each Tweet as an itemset. For this assignment, we are only interested in emojis that are food and drink. As such, you are supplied with the following emoji_set to filter to food and drink emojis:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "d7ac332d-5657-4b51-8d5e-72c97a058cc5",
   "metadata": {},
   "outputs": [
    {
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       "\n",
       "    .dataframe thead th {\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Tweet</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>RT @CalorieFixess: 🍗🌯🍔🍒 400 Calories https://t...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>RT @1_F_I_R_S_T: _ 🍈¹〉Grow your account fast! ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>RT @LegendDeols: 👉👉👉G€T Ready to dance💃🕺🕺🕺💃💃💃 ...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                               Tweet\n",
       "0  RT @CalorieFixess: 🍗🌯🍔🍒 400 Calories https://t...\n",
       "1  RT @1_F_I_R_S_T: _ 🍈¹〉Grow your account fast! ...\n",
       "2  RT @LegendDeols: 👉👉👉G€T Ready to dance💃🕺🕺🕺💃💃💃 ..."
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tweets_df.head(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "74865d58-774e-41ac-97cf-2c2e1d1f073a",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'🌯', '🍒', '🍔', '🍗'}"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "emojis_per_tweet = {}\n",
    "\n",
    "for i, row in tweets_df.iterrows():\n",
    "    temp = set()\n",
    "    tokens = row['Tweet'].split()\n",
    "    for token in tokens:\n",
    "        characters = [char for char in token]\n",
    "        for char in characters:\n",
    "            if char in emoji_set:\n",
    "                temp.add(char)\n",
    "    # emojis_per_tweet.append(temp)\n",
    "    emojis_per_tweet[i] = temp\n",
    "\n",
    "emojis_per_tweet[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "70f89050-0c9d-4713-b205-06d0c73c6a9f",
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   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Emojis</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Index</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>{🌯, 🍗, 🍒, 🍔}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>{🍍, 🍈, 🍉, 🍇, 🍊, 🍓}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>{🍸, 🥃}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>{🍟, 🍔}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>{🍌, ☕}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9953</th>\n",
       "      <td>{🥃, 🍻}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9954</th>\n",
       "      <td>{🍍, 🍏}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9955</th>\n",
       "      <td>{🥓, 🍳, ☕}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9956</th>\n",
       "      <td>{🍷, 🍹, 🍻}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9957</th>\n",
       "      <td>{🍾, 🥂}</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>9958 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                   Emojis\n",
       "Index                    \n",
       "0            {🌯, 🍗, 🍒, 🍔}\n",
       "1      {🍍, 🍈, 🍉, 🍇, 🍊, 🍓}\n",
       "2                  {🍸, 🥃}\n",
       "3                  {🍟, 🍔}\n",
       "4                  {🍌, ☕}\n",
       "...                   ...\n",
       "9953               {🥃, 🍻}\n",
       "9954               {🍍, 🍏}\n",
       "9955            {🥓, 🍳, ☕}\n",
       "9956            {🍷, 🍹, 🍻}\n",
       "9957               {🍾, 🥂}\n",
       "\n",
       "[9958 rows x 1 columns]"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unique_emoji_df = pd.DataFrame(data=emojis_per_tweet.items(), columns=([\"Index\", \"Emojis\"])).set_index(keys='Index')\n",
    "unique_emoji_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "8be8e946-1c42-4cf7-bc83-543eed75ccee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9958"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(unique_emoji_df.values)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7b47757-2f19-4295-9e7d-a5c83f0bc5d9",
   "metadata": {},
   "source": [
    "c) [5 points] Next, as we recommend utilizing the mlxtend package in this assignment to perform frequent itemset mining, you will need to transform the data. The mlxtend package requires that the itemsets be transformed into a matrix before being passed to its APIs, where each row represents an itemset and each column represents an item. Within this matrix, each cell encodes whether an item is in an itemset or not. We recommend the MultiLabelBinarizer function in scikit-learn to implement this transformation. Here is the documentation for the function: https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.MultiLabelBinarizer.html."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "3a0cedc6-2d15-427e-94e0-ff3239195d8c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 0 0 ... 0 0 0]\n",
      " [0 0 0 ... 0 0 0]\n",
      " [0 0 0 ... 0 0 0]\n",
      " ...\n",
      " [1 0 0 ... 0 0 0]\n",
      " [0 0 0 ... 0 0 0]\n",
      " [0 0 0 ... 0 0 0]]\n",
      "(9958, 105)\n"
     ]
    }
   ],
   "source": [
    "from sklearn.preprocessing import MultiLabelBinarizer\n",
    "mlb = MultiLabelBinarizer()\n",
    "emoji_matrix = mlb.fit_transform(unique_emoji_df['Emojis'])\n",
    "emoji_inverse = mlb.inverse_transform(emoji_matrix)\n",
    "\n",
    "print(emoji_matrix)\n",
    "print(emoji_matrix.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40d1738b-cb76-4d0d-b479-e6b5ee85d757",
   "metadata": {},
   "source": [
    "## 1.2 Exploratory Data Analysis (EDA) [9 points]\n",
    "\n",
    "Before we jump into analyzing a dataset, it is always wise to take a look at some summary statistics\n",
    "first. Some questions to consider:\n",
    "\n",
    "- [3 points] How many different emojis are used in the dataset?\n",
    "-  [3 points] How many emojis are used in a Tweet, on average? What does the distribution look like? (hint: plot the distribution!)\n",
    "-  [3 points] Which emojis are most popular (i.e., used most frequently) in the dataset? Please return the top 5."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "3c89e75a-8464-411a-ad86-b41084ce83ef",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of unique emojis used in the dataset: 105\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "num_rows, num_cols = emoji_matrix.shape\n",
    "print(\"Number of unique emojis used in the dataset: {}\".format(num_cols))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "cb0e6d58-c107-48a9-9b41-d77b2ca6382b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average number of emojis used per tweet: 2.6340630648724646\n"
     ]
    }
   ],
   "source": [
    "lengths = []\n",
    "for item in emoji_matrix:\n",
    "    lengths.append(item.sum())\n",
    "    \n",
    "print(\"Average number of emojis used per tweet: {}\".format(np.mean(lengths)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "e2c392f3-3182-469c-a782-f2c5cd48907d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "plot = sns.displot(lengths)\n",
    "plt.xlim(0, 10)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "5d5f4834-82f9-40bc-ad3d-cf9f9b56d45e",
   "metadata": {},
   "outputs": [],
   "source": [
    "import operator\n",
    "\n",
    "def sort_dictionary(dictionary):\n",
    "    return sorted(dictionary.items(), key=operator.itemgetter(1), reverse=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "4b5e9097-2029-4867-bf69-c441bf2eebd6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Top 5 most used emojis: [('🍻', 1809), ('🎂', 1481), ('🍔', 1382), ('🍾', 1078), ('🥂', 1028)]\n"
