10 Clustering and Association Rules Add-On.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Examples for lecture Clustering and Association Rules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import seaborn as sns; sns.set()\n",
    "from sklearn.datasets import make_blobs\n",
    "from sklearn.cluster import KMeans\n",
    "from tqdm.notebook import tqdm\n",
    "import pandas as pd\n",
    "from ipywidgets import interact\n",
    "\n",
    "from mlxtend.preprocessing import TransactionEncoder\n",
    "from mlxtend.frequent_patterns import apriori, association_rules\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# k-Means Clustering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## k-Means from Scratch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, _ = make_blobs(n_samples=20, centers=3, n_features=2, random_state=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x2055f783b00>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(12,7))\n",
    "ax.scatter(X[:, 0], X[:, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Randomly choose k cluster centers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def initialize_centroids(X, k):\n",
    "    centroids = X.copy()\n",
    "    np.random.shuffle(centroids)\n",
    "    return centroids[:k]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x20560c7a710>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "centroids = initialize_centroids(X, k=3)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(12,7))\n",
    "ax.scatter(X[:, 0], X[:, 1])\n",
    "ax.scatter(centroids[:, 0], centroids[:, 1], s=300, marker=\"*\", c=\"g\", edgecolor=\"k\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Assign each data point to its nearest cluster center"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def closest_centroid(X, centroids):\n",
    "    distances = np.sqrt(((X - centroids[:, np.newaxis])**2).sum(axis=2))\n",
    "    return np.argmin(distances, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 2, 2, 0, 0, 0, 2, 0, 2, 2, 1, 2, 0, 0, 2, 2, 2, 2, 0, 2],\n",
       "      dtype=int64)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "closest = closest_centroid(X, centroids)\n",
    "closest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Initial')"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(15,7))\n",
    "ax.scatter(X[:, 0], X[:, 1])\n",
    "ax.scatter(centroids[:, 0], centroids[:, 1], s=300, marker=\"*\", c=\"g\", edgecolor=\"k\")\n",
    "ax.set_title(\"Initial\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Update each cluster center to the mean of all assigned data points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "def move_centroids(X, closest, centroids):\n",
    "    return np.array([X[closest==k].mean(axis=0) for k in range(centroids.shape[0])])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.37860991, 0.50730234],\n",
       "       [3.58804674, 2.36702243],\n",
       "       [0.12345506, 4.03288833]])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "move_centroids(X, closest, centroids)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c1cfab4b0b5e4b3f8fbb759ffaa1bafb",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=0, description='iteration', max=11), Output()), _dom_classes=('widget-in…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_iterations = 10\n",
    "centroids_hist = [centroids]\n",
    "centroids_moved = centroids\n",
    "\n",
    "for i in range(num_iterations):\n",
