Week11 - Clustering.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "from sklearn.cluster import KMeans\n",
    "\n",
    "from sklearn.datasets import load_digits\n",
    "\n",
    "from sklearn.metrics import silhouette_score\n",
    "\n",
    "from sklearn.preprocessing import MinMaxScaler\n",
    "\n",
    "from sklearn.pipeline import Pipeline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## KMeans Clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "digits = load_digits()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's define parameters of KMeans clustering algorithm in a dictionarry object"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "kmeans_kwargs = {\"init\": \"random\",\n",
    "                    \"n_init\": 50,\n",
    "                    \"max_iter\": 500,\n",
    "                    \"random_state\": 0}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {color: black;background-color: white;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>Pipeline(steps=[(&#x27;Preprocess&#x27;, MinMaxScaler()),\n",
       "                (&#x27;Clustering&#x27;,\n",
       "                 KMeans(init=&#x27;random&#x27;, max_iter=500, n_clusters=10, n_init=50,\n",
       "                        random_state=0))])</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item sk-dashed-wrapped\"><div class=\"sk-label-container\"><div class=\"sk-label sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" ><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">Pipeline</label><div class=\"sk-toggleable__content\"><pre>Pipeline(steps=[(&#x27;Preprocess&#x27;, MinMaxScaler()),\n",
       "                (&#x27;Clustering&#x27;,\n",
       "                 KMeans(init=&#x27;random&#x27;, max_iter=500, n_clusters=10, n_init=50,\n",
       "                        random_state=0))])</pre></div></div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" ><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">MinMaxScaler</label><div class=\"sk-toggleable__content\"><pre>MinMaxScaler()</pre></div></div></div><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-3\" type=\"checkbox\" ><label for=\"sk-estimator-id-3\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">KMeans</label><div class=\"sk-toggleable__content\"><pre>KMeans(init=&#x27;random&#x27;, max_iter=500, n_clusters=10, n_init=50, random_state=0)</pre></div></div></div></div></div></div></div>"
      ],
      "text/plain": [
       "Pipeline(steps=[('Preprocess', MinMaxScaler()),\n",
       "                ('Clustering',\n",
       "                 KMeans(init='random', max_iter=500, n_clusters=10, n_init=50,\n",
       "                        random_state=0))])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipeline = Pipeline([(\"Preprocess\", MinMaxScaler()),\n",
    "                    (\"Clustering\", KMeans(n_clusters=10, **kmeans_kwargs))])\n",
    "\n",
    "pipeline.fit(digits.data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "cluster_centers = pipeline[-1].cluster_centers_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 288x288 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#visualising cluster centroids\n",
    "fig, ax = plt.subplots(5, 2, figsize=(4,4))\n",
    "for i, j in zip(ax.flat, cluster_centers.reshape(10, 8, 8)):\n",
    "    i.imshow(j)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Finding optimal K: Elbow method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "sse_digit = []\n",
    "\n",
    "scaled_digits = MinMaxScaler().fit_transform(digits.data)\n",
    "for k in range(1, 12):\n",
    "    kmeans = KMeans(n_clusters=k, **kmeans_kwargs)\n",
    "    kmeans.fit(scaled_digits)\n",
    "    sse_digit.append(kmeans.inertia_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotting\n",
    "\n",
    "plt.plot(range(1,12), sse_digit)\n",
    "plt.xticks(range(1,12))\n",
    "plt.xlabel(\"Number of Clusters\")\n",
    "plt.ylabel(\"SSE\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Slight elbow at $k=9$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Silhoutte"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sil_coef_digits = []\n",
    "for k in range(2, 15):\n",
    "    kmeans = KMeans(n_clusters=k, **kmeans_kwargs)\n",
    "    kmeans.fit(scaled_digits)\n",
    "    score = silhouette_score(digits.data, kmeans.labels_)\n",
    "    sil_coef_digits.append(score)\n",
    "\n",
    "plt.plot(range(2,15), sil_coef_digits)\n",
    "plt.xticks(range(2,15))\n",
    "plt.xlabel(\"Number of Clusters\")\n",
    "plt.ylabel(\"silhouette_score\")\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Heirarchical Agglomerative Clustering(HAC)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Two Approaches\n",
    "* Bottoms up - Starts by considering each data point as a cluster and then combines the closest clusters to form larger clusters\n",
    "* Top down - Entire data set is considered as one cluster, which is divide into smaller clusters in each step\n",
    "\n",
    "Linkage\n",
    "* A strategy to aggregate clusters\n",
    "* 4 types\n",
    "    * Single linkage -  Distance between closest points in two clusters\n",
    "    * Average linkage -  Average distance over all possible pairs\n",
    "    * Complete linkage - Distance between farthest points in two clusters\n",
    "    * Ward's Linkage -  Sum of squared distances within the clusters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "1. Calculate the distance matrix between pairs of clusters\n",
    "2. While all the objects are clustered into one.\n",
    "    * Detect the two closest groups and merge them"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## An Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.preprocessing import normalize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = np.array([(8,3), (5,3), (6,4), (1,6), (2,8)])\n",
    "scaled_X = normalize(X)\n",
    "plt.scatter(X[:,0], X[:,1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import scipy.cluster.hierarchy as shc\n",
    "plt.figure(figsize=(8,8))\n",
    "plt.title(\"Dendrograms\")\n",
    "dend = shc.dendrogram(shc.linkage(scaled_X, method='ward'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x24c20725b40>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.cluster import AgglomerativeClustering\n",
    "import numpy as np\n",
    "X = np.array([(8,3), (5,3), (6,4), (1,6), (2,8)])\n",
    "plt.scatter(X[:,0], X[:,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 1, 1], dtype=int64)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clustering = AgglomerativeClustering().fit(X)\n",
    "clustering.labels_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:,0], X[:,1], c=clustering.labels_)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.10.2 64-bit",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.2"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "369f2c481f4da34e4445cda3fffd2e751bd1c4d706f27375911949ba6bb62e1c"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}