     ]
    }
   ],
   "source": [
    "emoji_counter = {}\n",
    "\n",
    "for tup in emoji_inverse:\n",
    "    for item in tup:\n",
    "        if item not in emoji_counter.keys():\n",
    "            emoji_counter[item] = 1\n",
    "        else:\n",
    "            emoji_counter[item] += 1\n",
    "            \n",
    "top5_emojis = sort_dictionary(emoji_counter)[:5]\n",
    "print(\"Top 5 most used emojis: {}\".format(top5_emojis))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06cdea44-c646-46c1-a54b-d9c38f80d2fb",
   "metadata": {
    "tags": []
   },
   "source": [
    "## 2. The Apriori Algorithm [45 points]\n",
    "\n",
    "Now, it is time to apply the Apriori algorithm to the emoji dataset. The documentation for the\n",
    "apriori function can be found at http://rasbt.github.io/mlxtend/user_guide/frequent_patterns/apriori/."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "23f0a88b-1a54-48f5-a74b-9af31e6b6d4e",
   "metadata": {},
   "source": [
    "a) [10 points] Using apriori, create a function, `emoji_frequent_itemsets`, to find all the frequent\n",
    "k-itemsets with a minimal support of `min_support` in the emoji dataset. In other words, k and\n",
    "min_support should be arguments that are passed when the function is called, in addition to the\n",
    "matrix itself. Your function should return a Pandas DataFrame object with two columns:\n",
    "\n",
    "- The first one is named `support` and stores the support of the frequent itemsets.\n",
    "- The second column is named `itemsets` and stores the frequent itemset as a frozenset (the default return type of the apriori API).\n",
    "\n",
    "Make sure that you are only returning the frequent itemsets that have the specified number of\n",
    "emojis (k)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "453f0ca2-adb4-4a3b-b6c3-584652b7ec20",
   "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>☕</th>\n",
       "      <th>🌭</th>\n",
       "      <th>🌮</th>\n",
       "      <th>🌯</th>\n",
       "      <th>🌰</th>\n",
       "      <th>🌶</th>\n",
       "      <th>🌽</th>\n",
       "      <th>🍄</th>\n",
       "      <th>🍅</th>\n",
       "      <th>🍆</th>\n",
       "      <th>...</th>\n",
       "      <th>🥭</th>\n",
       "      <th>🥮</th>\n",
       "      <th>🥯</th>\n",
       "      <th>🦀</th>\n",
       "      <th>🦐</th>\n",
       "      <th>🦑</th>\n",
       "      <th>🦞</th>\n",
       "      <th>🧀</th>\n",
       "      <th>🧁</th>\n",
       "      <th>🧂</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>...</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>...</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>...</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>...</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>...</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9953</th>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>...</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9954</th>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>...</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9955</th>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>...</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9956</th>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>...</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9957</th>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>...</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>9958 rows × 105 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          ☕      🌭      🌮      🌯      🌰      🌶      🌽      🍄      🍅      🍆  \\\n",
       "0     False  False  False   True  False  False  False  False  False  False   \n",
       "1     False  False  False  False  False  False  False  False  False  False   \n",
       "2     False  False  False  False  False  False  False  False  False  False   \n",
       "3     False  False  False  False  False  False  False  False  False  False   \n",
       "4      True  False  False  False  False  False  False  False  False  False   \n",
       "...     ...    ...    ...    ...    ...    ...    ...    ...    ...    ...   \n",
       "9953  False  False  False  False  False  False  False  False  False  False   \n",
       "9954  False  False  False  False  False  False  False  False  False  False   \n",
       "9955   True  False  False  False  False  False  False  False  False  False   \n",
       "9956  False  False  False  False  False  False  False  False  False  False   \n",
       "9957  False  False  False  False  False  False  False  False  False  False   \n",
       "\n",
       "      ...      🥭      🥮      🥯      🦀      🦐      🦑      🦞      🧀      🧁  \\\n",
       "0     ...  False  False  False  False  False  False  False  False  False   \n",
       "1     ...  False  False  False  False  False  False  False  False  False   \n",
       "2     ...  False  False  False  False  False  False  False  False  False   \n",
       "3     ...  False  False  False  False  False  False  False  False  False   \n",
       "4     ...  False  False  False  False  False  False  False  False  False   \n",
       "...   ...    ...    ...    ...    ...    ...    ...    ...    ...    ...   \n",
       "9953  ...  False  False  False  False  False  False  False  False  False   \n",
       "9954  ...  False  False  False  False  False  False  False  False  False   \n",
       "9955  ...  False  False  False  False  False  False  False  False  False   \n",
       "9956  ...  False  False  False  False  False  False  False  False  False   \n",
       "9957  ...  False  False  False  False  False  False  False  False  False   \n",
       "\n",
       "          🧂  \n",
       "0     False  \n",
       "1     False  \n",
       "2     False  \n",
       "3     False  \n",
       "4     False  \n",
       "...     ...  \n",
       "9953  False  \n",
       "9954  False  \n",
       "9955  False  \n",
       "9956  False  \n",
       "9957  False  \n",
       "\n",
       "[9958 rows x 105 columns]"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from mlxtend.preprocessing import TransactionEncoder\n",
    "\n",
    "te = TransactionEncoder()\n",
    "te_array = te.fit_transform(emoji_inverse)\n",
    "k_df = pd.DataFrame(te_array, columns=te.columns_)\n",
    "k_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "ece21a43-aad0-494f-9a7f-536fa738144c",
   "metadata": {},
   "outputs": [],
   "source": [
    "from mlxtend.frequent_patterns import apriori\n",
    "\n",
    "def emoji_frequent_itemsets(k, min_support):\n",
    "    '''\n",
    "    Takes in k number of emojis\n",
    "    \n",
    "    This function returns a DataFrame object with two columns:\n",
    "     - The first one is named `support` and stores the support of the frequent itemsets.\n",
    "     - The second column is named `itemsets` and stores the frequent itemset as a frozenset \n",
    "         (the default return type of the apriori API).\n",
    "    '''\n",
    "    frequent_itemsets = apriori(k, min_support=min_support)\n",
    "    frequent_itemsets['length'] = frequent_itemsets['itemsets'].apply(lambda x: len(x))\n",
    "    return frequent_itemsets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "27fc54b7-510f-4f9d-a658-a405e8a53c92",
   "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>support</th>\n",
       "      <th>itemsets</th>\n",
       "      <th>length</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>155</th>\n",