    "    closest = closest_centroid(X, centroids_moved)\n",
    "    centroids_moved = move_centroids(X, closest, centroids_moved)\n",
    "    centroids_hist.append(centroids_moved)\n",
    "\n",
    "@interact(iteration=(0, len(centroids_hist)))\n",
    "def k_means_centroids(iteration=0):\n",
    "    fig, ax = plt.subplots(figsize=(15,7))\n",
    "    centroids = centroids_hist[iteration]\n",
    "    ax.scatter(X[:, 0], X[:, 1])\n",
    "    ax.scatter(centroids[:, 0], centroids[:, 1], s=300, marker=\"*\", c=\"g\", edgecolor=\"k\")\n",
    "    ax.set_title(\"Iteration {}\".format(iteration))\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implement the algorithm"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fit(X, k):\n",
    "    centroids = initialize_centroids(X, k)\n",
    "    closest_before = closest_centroid(X, centroids)\n",
    "\n",
    "    while True:\n",
    "        closest = closest_centroid(X, centroids)\n",
    "        centroids = move_centroids(X, closest, centroids)\n",
    "        \n",
    "        if np.all(closest == closest_before):\n",
    "            break\n",
    "        closest_before = closest\n",
    "    return closest, centroids "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x2055fe48668>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "closest, centroids = fit(X, k=3)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(15,7))\n",
    "ax.scatter(X[:, 0], X[:, 1])\n",
    "ax.scatter(centroids[:, 0], centroids[:, 1], s=300, marker=\"*\", c=\"g\", edgecolor=\"k\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scikit-Learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = KMeans(n_clusters=3, random_state=0).fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 0, 2, 1, 1, 0, 0, 1, 2, 2, 1, 2, 0, 1, 2, 0, 2, 0, 1, 2])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.labels_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "centroids = model.cluster_centers_\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(15,7))\n",
    "ax.scatter(X[:, 0], X[:, 1])\n",
    "ax.scatter(centroids[:, 0], centroids[:, 1], s=300, marker=\"*\", c=\"g\", edgecolor=\"k\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Distortion"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPgAAAB5CAYAAAAUPex2AAANxUlEQVR4Ae2dLbTUPBCGr0QikUgkEolEIpFIJBKHQyKRSCQSiUQikUgkEsl+59nvvIfc3DTbdpM0TV+xp/9pMjPPTDJNuzd///49+WcZ2AbGtIEbK3ZMxVqv1is2YMDdg3EPbmAbMOADK9dR3FHcgBtwR/CBbcCAD6xcR3BHcANuwB3BB7YBAz6wch3BHcENuAF3BB/YBgz4wMp1BHcEN+AG3BF8YBsw4AMr1xHcEdyAG3BH8IFtwIAPrFxHcEdwA27AHcEHtgEDPrByHcEdwQ24AXcEH9gGDPjAynUEdwQ34AbcEXxgG+gO8C9fvpw+ffp0y+h+/fp1+vjx4/n3+/fvW8ccpRylbAPTNtAV4B8+fDi9e/fu9OrVq9Pjx4/PIAP269evT1+/fj29f//+dHNzcwbdSp1WqmVj2cgGugH8z58/p+fPn5+hBmZAZhvgVVmWDx8+PP/CfV63QdsG0jbQDeB0zQXz27dvz4C/fPnyFtwokch+//79O/ut4LSCLZdjy6UbwBlna3z97NmzM+DsCw2UKH/v3r3T06dPb+0Pz/H6sQ3a+r+t/24Al2IE8aNHj+5ArK67Ir2u8fK2Ui0Py0M20B3ggvjNmzd3ACfZxtj858+fd46pQV7auG0D/2ygO8A1/v78+fMdiEmwPXny5LyfSE+23cr8p0zLwrKIbaA7wBlfE6Xj8TdJOPbjAGgE20T0uEHetpHbBv7ZQFeAE5WBWFE6VBQRnWNMgvn+/fv5EZqScuF5Xv+nXMvCsugKcIAlgscz2WSoTHTh2Thdc4/DbbyyCy+nbaErwK2oaUVZNpbNGhsw4AO/aLDGIHzNWI7EgBtwJyoHtgEDPrByHY3HisZr9GnADbgj+MA2YMAHVu4aj+9rxor6BtyAO4IPbAMGfGDlOhqPFY3X6NOAG3BH8IFtoDjgzA/nnW2mlfb0S72dtsYj+hpHxT3ZQHHA+QpLDDbA85LItT+msca/uc7kwYMHJ+a670k5ruv+ncm3b9/O3xPk/Ykt9FkccOaTA1MMud4Cq9VI3j7jXXIiNZ91iu/P9tQc91p1crn7B3StDnnbEQ74OhG9WmySbT4surbMNdcVB5xK6KMNMWTsX1PJNdfgOV+8eHELdKL/mrJ8zXFBXaN77JzvBsYvROmDJbWDXVjnKoBzAxoRA44Hi9/zDitTYx0hS7DUZ6uuUo22ucw+HQ/ROtVbZIio3u2PHz+aBJtqgGN8RMwYcn0aubVxyqsCe+t7+359glhDLwxRsXlyQ3EE537qVfLqc437x2VWBZxoLY8Vgt6qcXFjgZz6LE228ecLuWtQ6lZtitvo7TLOBH2i1yl5Ai92ER/HTvi0GF30VG9VgLcKNFUBp/FAFcIt77ZVV5kvsi5NdKTGU6Fi1cZwn9fLgLaFHBWF0evU/YEbkKeOT+1XAjjlHKauuWZ/dcCpXDgGFux8FjkXFa9pVO5a7klmM3dOfIw6p7pbOs+A7xdm6TBcomt0XhpwghrlrulFhvVbst4EcKDiO2uCW8vUP5csqXyrc6mvAR8L4pzt1AKcnBRjcx6h5e5f8lgTwKkwQqOrK7i1bNVVuUZoBvw4cMtW0XnJCM78jNZw05ZmgHMzfRlVcLO8NL69BsxS1xpwAx7b0pIxOOfSLWduRlxO7e2mgNMYvogaAs463fctxuNzhWvADXhsK3MB5zxyPnFGfojn4LFQ2AZkEmwx5D2/DGLADXhsy3MAZ6xNnikOXiTbWtl78wiOoPBeqZdEcmOeWMAttw24AY/t7RLgwD3111rs5/q4zBrbmwBOQ2hgHMUZp6QmB9Ro+JIyDbgBj+0lBzhwpwJYaO+txuObAY7AUq+W9vhCyFrAU/PxpeR4kkRKFpzbytPHBtxiG2fO+DT38gXnMI8i95iydF2veUxGfS/BjV7jMXnpNqi8TQGfGo/3Nu1zLeAYCsMOnh6ESgfu2INzDj0Y7sVsJ4ye31Yz/mQgNZfomfbmJh4pKZt6eaNW3a4BvFad1pa7KeBUGkMPjR+Fsx0DsLaBJa5bC3h47/gRYTwXGZB5ZEgPJk7KhOWMtM6LR8g2F8E1d6KlozPghb9hJU+OsvUjyrXqxlyCpgTg3IN58GofS82Jp1tHe4ncc9uMEyCqYYyX6t/rccE7lVwFauSEw2/p9Ax4YcAxQHnzEIBeprJSpxxIGCjnzAEpHGtjuCRkABvAc/eIy1aSMu4JxOf1uj0HXjn+XBe+RvsMeAXAiVwYeQg46z0kmUoCTiSK35NfM5uPqA8AcyN+CAIOSWP8a5fUIyx77voceOX0W9uAAa8AOIbBuDsGXN3YuYZT47ySgFO/2Jm1nsnHUAEnU+I31b2+pAfBC+hT56oLv6RnM1XWkv0GvBLgKIGIIsh76X6WBpx20ja1kyUGv8QI936u4J1KnqkLT6+udVsNeEXA53TdWiu8NOBqox4BCfQ5Dk1d81ZzmWvIWvCSg5gqXzKam4dh6EM+gwCxtlehuhjwSoCjIIydpFPLrKkUO7UsCTiZb8rTXGSGIAKcZa7LyhCGhBNy4pl5D8OXKZnl9gte3kmYOo92Io9w/A288fnYCbIk0lMucCNjbGhtfsCAVwAcr45HR1FrFRMrv9Q2hobSp8rDqDhn6rj2AyZt5Ltc2scy7q7zzDw8rnWMXo4POFpnl1WPa5caf08NS9A/8uSnngrtjttLLoP8BbmEMNmox5Ghc1hSZwNeGHAECtiMy6bGZEsUVPrcEoATfWkfxihIw3rK6LkXTiCe6IMTUXSXQ5nTpQ/v0cu6xt9E2VSdkJHkoONEZcDVNkscJWXFAYFIjwOM93MNdkZZYTnxugEvCDjGjqIxaiJcLOwettcCrmw17aMMfhhebKgYYvxJKzkDjJ3jRChFKSUiAb0H+Sypg8bfkofaRBms4+iIvHL47MdGkI+iOfs0M1BDnbl1oIzwnqnrDHhBwDXW6nk8eS3gQBr+UoCHx+P1OBLhJAAgZZy979P4mzYSgXHsJNIAm3YputKDIc/Afs6N7UMJyhpOzoAXAlxjz6VeuLURrwW8Rj0VudRdr3GPmmVqKCJgiahAGg9JqAORlmOpiKteX2q4k6o/98F5zDnfgBcAXJ4chacU0tO+ngBHXkQ9RXUiWQqAnuQX1kXjbyAK9y9dp+c3txcD2Axr6ClMjfvD+xvwKwHX47DWM7hCJS5Z7wlw4JZTJBrFGfkl7Wp9rsbfc8HM1Y9hDnqZisj0Cukl4PzUQ2RJtz9XLscM+BWAh4/Dtoo8YbLmkrI53hPgRCCMG9kRkZa2ZU57a52jXtvcySu5egA2Y3bKUm+G8wkeOEDlOZCTjnP+nCcPBnwl4Aha2dGtDJM6xM9Tc4bEsZ4AZ0xK1KZrXiPBdEkW1xwHPGS59vl0fG9FZ5JwyAO54ERSgUO9xjmPYQ34CsDxuEqMbGmYGIESPLHBTG33BPhUHfewH+eOLLdw7ugdR4CcgD3lBCRDA74CcHlvPQaRMFsuSbQwhs0pN1UfEkMoPXWMfTgsDHfquPf//9FGIvdS51pCdugbvfMEgkBzqQfH+egzF4j0rL5E/WqW0eSTTXocBmA1G5MrmwQLSlOCKndufIzx3FQyh3OBX4mc+Fpv9/FFVnqPjNf5zemmY7Mau6d0SBlb2nOqTql91QHHYwMWXaRUBWrvQxHhLLGped616+HytwediJxz1CPqqCrgSmww9mktWO6Nt8a56EdXu3U9RjQat2l7ZzVXB9UAJ3ICFI8mlo5551ae8+hG4Zk1mUETIAR1uCTTuqRsn7sfQ7au0rqqArgeh4Vw9bCeS5rYQNIGYrnsWy7FAacLTEKjB6DDOpSYPWVj37exH1F/xQFXxjyEq4d1Z7kNpwFf8Xz7iEJzm+0s9mIDxSP4XhruehrSI9iAAXevxU8WBrYBAz6wco8QodzGfE/MgBtwR/CBbcCAD6xcR7d8dDuCfAy4AXcEH9gGDPjAyj1ChHIb872UZoAzN51JMDXnpYfK5n6ee55Xfigvr48pq2aA80YZM9py79hea2TMNefdbcDmRRdPTx3TaK+1kyNd3wxwvnvNK5w1hcsL+Hxpg14CDsWAG/Ca9raHspsB3loYBtxwt7a5Hu9nwJ1kq9qr6tHoj1Sn6oCT7OJTtrmPFtYQuCO4I3gNu9pbmVUBZ0wM3IyL+apl/LkkPp9LYmztLydsA27Ac/ZxlGPVACeppnewWSeDHn/wkGw3IK795XoFBtyAHwXiXDurAR7+pQyPrmo/IosbacANeGwTR9yuBri64yz5wzeAaylgA27AW9pbr/eqBrgazNdOid6t/9HCgBtw2eCRl9UB158OpGawXZtkUy8hpUADbsBTdnG0fVUB5xEZ0Vv/BQWQSrwh6GuTbLk/sTPgBvxoMKfaWxVw/W2Rsuc8Nmv1bXIAn/Nn7ymheJ+dwyg2UBVwIiwRnMdZLd7u4nEcDoRxP3Bzb57D6zn7KEpzO+yA5tpAVcCpBHARyVv8bTAw00uY+s0Vis8zQKPYQHXARxGU22Ho92gDBtwvmzSdn7BHSPZcZwNuwA34wDZgwAdW7p4jj+teZkhkwA24I/jANmDAB1auo2CZKLhnORpwA+4IPrANGPCBlbvnyOO6l+l9GHAD7gg+sA0Y8IGV6yhYJgruWY4G3IA7gg9sAwZ8YOXuOfK47mV6HwbcgDuCD2wDBnxg5ToKlomCe5bjf5NWXLXdap14AAAAAElFTkSuQmCC"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "33.944715137557345"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.inertia_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Average