An-alternative-implementation-of-silhouette-coefficient.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "from sklearn.cluster import KMeans\n",
    "from sklearn.metrics import silhouette_score\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "X= np.random.rand(50,2)\n",
    "Y= 2 + np.random.rand(50,2)\n",
    "Z= np.concatenate((X,Y))\n",
    "Z=pd.DataFrame(Z) #converting into data frame for ease"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f9cb6a598d0>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(Z[0],Z[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Silhouette Score(n=2): 0.8174385396125128\n"
     ]
    }
   ],
   "source": [
    "KMean= KMeans(n_clusters=2)\n",
    "KMean.fit(Z)\n",
    "label=KMean.predict(Z)\n",
    "print(f'Silhouette Score(n=2): {silhouette_score(Z, label)}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.array(Z)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# See https://en.wikipedia.org/wiki/Silhouette_(clustering)\n",
    "\n",
    "def calculate_a_i(inner_index_i, X, cluster_i, label):\n",
    "    C_i = X[label == cluster_i]\n",
    "    # sum_c_i = 0\n",
    "    # for tt in range(len(C_i)):\n",
    "    #     if tt != inner_index_i:\n",
    "    #         sum_c_i += np.linalg.norm(C_i[inner_index_i]- C_i[tt])\n",
    "    sum_c_i = sum([np.linalg.norm(C_i[inner_index_i] - tt) for tt in C_i])\n",
    "    return  sum_c_i/(len(C_i) - 1)\n",
    " \n",
    "def calculate_b_i(inner_index_i, X, cluster_i, label):\n",
    "    C_i = X[label == cluster_i]\n",
    "    X_i = C_i[inner_index_i]\n",
    "    othter_cluster = [pp for pp in set(label) if pp != cluster_i]\n",
    "    min_pool = []\n",
    "    for kk in othter_cluster:\n",
    "        C_j = X[label == kk]\n",
    "        ttt = sum([np.linalg.norm(X_i - tt) for tt in C_j])/len(C_j)\n",
    "        min_pool.append(ttt)\n",
    "    return np.min(min_pool)\n",
    " \n",
    "def calculate_s_i(inner_index_i, X, cluster_i, label):\n",
    "    C_i = X[label == cluster_i]\n",
    "    if len(C_i) == 1:\n",
    "        s_i = 0\n",
    "    else:\n",
    "        a_ii = calculate_a_i(inner_index_i, X, cluster_i, label)\n",
    "        b_ii = calculate_b_i(inner_index_i, X, cluster_i, label)\n",
    "        s_i = (b_ii - a_ii)/np.max([b_ii,a_ii])\n",
    "    return s_i\n",
    " \n",
    "def silhouette_coefficient(X,label):\n",
    "    all_clu = set(label)\n",
    "    cal_mean = []\n",
    "    for cluster_i in all_clu:\n",
    "        X_I = X[label == cluster_i]\n",
    "        for inner_index_i in range(len(X_I)):\n",
    "            s_ii = calculate_s_i(inner_index_i, X, cluster_i, label)\n",
    "            cal_mean.append(s_ii)\n",
    "    return np.mean(cal_mean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8174385396125128"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "silhouette_score(X, label)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8174385396125128"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "silhouette_coefficient(X,label)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}