fuzzy_kmeans.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "homeless-trademark",
   "metadata": {},
   "source": [
    "# Fuzzy K-means"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "sunset-consortium",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "id": "agreed-apparel",
   "metadata": {},
   "outputs": [],
   "source": [
    "def euc(x, y):\n",
    "    return np.linalg.norm(x - y)\n",
    "\n",
    "def fuzzy_kmeans(X, M, n_clusters, b, threshold=0.5):\n",
    "    max_diff = np.Infinity\n",
    "    old_centers = []\n",
    "    \n",
    "    iterations = 0\n",
    "    while max_diff > threshold:\n",
    "        iterations += 1\n",
    "        \n",
    "        print('------------------------')\n",
    "        print('ITERATION', iterations)\n",
    "        print('------------------------')\n",
    "        # update centers\n",
    "        centers = []\n",
    "        for i in range(n_clusters):\n",
    "            m = M[:,i]\n",
    "            center = np.sum((m**b * X.T).T, axis=0) / np.sum((m**b).T, axis=0)\n",
    "            centers.append(center)\n",
    "        print('centers:', centers)\n",
    "\n",
    "\n",
    "        # update memberships\n",
    "        new_M = []\n",
    "        for j, x in enumerate(X):\n",
    "            print('................')\n",
    "            print('sample: ', j)\n",
    "            dists = []\n",
    "            for c, center in enumerate(centers):\n",
    "                dist = euc(x, center)\n",
    "                dists.append(dist)\n",
    "                print('distance from X[' + str(j) + '] to C[' + str(c) + ']: '+ str(dist))\n",
    "            dists = np.array(dists)\n",
    "            dists = (1/dists)**2\n",
    "            membership = []\n",
    "            for dist in dists:\n",
    "                membership.append(dist / np.sum(dists))\n",
    "            new_M.append(membership)\n",
    "            print('new membership: ', new_M[j])\n",
    "        if len(old_centers) > 0:\n",
    "            dists = []\n",
    "            for c, center in enumerate(centers):\n",
    "                dists.append(euc(center, old_centers[c]))\n",
    "            print('dists:', dists)\n",
    "            max_diff = max(dists)\n",
    "        print('MAX DIFF between iterations:', max_diff)\n",
    "        old_centers = centers\n",
    "        M = np.array(new_M)\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0b882261",
   "metadata": {},
   "source": [
    "## Examples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "id": "european-region",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.array([\n",
    "    [-1, 3],\n",
    "    [1, 4],\n",
    "    [0, 5],\n",
    "    [4, -1],\n",
    "    [3, 0],\n",
    "    [5, 1]\n",
    "])\n",
    "M = np.array([\n",
    "    [1, 0], \n",
    "    [0.5, 0.5],\n",
    "    [0.5, 0.5],\n",
    "    [0.5, 0.5],\n",
    "    [0.5, 0.5],\n",
    "    [0, 1]\n",
    "]) # Mii + Mij == 1 bc it's the proba to belong to one or another cluster"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "id": "aggressive-details",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------------------------\n",
      "ITERATION 1\n",
      "------------------------\n",
      "centers: [array([0.5, 2.5]), array([3.5, 1.5])]\n",
      "................\n",
      "sample:  0\n",
      "distance from X[0] to C[0]: 1.5811388300841898\n",
      "distance from X[0] to C[1]: 4.743416490252569\n",
      "new membership:  [0.9, 0.09999999999999999]\n",
      "................\n",
      "sample:  1\n",
      "distance from X[1] to C[0]: 1.5811388300841898\n",
      "distance from X[1] to C[1]: 3.5355339059327378\n",
      "new membership:  [0.8333333333333333, 0.16666666666666666]\n",
      "................\n",
      "sample:  2\n",
      "distance from X[2] to C[0]: 2.5495097567963922\n",
      "distance from X[2] to C[1]: 4.949747468305833\n",
      "new membership:  [0.7903225806451614, 0.2096774193548387]\n",
      "................\n",
      "sample:  3\n",
      "distance from X[3] to C[0]: 4.949747468305833\n",
      "distance from X[3] to C[1]: 2.5495097567963922\n",
