K-Means from Scratch.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So far, we have learnt about the introduction to K-Means algorithm. We have learnt in detail about the mathematics behind the K-means clustering algorithm and have learnt how Euclidean distance method is used in grouping the data items in K number of clusters. Here were are implementing K-means clustering from scratch using python. But the problem is how to choose the number of clusters? In this example, we are assigning the number of clusters ourselves and later we will be discussing about various ways of finding best number of clusters. This code is refenced from https://muthu.co/mathematics-behind-k-mean-clustering-algorithm/\n",
    "\n",
    "We will first import the required libraries:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import random as rd\n",
    "import matplotlib.pyplot as plt\n",
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "class K_Means:\n",
    "    \n",
    "    def __init__(self, k=2, tolerance = 0.001, max_iter = 500):\n",
    "        self.k = k\n",
    "        self.max_iterations = max_iter\n",
    "        self.tolerance = tolerance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have defined a kmeans class  with init consisting default value of k as 2, error tolerance as 0.001 and maximum iteration as 500.  \n",
    "Before diving to the code, lets remember some mathematical terms involved in K-means clustering:- centroids & euclidean distance. On a quick note centroid of a data is the average or mean of the data and euclidean distance is the distance between two points in the coordinate plane calculated using pythagoras theorem. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "    def euclidean_distance(self, point1, point2):\n",
    "            #return math.sqrt((point1[0]-point2[0])**2 + (point1[1]-point2[1])**2 + (point1[2]-point2[2])**2)   #sqrt((x1-x2)^2 + (y1-y2)^2)\n",
    "            return np.linalg.norm(point1-point2, axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We find the euclidean distance from each point to all the centroids. If you look for efficiency it is better to use the numpy function (np.linalg.norm(point1-point2, axis=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "    def fit(self, data):\n",
    "        self.centroids = {}\n",
    "        for i in range(self.k):\n",
    "            self.centroids[i] = data[i]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are various methods of assigning k - centroid initially. Mostly used is random selection but lets go with the most basic way.  We assign first k points from dataset as the initial centroids. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "       for i in range(self.max_iterations):\n",
    "            \n",
    "            self.classes = {}\n",
    "            for j in range(self.k):\n",
    "                self.classes[j] = []\n",
    "                \n",
    "            \n",
    "            for point in data:\n",
    "                distances = []\n",
    "                for index in self.centroids:\n",
    "                    distances.append(self.euclidean_distance(point,self.centroids[index]))\n",
    "                cluster_index = distances.index(min(distances))\n",
    "                self.classes[cluster_index].append(point)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Till now , we have defined kmeans class and initialized some default parameters. We have defined euclidean distance calculation function and we have also assigned initial k clusters. Now, In order to know which cluster an data items belongs to, we are calculating euclidean distance from the data items to each centroid. Data item closest to the cluster belongs to that respective cluster."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "            previous = dict(self.centroids)\n",
    "            for cluster_index in self.classes:\n",
    "                self.centroids[cluster_index] = np.average(self.classes[cluster_index], axis = 0)\n",
    "                \n",
    "            isOptimal = True\n",
    "            \n",
    "            for centroid in self.centroids:\n",
    "                original_centroid = previous[centroid]\n",
    "                curr = self.centroids[centroid]\n",
    "                if np.sum((curr - original_centroid)/original_centroid * 100.0) > self.tolerance:\n",
    "                    isOptimal = False\n",
    "            if isOptimal:\n",
    "                break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At the end of the first iteration, the centroid values are recalculated, usually taking the arithmetic mean of all points in the cluster.  In every iteration, new centroid values are calculated until successive iterations provide the same centroid value.  \n",
    "\n",
    "We've now completed the K Means scratch code of this Machine Learning tutorial series. Now lets test our code by clustering with random  generated data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "    #generate dummy cluster datasets\n",
    "    # Set three centers, the model should predict similar results\n",
    "    center_1 = np.array([1,1])\n",
    "    center_2 = np.array([5,5])\n",
    "    center_3 = np.array([8,1])\n",
    "\n",
    "    # Generate random data and center it to the three centers\n",
    "    cluster_1 = np.random.randn(100, 2) + center_1\n",
    "    cluster_2 = np.random.randn(100,2) + center_2\n",
    "    cluster_3 = np.random.randn(100,2) + center_3\n",
    "\n",