Distortion"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.6972357568778673"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.inertia_ / len(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Convergence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x205611e2b38>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = np.array([\n",
    "    [2, 2],\n",
    "    [2, 8],\n",
    "    [10, 8],\n",
    "    [10, 2]\n",
    "])\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(12,7))\n",
    "ax.set_xlim(0, 12)\n",
    "ax.set_ylim(0, 10)\n",
    "ax.scatter(X[:, 0], X[:, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Our implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x205606bf1d0>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "closest, centroids = fit(X, k=2)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(15,7))\n",
    "ax.scatter(X[:, 0], X[:, 1])\n",
    "ax.scatter(centroids[:, 0], centroids[:, 1], s=300, marker=\"*\", c=\"g\", edgecolor=\"k\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Scikit-Learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x2055f75b588>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = KMeans(n_clusters=2, random_state=0, n_init=10, init=\"k-means++\").fit(X)\n",
    "centroids = model.cluster_centers_\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(15,7))\n",
    "ax.scatter(X[:, 0], X[:, 1])\n",
    "ax.scatter(centroids[:, 0], centroids[:, 1], s=300, marker=\"*\", c=\"g\", edgecolor=\"k\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Number of Clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x2055f88e9b0>"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X, _ = make_blobs(n_samples=100, centers=4, n_features=2, random_state=0)\n",
    "fig, ax = plt.subplots(figsize=(12,7))\n",
    "ax.scatter(X[:, 0], X[:, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Elbow Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "dcc414a7c5644e2c806a7d95aca40054",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, max=9.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x2055f84d0b8>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "distortions = []\n",
    "k_values = range(1,10)\n",
    "for k in tqdm(k_values):\n",
    "    model = KMeans(n_clusters=k, random_state=0).fit(X)\n",
    "    distortions.append(model.inertia_)\n",
    "    \n",
    "pd.DataFrame(dict(x=k_values, y=distortions)).plot(x=\"x\", y=\"y\", xticks=k_values, grid=True, figsize=(8,6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Association Rules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                                     Items\n",
      "Id                                        \n",
      "1         [burger, salad, coke, ice cream]\n",
      "2         [burger, salad, coke, ice cream]\n",
      "3               [burger, fries, coke, pie]\n",
      "4          [burger, salad, coke, choc bar]\n",
      "5            [burger, salad, coke, muffin]\n",
      "6            [sandwich, fries, fanta, pie]\n",
      "7             [sandwich, fries, coke, pie]\n",
      "8   [sandwich, onion rings, water, muffin]\n"
     ]
    }
   ],
   "source": [
    "transactions = [\n",
    "    [\"burger\", \"salad\", \"coke\", \"ice cream\"],\n",