       "      <td>0.007833</td>\n",
       "      <td>(10, 12, 13)</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>156</th>\n",
       "      <td>0.009239</td>\n",
       "      <td>(24, 34, 23)</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>157</th>\n",
       "      <td>0.007030</td>\n",
       "      <td>(48, 46, 47)</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>158</th>\n",
       "      <td>0.011749</td>\n",
       "      <td>(57, 58, 59)</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>159</th>\n",
       "      <td>0.007532</td>\n",
       "      <td>(57, 58, 60)</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>160</th>\n",
       "      <td>0.007632</td>\n",
       "      <td>(57, 58, 61)</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>161</th>\n",
       "      <td>0.007230</td>\n",
       "      <td>(57, 58, 66)</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>162</th>\n",
       "      <td>0.007230</td>\n",
       "      <td>(57, 59, 60)</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>163</th>\n",
       "      <td>0.007732</td>\n",
       "      <td>(57, 59, 61)</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>164</th>\n",
       "      <td>0.007030</td>\n",
       "      <td>(57, 66, 59)</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>165</th>\n",
       "      <td>0.007732</td>\n",
       "      <td>(57, 66, 63)</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>166</th>\n",
       "      <td>0.007632</td>\n",
       "      <td>(58, 59, 60)</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>167</th>\n",
       "      <td>0.007532</td>\n",
       "      <td>(58, 59, 61)</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>168</th>\n",
       "      <td>0.007230</td>\n",
       "      <td>(58, 59, 63)</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>169</th>\n",
       "      <td>0.007933</td>\n",
       "      <td>(58, 59, 66)</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>170</th>\n",
       "      <td>0.010544</td>\n",
       "      <td>(65, 66, 63)</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      support      itemsets  length\n",
       "155  0.007833  (10, 12, 13)       3\n",
       "156  0.009239  (24, 34, 23)       3\n",
       "157  0.007030  (48, 46, 47)       3\n",
       "158  0.011749  (57, 58, 59)       3\n",
       "159  0.007532  (57, 58, 60)       3\n",
       "160  0.007632  (57, 58, 61)       3\n",
       "161  0.007230  (57, 58, 66)       3\n",
       "162  0.007230  (57, 59, 60)       3\n",
       "163  0.007732  (57, 59, 61)       3\n",
       "164  0.007030  (57, 66, 59)       3\n",
       "165  0.007732  (57, 66, 63)       3\n",
       "166  0.007632  (58, 59, 60)       3\n",
       "167  0.007532  (58, 59, 61)       3\n",
       "168  0.007230  (58, 59, 63)       3\n",
       "169  0.007933  (58, 59, 66)       3\n",
       "170  0.010544  (65, 66, 63)       3"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_ = emoji_frequent_itemsets(k_df, min_support=0.007)\n",
    "df_[df_.length == 3]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c26550c-c952-42d3-9e1f-7d8a868f77f9",
   "metadata": {},
   "source": [
    "## 2.1 Apriori Algorithm under the Hood [30 points]\n",
    "\n",
    "In this part of the assignment, we are going to continue our exploration in mining frequent\n",
    "itemsets. Specifically, we are going to examine a few key steps in the Apriori algorithm.\n",
    "\n",
    "### 2.1.1 Candidate Generation\n",
    "\n",
    "A critical step of the Apriori algorithm is candidate generation. That is, candidate\n",
    "(k+1)-itemsets should be generated from frequent k-itemsets. In the following exercise, we want\n",
    "you to generate candidate 3-itemsets based on the frequent 2-itemsets.\n",
    "\n",
    "a) [10 points] You will need to construct a `generate_candidate_3_itemsets` function, which\n",
    "takes in a list of frequent 2-itemsets and returns a list of the candidate 3-itemsets (\"candidate\"\n",
    "means that they may or may not be frequent). Please represent each itemset as a `set` in\n",
    "Python. Make sure that for each candidate 3-itemset in your returned list, at least one of its\n",
    "size-2 subset is a frequent 2-itemset, and your list does not contain duplicated itemsets.\n",
    "\n",
    "We have prepared the frequent 2-itemsets for you, which you can load from the file named\n",
    "itemsets_data/food_emoji_frequent_2_itemsets.csv. We will evaluate your function by\n",
    "feeding in the loaded 2-itemsets and examining the return value. Note that the loaded\n",
    "2-itemsets are different from what you will get with the `emoji_frequent_itemsets` function you\n",
    "implemented in the previous part, as we have eliminated the drink-related emojis to make the\n",
    "exercise more trackable.\n",
    "\n",
    "You will receive full points for this part of the question if (1) every candidate 3-itemset in your\n",
    "returned list is a superset of at least one frequent 2-itemset, (2) every 3-itemset that has a\n",
    "frequent size-2 subset is already in your list, and (3) your list does not contain duplicated sets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "28e06dce-7285-4dd9-a793-c4f35dbbb4aa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'🌭', '🍔'}"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "itemsets2 = pd.read_csv(\"itemsets_data/food_emoji_frequent_2_itemsets.csv\", header=None)\n",
    "freq2 = itemsets2.values.tolist()\n",
    "\n",
    "candidate_2_itemsets = []\n",
    "for item in freq2:\n",
    "    candidate_2_itemsets.append(set([char for char in item[0]]))\n",
    "\n",
    "candidate_2_itemsets[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "85b2dfa3-9ac3-434c-8eae-07feb19b12f7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{'🌭', '🍔', '🍕'},\n",
       " {'🌭', '🍕', '🍟'},\n",
       " {'🌭', '🍕', '🍦'},\n",
       " {'🌮', '🍔', '🍕'},\n",
       " {'🍇', '🍉', '🍊'},\n",
       " {'🍇', '🍉', '🍌'},\n",
       " {'🍇', '🍉', '🍑'},\n",
       " {'🍇', '🍉', '🍒'},\n",
       " {'🍇', '🍉', '🎂'},\n",
       " {'🍇', '🍊', '🍒'}]"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def generate_candidate_3_itemsets(freq2_list):\n",
    "    '''\n",
    "    Takes in a list of frequent 2-itemsets and returns a list of the\n",
    "    candidate 3-itemsets that for every candidate 3-itemset, at least\n",
    "    one two of the three objects are a frequent 2-itemset\n",
    "    '''\n",
    "    candidate_3_itemsets = []\n",
    "    \n",
    "    length = len(freq2_list)    \n",
    "    k = 3\n",
    "    \n",
    "    for i in range(length):\n",
    "        for j in range(i + 1, length):       \n",
    "            emoji1 = list(freq2_list[i])[:1]\n",
    "            emoji2 = list(freq2_list[j])[:1]            \n",
    "            if emoji1 == emoji2:\n",
    "                candidate_3_itemsets.append(freq2_list[i] | freq2_list[j])\n",
    "    \n",
    "    return candidate_3_itemsets\n",
    "            \n",
    "candidate_3_itemsets = generate_candidate_3_itemsets(candidate_2_itemsets)\n",
    "candidate_3_itemsets[:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33b201d1-d26d-4de9-99f7-f1b3fd286a0a",
   "metadata": {},
   "source": [
    "b) [10 points] Note that this pruning procedure won't give us the smallest set of candidates.\n",
    "Therefore, we can further prune the candidate itemsets by requiring all size-2 subsets of each\n",
    "candidate 3-itemset to be frequent.\n",
    "\n",