    "    data = np.concatenate((cluster_1, cluster_2, cluster_3), axis = 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we have created 3 groups of data of two dimension with different centre. We have defined the value of k as 3. Now lets fit the model created from scratch."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "    k_means = K_Means(K)\n",
    "    k_means.fit(data)\n",
    "    \n",
    "    \n",
    "    # Plotting starts here\n",
    "    colors = 10*[\"r\", \"g\", \"c\", \"b\", \"k\"]\n",
    "\n",
    "    for centroid in k_means.centroids:\n",
    "        plt.scatter(k_means.centroids[centroid][0], k_means.centroids[centroid][1], s = 130, marker = \"x\")\n",
    "\n",
    "    for cluster_index in k_means.classes:\n",
    "        color = colors[cluster_index]\n",
    "        for features in k_means.classes[cluster_index]:\n",
    "            plt.scatter(features[0], features[1], color = color,s = 30)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lets combine all the code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "class K_Means:\n",
    "    \n",
    "    def __init__(self, k=2, tolerance = 0.001, max_iter = 500):\n",
    "        self.k = k\n",
    "        self.max_iterations = max_iter\n",
    "        self.tolerance = tolerance\n",
    "    \n",
    "    def euclidean_distance(self, point1, point2):\n",
    "        #return math.sqrt((point1[0]-point2[0])**2 + (point1[1]-point2[1])**2 + (point1[2]-point2[2])**2)   #sqrt((x1-x2)^2 + (y1-y2)^2)\n",
    "        return np.linalg.norm(point1-point2, axis=0)\n",
    "        \n",
    "    def predict(self,data):\n",
    "        distances = [np.linalg.norm(data-self.centroids[centroid]) for centroid in self.centroids]\n",
    "        classification = distances.index(min(distances))\n",
    "        return classification\n",
    "    \n",
    "    def fit(self, data):\n",
    "        self.centroids = {}\n",
    "        for i in range(self.k):\n",
    "            self.centroids[i] = data[i]\n",
    "        \n",
    "        \n",
    "        for i in range(self.max_iterations):\n",
    "            self.classes = {}\n",
    "            for j in range(self.k):\n",
    "                self.classes[j] = []\n",
    "                \n",
    "            for point in data:\n",
    "                distances = []\n",
    "                for index in self.centroids:\n",
    "                    distances.append(self.euclidean_distance(point,self.centroids[index]))\n",
    "                cluster_index = distances.index(min(distances))\n",
    "                self.classes[cluster_index].append(point)\n",
    "            \n",
    "            previous = dict(self.centroids)\n",
    "            for cluster_index in self.classes:\n",
    "                self.centroids[cluster_index] = np.average(self.classes[cluster_index], axis = 0)\n",
    "            \n",
    "\n",
    "                \n",
    "            isOptimal = True\n",
    "            \n",
    "            for centroid in self.centroids:\n",
    "                original_centroid = previous[centroid]\n",
    "                curr = self.centroids[centroid]\n",
    "                if np.sum((curr - original_centroid)/original_centroid * 100.0) > self.tolerance:\n",
    "                    isOptimal = False\n",
    "            if isOptimal:\n",
    "                break\n",
    "\n",
    "\n",
    "                \n",
    "def main():\n",
    "    K=3\n",
    "    center_1 = np.array([1,1])\n",
    "    center_2 = np.array([5,5])\n",
    "    center_3 = np.array([8,1])\n",
    "\n",
    "    # Generate random data and center it to the three centers\n",
    "    cluster_1 = np.random.randn(100, 2) + center_1\n",
    "    cluster_2 = np.random.randn(100,2) + center_2\n",
    "    cluster_3 = np.random.randn(100,2) + center_3\n",
    "\n",
    "    data = np.concatenate((cluster_1, cluster_2, cluster_3), axis = 0)\n",
    "    \n",
    "    k_means = K_Means(K)\n",
    "    k_means.fit(data)\n",
    "    \n",
    "    \n",
    "    # Plotting starts here\n",
    "    colors = 10*[\"r\", \"g\", \"c\", \"b\", \"k\"]\n",
    "\n",
    "    for centroid in k_means.centroids:\n",
    "        plt.scatter(k_means.centroids[centroid][0], k_means.centroids[centroid][1], s = 130, marker = \"x\")\n",
    "\n",
    "    for cluster_index in k_means.classes:\n",
    "        color = colors[cluster_index]\n",
    "        for features in k_means.classes[cluster_index]:\n",
    "            plt.scatter(features[0], features[1], color = color,s = 30)\n",
    "    \n",
    "if __name__ == \"__main__\":\n",
    "    main()\n",
    "            "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# USING SCIKIT_ LEARN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7ff61863b340>"
      ]
     },
     "execution_count": 27,
     "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": [
    "from sklearn.cluster import KMeans\n",
    "center_1 = np.array([1,1])\n",
    "center_2 = np.array([5,5])\n",
    "center_3 = np.array([8,1])\n",
    "\n",
    "    # Generate random data and center it to the three centers\n",
    "cluster_1 = np.random.randn(100,2) + center_1\n",
    "cluster_2 = np.random.randn(100,2) + center_2\n",
    "cluster_3 = np.random.randn(100,2) + center_3\n",
    "\n",
    "data = np.concatenate((cluster_1, cluster_2, cluster_3), axis = 0)\n",
    "kmeans = KMeans(n_clusters=3)\n",
    "kmeans.fit(data)\n",
    "plt.scatter(data[:,0],data[:,1], c=kmeans.labels_, cmap='rainbow')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Completed !!\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "AIHUBPROJECTS.COM"
   ]
  }
 ],
 "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": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}