    "    [\"burger\", \"salad\", \"coke\", \"ice cream\"],\n",
    "    [\"burger\", \"fries\", \"coke\", \"pie\"],\n",
    "    [\"burger\", \"salad\", \"coke\", \"choc bar\"],\n",
    "    [\"burger\", \"salad\", \"coke\", \"muffin\"],\n",
    "    [\"sandwich\", \"fries\", \"fanta\", \"pie\"],\n",
    "    [\"sandwich\", \"fries\", \"coke\", \"pie\"],\n",
    "    [\"sandwich\", \"onion rings\", \"water\", \"muffin\"]\n",
    "]\n",
    "\n",
    " \n",
    "transactions = pd.DataFrame(data={\"Items\":transactions}, index=range(1,9))\n",
    "transactions.index.name = 'Id'\n",
    "\n",
    "with pd.option_context('display.max_colwidth', 80):\n",
    "    print(transactions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Apriori Algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Encode ransactions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "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>burger</th>\n",
       "      <th>choc bar</th>\n",
       "      <th>coke</th>\n",
       "      <th>fanta</th>\n",
       "      <th>fries</th>\n",
       "      <th>ice cream</th>\n",
       "      <th>muffin</th>\n",
       "      <th>onion rings</th>\n",
       "      <th>pie</th>\n",
       "      <th>salad</th>\n",
       "      <th>sandwich</th>\n",
       "      <th>water</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>True</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>True</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>True</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>True</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\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",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>True</td>\n",
       "      <td>True</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>True</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>True</td>\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>True</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</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>True</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   burger  choc bar   coke  fanta  fries  ice cream  muffin  onion rings  \\\n",
       "0    True     False   True  False  False       True   False        False   \n",
       "1    True     False   True  False  False       True   False        False   \n",
       "2    True     False   True  False   True      False   False        False   \n",
       "3    True      True   True  False  False      False   False        False   \n",
       "4    True     False   True  False  False      False    True        False   \n",
       "5   False     False  False   True   True      False   False        False   \n",
       "6   False     False   True  False   True      False   False        False   \n",
       "7   False     False  False  False  False      False    True         True   \n",
       "\n",
       "     pie  salad  sandwich  water  \n",
       "0  False   True     False  False  \n",
       "1  False   True     False  False  \n",
       "2   True  False     False  False  \n",
       "3  False   True     False  False  \n",
       "4  False   True     False  False  \n",
       "5   True  False      True  False  \n",
       "6   True  False      True  False  \n",
       "7  False  False      True   True  "
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "te = TransactionEncoder()\n",
    "te_ary = te.fit_transform(transactions.Items.values.tolist())\n",