    "Think about the example you've seen in the lecture. Suppose {🍺,🍼}, {🍺,🍋}, {🍼,🍭}, {🍼,\n",
    "🍋} are all the frequent 2-itemsets. In the lecture, we said {🍺, 🍼, 🍋}, {🍺, 🍼, 🍭}, {🍼,🍭,\n",
    "🍋} are candidate 3-itemsets because each 3-itemset is a superset of at least one frequent\n",
    "2-itemset. However, a larger itemset can never be frequent as long as one of its subset is not\n",
    "frequent. In this case, {🍺, 🍼, 🍭} can never been frequent because {🍺, 🍭} is not frequent.\n",
    "Neither can {🍼, 🍭, 🍋}, as the subset {🍭, 🍋} is not frequent. Ideally, we should be able to\n",
    "exclude the two candidate 3-itemsets {🍺, 🍼, 🍭} and {🍼, 🍭,🍋} even without scanning the\n",
    "database for counting.\n",
    "\n",
    "For this exercise, please prune your generated candidate 3-itemsets by requiring all their\n",
    "subsets to be frequent. You will receive full points for this part if the pruning is done correctly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "f45e6f96-45aa-4016-ad40-af103667db19",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of Itemsets before Pruning: 155\n",
      "========================================\n",
      "1: Match found for ['🍕', '🌭', '🍔']: 🌭-🍔\n",
      "2: Match found for ['🍟', '🍕', '🌭']: 🍕-🌭\n",
      "3: Match found for ['🍕', '🌭', '🍦']: 🍕-🌭\n",
      "4: Match found for ['🌮', '🍕', '🍔']: 🌮-🍔\n",
      "5: Match found for ['🍉', '🍇', '🍊']: 🍉-🍇\n",
      "6: Match found for ['🍌', '🍉', '🍇']: 🍉-🍇\n",
      "7: Match found for ['🍉', '🍇', '🍑']: 🍉-🍇\n",
      "8: Match found for ['🍉', '🍇', '🍒']: 🍉-🍇\n",
      "9: Match found for ['🍉', '🍇', '🎂']: 🍉-🍇\n",
      "10: Match found for ['🍇', '🍒', '🍊']: 🍇-🍊\n",
      "11: Match found for ['🍍', '🍉', '🍇']: 🍉-🍇\n",
      "12: Match found for ['🍍', '🍇', '🍊']: 🍇-🍊\n",
      "13: Match found for ['🍍', '🍇', '🍏']: 🍍-🍇\n",
      "14: Match found for ['🍍', '🍇', '🍓']: 🍍-🍇\n",
      "15: Match found for ['🍍', '🥝', '🍇']: 🍍-🍇\n",
      "16: Match found for ['🍎', '🍉', '🍇']: 🍉-🍇\n",
      "17: Match found for ['🍎', '🍇', '🍊']: 🍇-🍊\n",
      "18: Match found for ['🍎', '🍇', '🍏']: 🍎-🍇\n",
      "19: Match found for ['🍎', '🍇', '🍐']: 🍎-🍇\n",
      "20: Match found for ['🍎', '🍇', '🍒']: 🍎-🍇\n",
      "21: Match found for ['🍓', '🍉', '🍇']: 🍉-🍇\n",
      "22: Match found for ['🍓', '🍇', '🍊']: 🍇-🍊\n",
      "23: Match found for ['🍓', '🍋', '🍇']: 🍓-🍇\n",
      "24: Match found for ['🍓', '🍇', '🍌']: 🍓-🍇\n",
      "25: Match found for ['🍓', '🍇', '🍎']: 🍎-🍇\n",
      "26: Match found for ['🍓', '🍇', '🍏']: 🍓-🍇\n",
      "27: Match found for ['🍓', '🍇', '🍑']: 🍓-🍇\n",
      "28: Match found for ['🍓', '🍇', '🍒']: 🍇-🍒\n",
      "29: Match found for ['🥝', '🍇', '🍉']: 🍉-🍇\n",
      "30: Match found for ['🥝', '🍇', '🍊']: 🍇-🍊\n",
      "31: Match found for ['🍉', '🍌', '🍊']: 🍉-🍊\n",
      "32: Match found for ['🍉', '🍑', '🍊']: 🍉-🍊\n",
      "33: Match found for ['🍉', '🍒', '🍊']: 🍉-🍊\n",
      "34: Match found for ['🍉', '🍊', '🎂']: 🍉-🍊\n",
      "35: Match found for ['🍋', '🍉', '🍊']: 🍉-🍊\n",
      "36: Match found for ['🍉', '🍌', '🍑']: 🍉-🍌\n",
      "37: Match found for ['🍉', '🍌', '🍒']: 🍉-🍌\n",
      "38: Match found for ['🍉', '🍌', '🎂']: 🍉-🍌\n",
      "39: Match found for ['🍍', '🍉', '🍊']: 🍉-🍊\n",
      "40: Match found for ['🍍', '🍉', '🍏']: 🍍-🍉\n",
      "41: Match found for ['🍍', '🍉', '🍓']: 🍍-🍉\n",
      "42: Match found for ['🍍', '🍉', '🥝']: 🍍-🍉\n",
      "43: Match found for ['🍎', '🍉', '🍊']: 🍉-🍊\n",
      "44: Match found for ['🍎', '🍉', '🍏']: 🍎-🍉\n",
      "45: Match found for ['🍎', '🍉', '🍐']: 🍎-🍉\n",
      "46: Match found for ['🍎', '🍉', '🍒']: 🍎-🍉\n",
      "47: Match found for ['🍉', '🍒', '🍑']: 🍉-🍑\n",
      "48: Match found for ['🍉', '🍑', '🎂']: 🍉-🍑\n",
      "49: Match found for ['🍉', '🍒', '🎂']: 🍉-🍒\n",
      "50: Match found for ['🍓', '🍉', '🍊']: 🍉-🍊\n",
      "51: Match found for ['🍓', '🍉', '🍋']: 🍋-🍉\n",
      "52: Match found for ['🍓', '🍉', '🍌']: 🍉-🍌\n",
      "53: Match found for ['🍓', '🍉', '🍎']: 🍎-🍉\n",
      "54: Match found for ['🍓', '🍉', '🍏']: 🍓-🍉\n",
      "55: Match found for ['🍓', '🍉', '🍑']: 🍉-🍑\n",
      "56: Match found for ['🍓', '🍉', '🍒']: 🍉-🍒\n",
      "57: Match found for ['🥝', '🍉', '🍊']: 🍉-🍊\n",
      "58: Match found for ['🍍', '🍏', '🍊']: 🍍-🍊\n",
      "59: Match found for ['🍍', '🍊', '🍓']: 🍍-🍊\n",
      "60: Match found for ['🍍', '🥝', '🍊']: 🍍-🍊\n",
      "61: Match found for ['🍎', '🍏', '🍊']: 🍎-🍊\n",
      "62: Match found for ['🍎', '🍐', '🍊']: 🍎-🍊\n",
      "63: Match found for ['🍎', '🍒', '🍊']: 🍎-🍊\n",
      "64: Match found for ['🍓', '🍋', '🍊']: 🍋-🍊\n",
      "65: Match found for ['🍓', '🍌', '🍊']: 🍌-🍊\n",
      "66: Match found for ['🍓', '🍊', '🍎']: 🍎-🍊\n",
      "67: Match found for ['🍓', '🍏', '🍊']: 🍏-🍊\n",
      "68: Match found for ['🍓', '🍑', '🍊']: 🍑-🍊\n",
      "69: Match found for ['🍓', '🍒', '🍊']: 🍓-🍊\n",
      "70: Match found for ['🍓', '🍋', '🍌']: 🍓-🍋\n",
      "71: Match found for ['🍓', '🍋', '🍎']: 🍓-🍋\n",
      "72: Match found for ['🍓', '🍋', '🍏']: 🍓-🍋\n",
      "73: Match found for ['🍓', '🍋', '🍑']: 🍓-🍋\n",
      "74: Match found for ['🍓', '🍋', '🍒']: 🍓-🍋\n",
      "75: Match found for ['🍓', '🍌', '🍎']: 🍓-🍌\n",
      "76: Match found for ['🍓', '🍌', '🍏']: 🍓-🍌\n",
      "77: Match found for ['🍓', '🍌', '🍑']: 🍓-🍌\n",
      "78: Match found for ['🍓', '🍌', '🍒']: 🍓-🍌\n",
      "79: Match found for ['🍍', '🍏', '🍓']: 🍍-🍏\n",
      "80: Match found for ['🍍', '🥝', '🍏']: 🍍-🍏\n",
      "81: Match found for ['🍍', '🥝', '🍓']: 🍍-🍓\n",
      "82: Match found for ['🍎', '🍐', '🍏']: 🍎-🍏\n",
      "83: Match found for ['🍎', '🍒', '🍏']: 🍎-🍏\n",
      "84: Match found for ['🍎', '🍐', '🍒']: 🍎-🍐\n",
      "85: Match found for ['🍓', '🍏', '🍎']: 🍎-🍏\n",
      "86: Match found for ['🍓', '🍑', '🍎']: 🍓-🍎\n",
      "87: Match found for ['🍓', '🍒', '🍎']: 🍎-🍒\n",
      "88: Match found for ['🍓', '🍑', '🍏']: 🍓-🍏\n",
      "89: Match found for ['🍓', '🍒', '🍏']: 🍓-🍏\n",
      "90: Match found for ['🍓', '🍒', '🍑']: 🍒-🍑\n",
      "91: Match found for ['🍕', '🍟', '🍔']: 🍕-🍔\n",
      "92: Match found for ['🍕', '🍦', '🍔']: 🍕-🍔\n",
      "93: Match found for ['🍗', '🍕', '🍔']: 🍕-🍔\n",
      "94: Match found for ['🍗', '🍖', '🍔']: 🍗-🍔\n",
      "95: Match found for ['🍗', '🍟', '🍔']: 🍗-🍔\n",
      "96: Match found for ['🍩', '🍦', '🍔']: 🍦-🍔\n",
      "97: Match found for ['🎂', '🍦', '🍔']: 🍦-🍔\n",
      "98: Match found for ['🍖', '🍗', '🍕']: 🍗-🍕\n",
      "99: Match found for ['🍗', '🍕', '🍟']: 🍗-🍕\n",
      "100: Match found for ['🍕', '🍟', '🍦']: 🍕-🍟\n",
      "101: Match found for ['🍗', '🍖', '🍟']: 🍗-🍖\n",
      "102: Match found for ['🍧', '🍦', '🍰']: 🍧-🍦\n",
      "103: Match found for ['🍧', '🍦', '🎂']: 🍧-🍦\n",
      "104: Match found for ['🍨', '🍧', '🍦']: 🍧-🍦\n",
      "105: Match found for ['🍨', '🍫', '🍦']: 🍨-🍦\n",
      "106: Match found for ['🍨', '🍰', '🍦']: 🍨-🍦\n",
      "107: Match found for ['🍨', '🍦', '🎂']: 🍨-🍦\n",
      "108: Match found for ['🎂', '🍦', '🍩']: 🍦-🍩\n",
      "109: Match found for ['🍪', '🍦', '🍩']: 🍦-🍩\n",
      "110: Match found for ['🍫', '🍦', '🍩']: 🍦-🍩\n",
      "111: Match found for ['🍫', '🍪', '🍦']: 🍪-🍦\n",
      "112: Match found for ['🍫', '🍦', '🍬']: 🍫-🍦\n",
      "113: Match found for ['🍫', '🍭', '🍦']: 🍫-🍦\n",
      "114: Match found for ['🍫', '🍰', '🍦']: 🍫-🍦\n",
      "115: Match found for ['🍫', '🍦', '🎂']: 🍫-🍦\n",
      "116: Match found for ['🍭', '🍦', '🍬']: 🍭-🍦\n",
      "117: Match found for ['🍭', '🍦', '🎂']: 🍭-🍦\n",
      "118: Match found for ['🍰', '🍦', '🍩']: 🍦-🍩\n",
      "119: Match found for ['🍰', '🍪', '🍦']: 🍪-🍦\n",
      "120: Match found for ['🍰', '🍦', '🍬']: 🍰-🍦\n",
      "121: Match found for ['🍰', '🍭', '🍦']: 🍭-🍦\n",
      "122: Match found for ['🍰', '🍦', '🎂']: 🍰-🍦\n",
      "123: Match found for ['🍨', '🍫', '🍧']: 🍨-🍧\n",
      "124: Match found for ['🍨', '🍧', '🍰']: 🍨-🍧\n",
