K_MeansClustering.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/nagababumo/iiitfmmlassignments/blob/main/K_MeansClustering.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KSVIRwShuG11"
      },
      "source": [
        "Lab by Nikunj Nawal\n",
        "\n",
        "nikunj.nawal@research.iiit.ac.in"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XWsDgHdl5dOG"
      },
      "source": [
        "# K-Means\n",
        "\n",
        "K-Means algorithm is a centroid based clustering algorithm where the sum of distances of points from the centroid of each cluster is minimized. The final output is a set of K clusters .ie. the cluster assigned to each point and the K centroids of the clusters."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "smmi2Hm_6dtJ"
      },
      "source": [
        "### The Algorithm\n",
        "> 1.   Initialize K centroids to K points randomly and set each point's initial cluster as the centroid closest to it.\n",
        "2.   While the clusers are changing - \\\\\n",
        "a. Assign the new centroids as the centroids of the points which have the same assigned cluster. \\\\\n",
        "b. Assign the new clusters to the points as the closest centroid.\n",
        "3. Return the assignments and the centroids.\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vQWLS_wq_WVt"
      },
      "source": [
        "### Part 1 - Implementation of KMeans and testing on Synthetic Datasets"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jYTNMyeL8rKH"
      },
      "source": [
        "# Importing necessary libraries\n",
        "\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn.datasets import make_blobs"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PGIO_edJ4uhB",
        "outputId": "cb0014c6-3bca-4acc-f8b1-90492247dbfd"
      },
      "source": [
        "# Generating Synthetic Data\n",
        "\n",
        "k=2\n",
        "color=[\"darkturquoise\",\"darkorange\",\"teal\",\"darkviolet\",\"tomato\", \"yellowgreen\",\"hotpink\",\"gold\"]\n",
        "\n",
        "X,_=make_blobs(n_samples=500, n_features=2, centers=k, random_state=10)\n",
        "print(\"Shape = \" + str(X.shape))\n",
        "\n",
        "print(\"Sample:\")\n",
        "print(X[:7])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Shape = (500, 2)\n",
            "Sample:\n",
            "[[ 5.83801528 -9.29715058]\n",
            " [ 5.67102739 -9.76225984]\n",
            " [ 3.15598083  5.95298368]\n",
            " [ 3.87586762  5.94663718]\n",
            " [ 3.94478532  4.85652467]\n",
            " [ 2.82983681  4.85628288]\n",
            " [ 4.99059695 -9.04869246]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "####Define all the functions & varibles needed to do clustering"
      ],
      "metadata": {
        "id": "WVLsu-efLqIk"
      }
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GHfSomXy91rb"
      },
      "source": [
        "#Create an empty dictionary to store the cluster name, centroid and points associated with the cluster.\n",
        "clusters={}\n",
        "\n",
        "def initializeClusterCentroids():\n",
        "  #For each cluster, initialize its properties\n",
        "  for i in range(k):\n",
        "      center = np.random.randint(-8, 10, size= (X.shape[1],), )\n",
        "      points = []\n",
        "      \n",
        "      cluster = {\n",
        "          'center' : center,\n",
        "          'points' : points,\n",
        "          'color' : color[i]\n",
        "      }\n",
        "      clusters[i] = cluster #looping over clusters dictionary \n",
        "\n",
        "#Calculate euclidean distance between v1 and v2\n",
        "def distance(v1, v2):\n",
        "    return np.sum((v2-v1)**2)**0.5\n",
        "\n",
        "def assignPointsToCluster(clusters, X):\n",
        "    for ix in range(X.shape[0]):#iterate for all datapoints\n",
        "\n",
        "        #Foe each datapoint, find the distance to k centroids\n",
        "        distance_of_i = [] \n",
        "        for kx in range(k):\n",