    "df = pd.DataFrame(te_ary, columns=te.columns_)\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Extract frequent item sets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "        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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.625</td>\n",
       "      <td>(burger)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.750</td>\n",
       "      <td>(coke)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.500</td>\n",
       "      <td>(salad)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.625</td>\n",
       "      <td>(coke, burger)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.500</td>\n",
       "      <td>(salad, burger)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.500</td>\n",
       "      <td>(salad, coke)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.500</td>\n",
       "      <td>(salad, coke, burger)</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   support               itemsets\n",
       "0    0.625               (burger)\n",
       "1    0.750                 (coke)\n",
       "2    0.500                (salad)\n",
       "3    0.625         (coke, burger)\n",
       "4    0.500        (salad, burger)\n",
       "5    0.500          (salad, coke)\n",
       "6    0.500  (salad, coke, burger)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "freq_itemsets = apriori(df, use_colnames=True, min_support=0.5)\n",
    "freq_itemsets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Generate rules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "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>(coke)</td>\n",
       "      <td>(burger)</td>\n",
       "      <td>0.750</td>\n",
       "      <td>0.625</td>\n",
       "      <td>0.625</td>\n",
       "      <td>0.833333</td>\n",
       "      <td>1.333333</td>\n",
       "      <td>0.15625</td>\n",
       "      <td>2.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>(burger)</td>\n",
       "      <td>(coke)</td>\n",
       "      <td>0.625</td>\n",
       "      <td>0.750</td>\n",
       "      <td>0.625</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.333333</td>\n",
       "      <td>0.15625</td>\n",
       "      <td>inf</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>(salad)</td>\n",
       "      <td>(burger)</td>\n",
       "      <td>0.500</td>\n",
       "      <td>0.625</td>\n",
       "      <td>0.500</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.600000</td>\n",
       "      <td>0.18750</td>\n",
       "      <td>inf</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>(burger)</td>\n",
       "      <td>(salad)</td>\n",
       "      <td>0.625</td>\n",
       "      <td>0.500</td>\n",
       "      <td>0.500</td>\n",
       "      <td>0.800000</td>\n",
       "      <td>1.600000</td>\n",
       "      <td>0.18750</td>\n",
       "      <td>2.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>(salad)</td>\n",
       "      <td>(coke)</td>\n",
       "      <td>0.500</td>\n",
       "      <td>0.750</td>\n",
       "      <td>0.500</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.333333</td>\n",
       "      <td>0.12500</td>\n",
       "      <td>inf</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>(salad, coke)</td>\n",
       "      <td>(burger)</td>\n",
       "      <td>0.500</td>\n",
       "      <td>0.625</td>\n",
       "      <td>0.500</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.600000</td>\n",