      "125: Match found for ['🍨', '🍧', '🎂']: 🍨-🍧\n",
      "126: Match found for ['🍧', '🍰', '🎂']: 🍧-🍰\n",
      "127: Match found for ['🍨', '🍫', '🍰']: 🍨-🍫\n",
      "128: Match found for ['🍨', '🍫', '🎂']: 🍨-🍫\n",
      "129: Match found for ['🍨', '🍰', '🎂']: 🍨-🍰\n",
      "130: Match found for ['🍫', '🍪', '🍩']: 🍪-🍩\n",
      "131: Match found for ['🍫', '🍬', '🍩']: 🍫-🍩\n",
      "132: Match found for ['🍫', '🍭', '🍩']: 🍫-🍩\n",
      "133: Match found for ['🍫', '🍰', '🍩']: 🍫-🍩\n",
      "134: Match found for ['🍫', '🎂', '🍩']: 🍫-🍩\n",
      "135: Match found for ['🍰', '🍪', '🍩']: 🍪-🍩\n",
      "136: Match found for ['🍰', '🍬', '🍩']: 🍰-🍩\n",
      "137: Match found for ['🍰', '🍭', '🍩']: 🍰-🍩\n",
      "138: Match found for ['🍰', '🎂', '🍩']: 🍰-🍩\n",
      "139: Match found for ['🍫', '🍪', '🍬']: 🍫-🍪\n",
      "140: Match found for ['🍭', '🍫', '🍪']: 🍫-🍪\n",
      "141: Match found for ['🍫', '🍰', '🍪']: 🍫-🍪\n",
      "142: Match found for ['🍫', '🍪', '🎂']: 🍫-🍪\n",
      "143: Match found for ['🍰', '🍪', '🍬']: 🍰-🍪\n",
      "144: Match found for ['🍭', '🍰', '🍪']: 🍰-🍪\n",
      "145: Match found for ['🍰', '🍪', '🎂']: 🍰-🍪\n",
      "146: Match found for ['🍫', '🍭', '🍬']: 🍫-🍬\n",
      "147: Match found for ['🍫', '🍰', '🍬']: 🍫-🍬\n",
      "148: Match found for ['🍫', '🎂', '🍬']: 🍫-🍬\n",
      "149: Match found for ['🍫', '🍰', '🍭']: 🍫-🍭\n",
      "150: Match found for ['🍫', '🍭', '🎂']: 🍫-🍭\n",
      "151: Match found for ['🍫', '🍰', '🎂']: 🍫-🍰\n",
      "152: Match found for ['🍭', '🎂', '🍬']: 🍭-🍬\n",
      "153: Match found for ['🍰', '🍭', '🍬']: 🍭-🍬\n",
      "154: Match found for ['🍰', '🎂', '🍬']: 🍰-🍬\n",
      "155: Match found for ['🍰', '🍭', '🎂']: 🍰-🍭\n"
     ]
    }
   ],
   "source": [
    "def prune_candidate_3_itemsets(list_of_candidate_3_itemsets):\n",
    "    '''\n",
    "    Confirms that each candidate 3-itemset is a superset of at least one candidate 2-itemset,\n",
    "    displaying that a match has been found and dropping supersets if needed\n",
    "    '''\n",
    "    print(\"Number of Itemsets before Pruning: {}\".format(len(candidate_3_itemsets)))\n",
    "    print('='*40)\n",
    "    \n",
    "    pruned = []\n",
    "\n",
    "    for i, itemset3 in enumerate(candidate_3_itemsets):\n",
    "        itemset3 = list(itemset3)\n",
    "\n",
    "        try:\n",
    "            for itemset2 in candidate_2_itemsets:\n",
    "                itemset2 = list(itemset2)\n",
    "                if itemset2[0] in itemset3 and itemset2[1] in itemset3:\n",
    "                    print(\"{}: Match found for {}: {}-{}\".format(i + 1, itemset3, itemset2[0], itemset2[1]))\n",
    "                    pruned.append(set(itemset3))\n",
    "                    break\n",
    "\n",
    "                else:\n",
    "                    continue\n",
    "        except:\n",
    "            print(\"No subsets found. Dropping superset: {}\".format(itemset3))\n",
    "            \n",
    "    return pruned\n",
    "    \n",
    "pruned = prune_candidate_3_itemsets(candidate_3_itemsets)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c2955bdc-e019-46b5-99ff-62464e59a480",
   "metadata": {},
   "source": [
    "### 2.1.2 Database Scan\n",
    "\n",
    "a) [10 points] With the candidate itemsets ready, the final step in one iteration of the Apriori\n",
    "algorithm is to scan the database (in our case, you can scan the `emoji_matrix` created above\n",
    "in 1.1c) and count the occurrence of each candidate itemset, divide it by the total number of\n",
    "records to derive the support, and output candidate itemsets whose support meets a chosen\n",
    "threshold.\n",
    "\n",
    "To do so, please construct a new function, `calculate_frequent_itemsets`, where the input\n",
    "(`candidate_itemsets`) is a list of the candidate 3-itemsets from the previous section. Your\n",
    "function should return a complete list of frequent 3-itemsets with a minimal support of\n",
    "`min_support` (i.e., an argument passed to the function). The returned list should not contain\n",
    "duplicated itemsets. The order of the list does not matter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "2acdde8f-bf06-4aee-9738-a193497f2e74",
   "metadata": {},
   "outputs": [],
   "source": [
    "# k_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "9eb027a8-acab-4de9-9717-2e7494d3179f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Match found\n",
      "Match found\n",
      "Match found\n",
      "No match found\n",
      "No match found\n",
      "No match found\n",
      "No match found\n",
      "No match found\n",
      "No match found\n",
      "No match found\n",
      "No match found\n",
      "No match found\n",
      "No match found\n",
      "No match found\n",
      "No match found\n",
      "No match found\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[(frozenset({'🍇', '🍉', '🍊'}), 0.007832898172323759),\n",
       " (frozenset({'🍔', '🍕', '🍟'}), 0.009238802972484434),\n",
       " (frozenset({'🍫', '🍬', '🍭'}), 0.007029524000803374)]"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def calculate_frequent_itemsets(candidate_3_itemsets, min_support):\n",
    "    '''\n",
    "    Takes in a list of the candidate 3-itemsets and returns a complete list of frequent 3-itemsets with a\n",
    "    minimal support of a min_support. \n",
    "    '''\n",
    "    from mlxtend.frequent_patterns import apriori\n",
    "\n",
    "    #Generate associations\n",
    "    frequent_itemsets = apriori(k_df, min_support=min_support, use_colnames=True)\n",
    "    frequent_itemsets['length'] = frequent_itemsets['itemsets'].apply(lambda x: len(x))\n",
    "    frequent_3_itemsets = frequent_itemsets[frequent_itemsets['length'] == 3]\n",
    "    #print(frequent_3_itemsets)\n",
    "    \n",
    "    associations = list(zip(\n",
    "        frequent_3_itemsets['itemsets'].tolist(),\n",
    "        frequent_3_itemsets['support'].tolist(),\n",
    "    ))\n",
    "    \n",
    "    #Confirm associations are in the frequent 3 itemsets\n",
    "    relevant_frequent_itemsets = []\n",
    "    for tup in associations:\n",
    "        froz_set = tup[0]\n",
    "        support_score = tup[1]\n",
    "        \n",
    "        if froz_set in candidate_3_itemsets:\n",
    "            print(\"Match found\")\n",
    "            #relevant_frequent_itemsets.append(froz_set)\n",
    "            relevant_frequent_itemsets.append((froz_set, support_score))\n",
    "        else:\n",
    "            print(\"No match found\")\n",
    "    \n",
    "    return relevant_frequent_itemsets\n",
    "    \n",
    "calculate_frequent_itemsets(candidate_3_itemsets, min_support=0.007)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ff0460a-0f7a-425b-921b-f374cff7923c",
   "metadata": {},
   "source": [
    "## 3. Evaluating Frequent Itemsets [25 points]\n",
    "\n",
    "Even though you may have found all the frequent itemsets, not all of them are “interesting”.\n",
    "People have developed various measurements of the interestingness of patterns. Most of them\n",
    "split the itemset into an antecedent item(set) and a consequent item(set), and then measure the\n",
    "correlation between the antecedent and the consequent. Let's try some of such measurements\n",
    "implemented by the `mlxtend.frequent_patterns.association_rules` API. For more information\n",
    "about the API, visit the documentation at http://rasbt.github.io/mlxtend/user_guide/frequent_patterns/association_rules/.\n",
    "\n",
    "a) [10 points] First, apply the apriori function to 'emoji_matrix' created in section 1.1c with a\n",