      "new membership:  [0.2096774193548387, 0.7903225806451614]\n",
      "................\n",
      "sample:  4\n",
      "distance from X[4] to C[0]: 3.5355339059327378\n",
      "distance from X[4] to C[1]: 1.5811388300841898\n",
      "new membership:  [0.16666666666666666, 0.8333333333333333]\n",
      "................\n",
      "sample:  5\n",
      "distance from X[5] to C[0]: 4.743416490252569\n",
      "distance from X[5] to C[1]: 1.5811388300841898\n",
      "new membership:  [0.09999999999999999, 0.9]\n",
      "MAX DIFF between iterations: inf\n",
      "------------------------\n",
      "ITERATION 2\n",
      "------------------------\n",
      "centers: [array([0.08758664, 3.75288345]), array([3.91241336, 0.24711655])]\n",
      "................\n",
      "sample:  0\n",
      "distance from X[0] to C[0]: 1.3227540216452427\n",
      "distance from X[0] to C[1]: 5.6311785863800585\n",
      "new membership:  [0.9477081284877458, 0.05229187151225423]\n",
      "................\n",
      "sample:  1\n",
      "distance from X[1] to C[0]: 0.9452855226028499\n",
      "distance from X[1] to C[1]: 4.7503984837318045\n",
      "new membership:  [0.9619108945194464, 0.03808910548055346]\n",
      "................\n",
      "sample:  2\n",
      "distance from X[2] to C[0]: 1.2501884278980109\n",
      "distance from X[2] to C[1]: 6.156044133064177\n",
      "new membership:  [0.9603908507889463, 0.03960914921105383]\n",
      "................\n",
      "sample:  3\n",
      "distance from X[3] to C[0]: 6.156044133064177\n",
      "distance from X[3] to C[1]: 1.2501884278980113\n",
      "new membership:  [0.03960914921105386, 0.9603908507889463]\n",
      "................\n",
      "sample:  4\n",
      "distance from X[4] to C[0]: 4.750398483731805\n",
      "distance from X[4] to C[1]: 0.94528552260285\n",
      "new membership:  [0.038089105480553456, 0.9619108945194464]\n",
      "................\n",
      "sample:  5\n",
      "distance from X[5] to C[0]: 5.6311785863800585\n",
      "distance from X[5] to C[1]: 1.3227540216452425\n",
      "new membership:  [0.05229187151225421, 0.9477081284877458]\n",
      "dists: [1.319015435565606, 1.3190154355656056]\n",
      "MAX DIFF between iterations: 1.319015435565606\n",
      "------------------------\n",
      "ITERATION 3\n",
      "------------------------\n",
      "centers: [array([0.01868851, 4.00085372]), array([ 3.98131149e+00, -8.53717173e-04])]\n",
      "................\n",
      "sample:  0\n",
      "distance from X[0] to C[0]: 1.4280876856335796\n",
      "distance from X[0] to C[1]: 5.815375071332313\n",
      "new membership:  [0.9431247362918644, 0.05687526370813568]\n",
      "................\n",
      "sample:  1\n",
      "distance from X[1] to C[0]: 0.9813118641669383\n",
      "distance from X[1] to C[1]: 4.989493830377664\n",
      "new membership:  [0.9627592169468244, 0.03724078305317552]\n",
      "................\n",
      "sample:  2\n",
      "distance from X[2] to C[0]: 0.9993210469057946\n",
      "distance from X[2] to C[1]: 6.392134158740934\n",
      "new membership:  [0.976142146350223, 0.02385785364977687]\n",
      "................\n",
      "sample:  3\n",
      "distance from X[3] to C[0]: 6.392134158740935\n",
      "distance from X[3] to C[1]: 0.999321046905795\n",
      "new membership:  [0.023857853649776883, 0.976142146350223]\n",
      "................\n",
      "sample:  4\n",
      "distance from X[4] to C[0]: 4.989493830377664\n",
      "distance from X[4] to C[1]: 0.9813118641669392\n",
      "new membership:  [0.03724078305317558, 0.9627592169468243]\n",
      "................\n",
      "sample:  5\n",
      "distance from X[5] to C[0]: 5.815375071332312\n",
      "distance from X[5] to C[1]: 1.428087685633579\n",
      "new membership:  [0.05687526370813563, 0.9431247362918643]\n",
      "dists: [0.25736395608609824, 0.2573639560860984]\n",
      "MAX DIFF between iterations: 0.2573639560860984\n"
     ]
    }
   ],
   "source": [
    "fuzzy_kmeans(X, M, 2, 2, threshold=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "detailed-windsor",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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