       "      <td>0.18750</td>\n",
       "      <td>inf</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>(salad, burger)</td>\n",
       "      <td>(coke)</td>\n",
       "      <td>0.500</td>\n",
       "      <td>0.750</td>\n",
       "      <td>0.500</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.333333</td>\n",
       "      <td>0.12500</td>\n",
       "      <td>inf</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>(coke, burger)</td>\n",
       "      <td>(salad)</td>\n",
       "      <td>0.625</td>\n",
       "      <td>0.500</td>\n",
       "      <td>0.500</td>\n",
       "      <td>0.800000</td>\n",
       "      <td>1.600000</td>\n",
       "      <td>0.18750</td>\n",
       "      <td>2.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>(salad)</td>\n",
       "      <td>(coke, burger)</td>\n",
       "      <td>0.500</td>\n",
       "      <td>0.625</td>\n",
       "      <td>0.500</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.600000</td>\n",
       "      <td>0.18750</td>\n",
       "      <td>inf</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>(burger)</td>\n",
       "      <td>(salad, coke)</td>\n",
       "      <td>0.625</td>\n",
       "      <td>0.500</td>\n",
       "      <td>0.500</td>\n",
       "      <td>0.800000</td>\n",
       "      <td>1.600000</td>\n",
       "      <td>0.18750</td>\n",
       "      <td>2.50</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       antecedents     consequents  antecedent support  consequent support  \\\n",
       "0           (coke)        (burger)               0.750               0.625   \n",
       "1         (burger)          (coke)               0.625               0.750   \n",
       "2          (salad)        (burger)               0.500               0.625   \n",
       "3         (burger)         (salad)               0.625               0.500   \n",
       "4          (salad)          (coke)               0.500               0.750   \n",
       "5    (salad, coke)        (burger)               0.500               0.625   \n",
       "6  (salad, burger)          (coke)               0.500               0.750   \n",
       "7   (coke, burger)         (salad)               0.625               0.500   \n",
       "8          (salad)  (coke, burger)               0.500               0.625   \n",
       "9         (burger)   (salad, coke)               0.625               0.500   \n",
       "\n",
       "   support  confidence      lift  leverage  conviction  \n",
       "0    0.625    0.833333  1.333333   0.15625        2.25  \n",
       "1    0.625    1.000000  1.333333   0.15625         inf  \n",
       "2    0.500    1.000000  1.600000   0.18750         inf  \n",
       "3    0.500    0.800000  1.600000   0.18750        2.50  \n",
       "4    0.500    1.000000  1.333333   0.12500         inf  \n",
       "5    0.500    1.000000  1.600000   0.18750         inf  \n",
       "6    0.500    1.000000  1.333333   0.12500         inf  \n",
       "7    0.500    0.800000  1.600000   0.18750        2.50  \n",
       "8    0.500    1.000000  1.600000   0.18750         inf  \n",
       "9    0.500    0.800000  1.600000   0.18750        2.50  "
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Execute the following code to show the solution\n",
    "association_rules(freq_itemsets, metric='confidence', min_threshold=0.75)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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