    "min_support of 0.005 and use_colnames = True. Then, apply the association_rules function to\n",
    "the result with metric = \"lift\" and min_threshold = 3 (meaning to only return values where lift is\n",
    "equal to or greater than 3)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "2ed34fda-9d48-4318-8fae-dbc62606702b",
   "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>antecedents</th>\n",
       "      <th>consequents</th>\n",
       "      <th>antecedent support</th>\n",
       "      <th>consequent support</th>\n",
       "      <th>support</th>\n",
       "      <th>confidence</th>\n",
       "      <th>lift</th>\n",
       "      <th>leverage</th>\n",
       "      <th>conviction</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>(☕)</td>\n",
       "      <td>(🍩)</td>\n",
       "      <td>0.058747</td>\n",
       "      <td>0.031332</td>\n",
       "      <td>0.008435</td>\n",
       "      <td>0.143590</td>\n",
       "      <td>4.582906</td>\n",
       "      <td>0.006595</td>\n",
       "      <td>1.131080</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>(🍩)</td>\n",
       "      <td>(☕)</td>\n",
       "      <td>0.031332</td>\n",
       "      <td>0.058747</td>\n",
       "      <td>0.008435</td>\n",
       "      <td>0.269231</td>\n",
       "      <td>4.582906</td>\n",
       "      <td>0.006595</td>\n",
       "      <td>1.288031</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>(🌭)</td>\n",
       "      <td>(🍔)</td>\n",
       "      <td>0.019381</td>\n",
       "      <td>0.138783</td>\n",
       "      <td>0.011348</td>\n",
       "      <td>0.585492</td>\n",
       "      <td>4.218764</td>\n",
       "      <td>0.008658</td>\n",
       "      <td>2.077686</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>(🍔)</td>\n",
       "      <td>(🌭)</td>\n",
       "      <td>0.138783</td>\n",
       "      <td>0.019381</td>\n",
       "      <td>0.011348</td>\n",
       "      <td>0.081766</td>\n",
       "      <td>4.218764</td>\n",
       "      <td>0.008658</td>\n",
       "      <td>1.067939</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>(🍕)</td>\n",
       "      <td>(🌭)</td>\n",
       "      <td>0.044286</td>\n",
       "      <td>0.019381</td>\n",
       "      <td>0.005021</td>\n",
       "      <td>0.113379</td>\n",
       "      <td>5.849870</td>\n",
       "      <td>0.004163</td>\n",
       "      <td>1.106017</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>511</th>\n",
       "      <td>(🍸, 🍹)</td>\n",
       "      <td>(🍺, 🍻)</td>\n",
       "      <td>0.023298</td>\n",
       "      <td>0.042478</td>\n",
       "      <td>0.005122</td>\n",
       "      <td>0.219828</td>\n",
       "      <td>5.175043</td>\n",
       "      <td>0.004132</td>\n",
       "      <td>1.227320</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>512</th>\n",
       "      <td>(🍻)</td>\n",
       "      <td>(🍺, 🍸, 🍹)</td>\n",
       "      <td>0.181663</td>\n",
       "      <td>0.007632</td>\n",
       "      <td>0.005122</td>\n",
       "      <td>0.028192</td>\n",
       "      <td>3.693943</td>\n",
       "      <td>0.003735</td>\n",
       "      <td>1.021157</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>513</th>\n",
       "      <td>(🍺)</td>\n",
       "      <td>(🍹, 🍸, 🍻)</td>\n",
       "      <td>0.079634</td>\n",
       "      <td>0.007532</td>\n",
       "      <td>0.005122</td>\n",
       "      <td>0.064313</td>\n",
       "      <td>8.539016</td>\n",
       "      <td>0.004522</td>\n",
       "      <td>1.060684</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>514</th>\n",
       "      <td>(🍸)</td>\n",
       "      <td>(🍺, 🍹, 🍻)</td>\n",
       "      <td>0.052018</td>\n",
       "      <td>0.006527</td>\n",
       "      <td>0.005122</td>\n",
       "      <td>0.098456</td>\n",
       "      <td>15.083398</td>\n",
       "      <td>0.004782</td>\n",
       "      <td>1.101967</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>515</th>\n",
       "      <td>(🍹)</td>\n",
       "      <td>(🍺, 🍸, 🍻)</td>\n",
       "      <td>0.061759</td>\n",
       "      <td>0.006929</td>\n",
       "      <td>0.005122</td>\n",
       "      <td>0.082927</td>\n",
       "      <td>11.967904</td>\n",
       "      <td>0.004694</td>\n",
       "      <td>1.082870</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>516 rows × 9 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    antecedents consequents  antecedent support  consequent support   support  \\\n",
       "0           (☕)         (🍩)            0.058747            0.031332  0.008435   \n",
       "1           (🍩)         (☕)            0.031332            0.058747  0.008435   \n",
       "2           (🌭)         (🍔)            0.019381            0.138783  0.011348   \n",
       "3           (🍔)         (🌭)            0.138783            0.019381  0.011348   \n",
       "4           (🍕)         (🌭)            0.044286            0.019381  0.005021   \n",
       "..          ...         ...                 ...                 ...       ...   \n",
       "511      (🍸, 🍹)      (🍺, 🍻)            0.023298            0.042478  0.005122   \n",
       "512         (🍻)   (🍺, 🍸, 🍹)            0.181663            0.007632  0.005122   \n",
       "513         (🍺)   (🍹, 🍸, 🍻)            0.079634            0.007532  0.005122   \n",
       "514         (🍸)   (🍺, 🍹, 🍻)            0.052018            0.006527  0.005122   \n",
       "515         (🍹)   (🍺, 🍸, 🍻)            0.061759            0.006929  0.005122   \n",
       "\n",
       "     confidence       lift  leverage  conviction  \n",
       "0      0.143590   4.582906  0.006595    1.131080  \n",
       "1      0.269231   4.582906  0.006595    1.288031  \n",
       "2      0.585492   4.218764  0.008658    2.077686  \n",
       "3      0.081766   4.218764  0.008658    1.067939  \n",
       "4      0.113379   5.849870  0.004163    1.106017  \n",
       "..          ...        ...       ...         ...  \n",
       "511    0.219828   5.175043  0.004132    1.227320  \n",
       "512    0.028192   3.693943  0.003735    1.021157  \n",
       "513    0.064313   8.539016  0.004522    1.060684  \n",
       "514    0.098456  15.083398  0.004782    1.101967  \n",
       "515    0.082927  11.967904  0.004694    1.082870  \n",
       "\n",
       "[516 rows x 9 columns]"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from mlxtend.frequent_patterns import apriori\n",
    "from mlxtend.frequent_patterns import association_rules\n",
    "\n",
    "frequent_itemsets = apriori(k_df, min_support=0.005, use_colnames=True)\n",
    "rules = association_rules(frequent_itemsets, metric=\"lift\", min_threshold=3)\n",
    "rules"
   ]
  },
  {
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"
    }
   },
   "cell_type": "markdown",
   "id": "8fe92684-db64-4059-a801-1b41e27a26ca",
   "metadata": {},
   "source": [
    "b) [10 points] Next, we ask that you implement another interestingness measurement, the (full) mutual information. The measurement is defined as such:\n",
    "\n",
    "![image.png](attachment:88f1a6e4-5096-4929-aff6-1b861b95fb70.png)\n",
    "\n",
    "Please construct a function, ‘mi’, that uses the three support values ((1) antecedent support, (2) consequent support and (3) support) to compute the mutual information. All three parameters are in [0, 1], and you can assume the validity of the input. Use 2 as the log base."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "08cf95b7-565b-4c30-8bd0-51a98de57183",
   "metadata": {},
   "outputs": [],
   "source": [
    "def mi(dataframe):\n",
    "    from math import log2\n",
    "    '''\n",
    "    Mutual Information is an interestingness measurement for associations that measures the mutual \n",
    "    dependence between two random variables (X, Y)\n",
    "    \n",
    "    I(antecedent; consequent) = log2 * (P(antecedent, consequent) / P(antecedent)P(consequent))\n",
    "    \n",
    "    '''    \n",
    "    zipped = list(zip(\n",
    "        dataframe['antecedent support'].tolist(),\n",
    "        dataframe['consequent support'].tolist(),\n",
    "        dataframe['support'].tolist()))\n",
    "    \n",
    "    mutual_info_dict = {}\n",
    "    for i, tup in enumerate(zipped):\n",
    "        antecedent_support = tup[0]\n",
    "        consequent_support = tup[1]\n",
    "        \n",
    "        support = tup[2]\n",
    "        support_xneg = (1-antecedent_support) * consequent_support\n",
    "        support_yneg = antecedent_support * (1-consequent_support)\n",
    "        support_xyneg = (1-antecedent_support) * (1-consequent_support)\n",
    "        \n",
    "        p_normal = support * log2((support) / (antecedent_support * consequent_support))\n",
    "        p_xneg = support_xneg * log2((support_xneg) / ((1-antecedent_support) * (consequent_support)))\n",
    "        p_yneg = support_yneg * log2((support_yneg) / ((antecedent_support) * (1-consequent_support)))\n",
    "        p_xyneg = support_xyneg * log2((support_xyneg) / ((1-antecedent_support) * (1-consequent_support)))\n",
    "                        \n",
    "        mi = p_normal + p_xneg + p_yneg + p_xyneg\n",
    "        mutual_info_dict[i] = mi\n",
    "    \n",
    "    return mutual_info_dict\n",
    "    \n",
    "mi_dict = mi(rules)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "091220ed-767a-4e0a-ba1d-0bc646ddcce2",
   "metadata": {},
   "source": [
    "c) [5 points] Then, use this function to add the mutual information value to each row of the DataFrame above (i.e., the results of applying association_rules)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "cb9381e5-9cb9-4d22-ac5b-677ef3f057b3",
   "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>antecedents</th>\n",
       "      <th>consequents</th>\n",
       "      <th>antecedent support</th>\n",
       "      <th>consequent support</th>\n",
       "      <th>support</th>\n",
       "      <th>confidence</th>\n",
       "      <th>lift</th>\n",
       "      <th>leverage</th>\n",
       "      <th>conviction</th>\n",
       "      <th>mutual info</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>(☕)</td>\n",
       "      <td>(🍩)</td>\n",
       "      <td>0.058747</td>\n",
       "      <td>0.031332</td>\n",
       "      <td>0.008435</td>\n",
       "      <td>0.143590</td>\n",
       "      <td>4.582906</td>\n",
       "      <td>0.006595</td>\n",
       "      <td>1.131080</td>\n",
       "      <td>0.018526</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>(🍩)</td>\n",
       "      <td>(☕)</td>\n",
       "      <td>0.031332</td>\n",
       "      <td>0.058747</td>\n",
       "      <td>0.008435</td>\n",
       "      <td>0.269231</td>\n",
       "      <td>4.582906</td>\n",
       "      <td>0.006595</td>\n",
       "      <td>1.288031</td>\n",
       "      <td>0.018526</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>(🌭)</td>\n",
       "      <td>(🍔)</td>\n",
       "      <td>0.019381</td>\n",
       "      <td>0.138783</td>\n",
       "      <td>0.011348</td>\n",
       "      <td>0.585492</td>\n",
       "      <td>4.218764</td>\n",
       "      <td>0.008658</td>\n",
       "      <td>2.077686</td>\n",
       "      <td>0.023567</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>(🍔)</td>\n",
       "      <td>(🌭)</td>\n",
       "      <td>0.138783</td>\n",
       "      <td>0.019381</td>\n",
       "      <td>0.011348</td>\n",
       "      <td>0.081766</td>\n",
       "      <td>4.218764</td>\n",
       "      <td>0.008658</td>\n",
       "      <td>1.067939</td>\n",
       "      <td>0.023567</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>(🍕)</td>\n",
       "      <td>(🌭)</td>\n",
       "      <td>0.044286</td>\n",
       "      <td>0.019381</td>\n",
       "      <td>0.005021</td>\n",
       "      <td>0.113379</td>\n",
       "      <td>5.849870</td>\n",
       "      <td>0.004163</td>\n",
       "      <td>1.106017</td>\n",
       "      <td>0.012796</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>511</th>\n",
       "      <td>(🍸, 🍹)</td>\n",
       "      <td>(🍺, 🍻)</td>\n",
       "      <td>0.023298</td>\n",
       "      <td>0.042478</td>\n",
       "      <td>0.005122</td>\n",
       "      <td>0.219828</td>\n",
       "      <td>5.175043</td>\n",
       "      <td>0.004132</td>\n",
       "      <td>1.227320</td>\n",
       "      <td>0.012146</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>512</th>\n",
       "      <td>(🍻)</td>\n",
       "      <td>(🍺, 🍸, 🍹)</td>\n",
       "      <td>0.181663</td>\n",
       "      <td>0.007632</td>\n",
       "      <td>0.005122</td>\n",
       "      <td>0.028192</td>\n",
       "      <td>3.693943</td>\n",
       "      <td>0.003735</td>\n",
       "      <td>1.021157</td>\n",
       "      <td>0.009655</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>513</th>\n",
       "      <td>(🍺)</td>\n",
       "      <td>(🍹, 🍸, 🍻)</td>\n",
       "      <td>0.079634</td>\n",
       "      <td>0.007532</td>\n",
       "      <td>0.005122</td>\n",
       "      <td>0.064313</td>\n",
       "      <td>8.539016</td>\n",
       "      <td>0.004522</td>\n",
       "      <td>1.060684</td>\n",
       "      <td>0.015846</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>514</th>\n",
       "      <td>(🍸)</td>\n",
       "      <td>(🍺, 🍹, 🍻)</td>\n",
       "      <td>0.052018</td>\n",
       "      <td>0.006527</td>\n",
       "      <td>0.005122</td>\n",
       "      <td>0.098456</td>\n",
       "      <td>15.083398</td>\n",
       "      <td>0.004782</td>\n",
       "      <td>1.101967</td>\n",
       "      <td>0.020050</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>515</th>\n",
       "      <td>(🍹)</td>\n",
       "      <td>(🍺, 🍸, 🍻)</td>\n",
       "      <td>0.061759</td>\n",
       "      <td>0.006929</td>\n",
       "      <td>0.005122</td>\n",
       "      <td>0.082927</td>\n",
       "      <td>11.967904</td>\n",
       "      <td>0.004694</td>\n",
       "      <td>1.082870</td>\n",
       "      <td>0.018341</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>516 rows × 10 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    antecedents consequents  antecedent support  consequent support   support  \\\n",
       "0           (☕)         (🍩)            0.058747            0.031332  0.008435   \n",
       "1           (🍩)         (☕)            0.031332            0.058747  0.008435   \n",
       "2           (🌭)         (🍔)            0.019381            0.138783  0.011348   \n",
       "3           (🍔)         (🌭)            0.138783            0.019381  0.011348   \n",
       "4           (🍕)         (🌭)            0.044286            0.019381  0.005021   \n",
       "..          ...         ...                 ...                 ...       ...   \n",
       "511      (🍸, 🍹)      (🍺, 🍻)            0.023298            0.042478  0.005122   \n",
       "512         (🍻)   (🍺, 🍸, 🍹)            0.181663            0.007632  0.005122   \n",
       "513         (🍺)   (🍹, 🍸, 🍻)            0.079634            0.007532  0.005122   \n",
       "514         (🍸)   (🍺, 🍹, 🍻)            0.052018            0.006527  0.005122   \n",
       "515         (🍹)   (🍺, 🍸, 🍻)            0.061759            0.006929  0.005122   \n",
       "\n",
       "     confidence       lift  leverage  conviction  mutual info  \n",
       "0      0.143590   4.582906  0.006595    1.131080     0.018526  \n",
       "1      0.269231   4.582906  0.006595    1.288031     0.018526  \n",
       "2      0.585492   4.218764  0.008658    2.077686     0.023567  \n",
       "3      0.081766   4.218764  0.008658    1.067939     0.023567  \n",
       "4      0.113379   5.849870  0.004163    1.106017     0.012796  \n",
       "..          ...        ...       ...         ...          ...  \n",
       "511    0.219828   5.175043  0.004132    1.227320     0.012146  \n",
       "512    0.028192   3.693943  0.003735    1.021157     0.009655  \n",
       "513    0.064313   8.539016  0.004522    1.060684     0.015846  \n",
       "514    0.098456  15.083398  0.004782    1.101967     0.020050  \n",
       "515    0.082927  11.967904  0.004694    1.082870     0.018341  \n",
       "\n",
       "[516 rows x 10 columns]"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rules['mutual info'] = pd.Series(mi_dict)\n",
    "rules"
   ]
  },
  {
   "attachments": {
    "a46b25ca-1ff9-4b5e-b169-c62a012f55ea.png": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "308d6580-c2db-400b-ae6c-cf6edacb8ec1",
   "metadata": {},
   "source": [
    "## 4.1 Jaccard Similarity\n",
    "\n",
    "Jaccard similarity is a simple but powerful measurement of itemset similarity, defined as follows:\n",
    "\n",
    "![image.png](attachment:a46b25ca-1ff9-4b5e-b169-c62a012f55ea.png)\n",
    "\n",
    "a) [5 points] Complete a function, ‘jaccard_similarity’, to calculate the Jaccard similarity between two sets. You may assume that at least one of the sets is not empty."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "e5ea98d2-3cf0-42ea-bad7-ddbb54591d1d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def jaccard_similarity(set1, set2):\n",
    "    '''\n",
    "    Takes two sets and calculates a jaccard similarity score\n",
    "    given that at least one set is not empty\n",
    "    '''\n",
    "    intersection = len(list(set1.intersection(set2)))\n",
    "    union = (len(set1) + len(set2)) - intersection\n",
    "    return intersection / union"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "0f171fb8-6a4d-4f17-9d06-29381aa3f095",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Test\n",
    "a = {'🍔', '🍗', '🌮'}\n",
    "b = {'🍔', '🍟', '🌮'}\n",
    "\n",
    "jaccard_similarity(a, b)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e46d616-8911-4c66-986d-1fa345d19da8",
   "metadata": {},
   "source": [
    "b) [5 points] With this Jaccard similarity function, please calculate the Jaccard similarity between any given Tweet with all other Tweets and find the Tweets that are most similar (i.e., have the highest jaccard similarity values) in terms of the set of food/drink emojis used. How would you interpret the results?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "76047f85-2982-4b61-87ac-c72e2a1d3241",
   "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>Emojis</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Index</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>{🌯, 🍗, 🍒, 🍔}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>{🍍, 🍈, 🍉, 🍇, 🍊, 🍓}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>{🍸, 🥃}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>{🍟, 🍔}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>{🍌, ☕}</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   Emojis\n",
       "Index                    \n",
       "0            {🌯, 🍗, 🍒, 🍔}\n",
       "1      {🍍, 🍈, 🍉, 🍇, 🍊, 🍓}\n",
       "2                  {🍸, 🥃}\n",
       "3                  {🍟, 🍔}\n",
       "4                  {🍌, ☕}"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unique_emoji_df.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "58df0855-8151-4688-b456-e303f38f84ba",
   "metadata": {},
   "outputs": [],
   "source": [
    "results = {}\n",
    "first_three_rows = unique_emoji_df.iloc[:3]\n",
    "counter = 1\n",
    "for row1 in first_three_rows.iterrows():\n",
    "    set1 = row1[1]['Emojis']\n",
    "    scores = []\n",
    "    for row2 in unique_emoji_df.iterrows():\n",
    "        set2 = row2[1]['Emojis']\n",
    "        jaccard_score = jaccard_similarity(set1, set2)\n",
    "        \n",
    "        if jaccard_score == 0: #Way of speeding up formula: skip jaccard scores of 0\n",
    "            pass\n",
    "        else:\n",
    "            scores.append((set2, jaccard_score))\n",
    "    results[counter] = (set1, scores)\n",
    "    counter += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "3c2e5dea-81cd-4854-b4c2-632491658fba",
   "metadata": {},
   "outputs": [],
   "source": [
    "def Sort_Tuple(tup): \n",
    "    lst = len(tup) \n",
    "    for i in range(0, lst): \n",
    "        for j in range(0, lst-i-1): \n",
    "            if (tup[j][1] > tup[j + 1][1]): \n",
    "                temp = tup[j] \n",
    "                tup[j]= tup[j + 1] \n",
    "                tup[j + 1]= temp \n",
    "    return tup\n",
    "\n",
    "def removeDuplicates(lst):\n",
    "    return [[a, b] for i, [a, b] in enumerate(lst) if not any(c == b for _, c in lst[:i])]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "755963ad-dac8-427a-9d15-3e239cdfbdd8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tweet 1 Set: {'🌯', '🍗', '🍒', '🍔'}\n",
      "Tweet 2 Set: {'🍍', '🍈', '🍉', '🍇', '🍊', '🍓'}\n",
      "Tweet 3 Set: {'🍸', '🥃'}\n",
      "\n"
     ]
    }
   ],
   "source": [
    "tweet1 = results[1][1]\n",
    "print(\"Tweet 1 Set: {}\".format(results[1][0]))\n",
    "tweet2 = results[2][1]\n",
    "print(\"Tweet 2 Set: {}\".format(results[2][0]))\n",
    "tweet3 = results[3][1]\n",
    "print(\"Tweet 3 Set: {}\".format(results[3][0]))\n",
    "print(\"\")\n",
    "\n",
    "for i, tweet in enumerate([tweet1, tweet2, tweet3]):\n",
    "    tweet_sorted = Sort_Tuple(tweet)[::-1]\n",
    "    no_duplicates = removeDuplicates(tweet_sorted)\n",
    "    top3_tuples = no_duplicates[1:4] #skip 0 as that is just an exact match of itself\n",
    "    \n",
    "    print(\"Tweet #{} top Jaccard Similarity scores\".format(i + 1))\n",
    "    # print(\"{}\".format(emojis))\n",
    "    \n",
    "    for i, score in enumerate(top3_tuples):\n",
    "        print(\"{}: (Score: {}), emojis: {}\".format(i, round(score[1], 3), score[0]))\n",
    "    print(\"\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ca6ce0e-2de7-4e5c-8cfe-ead5146444c2",
   "metadata": {},
   "source": [
    "The results above appear to be an accurate implementations of the Jaccard Similarity function. The first three tweets in the Tweet dataframe were explored above (it would be too time consuming to comb through all 10K tweets) and the top 3 emoji sets in a given tweet and their Jaccard Similarity score were listed in order by score. The first tweet referenced {'🌯', '🍔', '🍒', '🍗'} appears to have a 0.75 Jaccard Similarity score with {'🌯', '🍔', '🍗'}, a set of emojis missing just one of the emojis from the original reference tweet. The results following also demonstrate a trend that the presence of emojis from the reference tweet in the compared tweets indicating commonality is crucial for a high Jaccard Similarity score. "
   ]
  }
 ],
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