        "            d = distance(X[ix], clusters[kx]['center']) #we have find distance b/w \n",
        "            #all the point with all the five (k) cluster centers\n",
        "            distance_of_i.append(d)\n",
        "          \n",
        "        #Based on the distances to k centroid, pick which cluster to assign it to\n",
        "        #here we want find the minimum distance of cluster centers\n",
        "        cluster_to_choose = np.argmin(distance_of_i)\n",
        "        clusters[cluster_to_choose]['points'].append(X[ix]) \n",
        "\n",
        "#STEP 3: UPDATE CLUSTER CENTROIDS\n",
        "def updateCluster(clusters):\n",
        "    for kx in range(k):\n",
        "        cluster_points = clusters[kx]['points']\n",
        "        \n",
        "        cluster_points = np.array(cluster_points)\n",
        "        #here pts are array of list but we want array of array so\n",
        "        \n",
        "        if len(cluster_points)>0:\n",
        "            new_center = np.mean(cluster_points, axis=0) #axis is along rows so will \n",
        "            #find mean of all the feature seprately it will give 2,0 when we have cluster pts 50,2\n",
        "            clusters[kx]['center'] = new_center\n",
        "            clusters[kx]['points'] = [] # clear the points in a cluster list (emptying pts)\n",
        "            #as we have to do step 2 after step 3 again till not converge"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "H95Y7_Es-5pl"
      },
      "source": [
        "#We need to visualize this too. Lets define a function that can do that!\n",
        "def plotclusters(clusters, plot):\n",
        "    for kx in range(k):\n",
        "        cluster_points = clusters[kx]['points']\n",
        "        cluster_color = clusters[kx]['color']\n",
        "        cluster_center = clusters[kx]['center']\n",
        "        cluster_points = np.array(cluster_points)\n",
        "        \n",
        "        #plotting points associated /nearest to the cluster centers\n",
        "        if len(cluster_points) > 0:\n",
        "          plot.scatter(cluster_points[:, 0], cluster_points[:, 1], s = 2, c = cluster_color)\n",
        "        \n",
        "        plot.scatter(cluster_center[0], cluster_center[1], s = 250, c = cluster_color, marker=\"o\")"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jxdYCXL9_2Ol"
      },
      "source": [
        "We can now run and visualize how the clusters evolve."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 607
        },
        "id": "gcTPXjLe-7nC",
        "outputId": "f396802f-3cb5-4ba3-9ca5-16e5b0787a2c"
      },
      "source": [
        "#Plotting the initial dataset\n",
        "fig, axs = plt.subplots(2, 3)\n",
        "fig.set_size_inches(15, 10)\n",
        "axs[0, 0].scatter(X[:,0],X[:,1], s = 2, c = 'black')\n",
        "axs[0, 0].set_title('Dataset')\n",
        "\n",
        "np.random.seed(1)\n",
        "initializeClusterCentroids()\n",
        "\n",
        "#Now, lets plot the centroids it has initalized\n",
        "axs[0, 1].set_title('Centroid Initialization')\n",
        "axs[0, 1].scatter(X[:, 0], X[:, 1], s = 2, c = 'black')\n",
        "for i in range(k):#for all the clusters\n",
        "    center = clusters[i]['center'] #its cluster's center\n",
        "    axs[0, 1].scatter(center[0], center[1], c=clusters[i]['color'], s=250, marker=\"o\")\n",
        "\n",
        "#CLUSTERING EPOCH 1\n",
        "axs[0, 2].set_title('Iteration 1')\n",
        "assignPointsToCluster(clusters, X)\n",
        "plotclusters(clusters, axs[0, 2])\n",
        "updateCluster(clusters)\n",
        "\n",
        "#CLUSTERING EPOCH 2\n",
        "axs[1, 0].set_title('Iteration 2')\n",
        "assignPointsToCluster(clusters, X)\n",
        "plotclusters(clusters, axs[1, 0])\n",
        "updateCluster(clusters)\n",
        "\n",
        "#CLUSTERING EPOCH 3\n",
        "axs[1, 1].set_title('Iteration 3')\n",
        "assignPointsToCluster(clusters, X)\n",
        "plotclusters(clusters, axs[1, 1])\n",
        "updateCluster(clusters)\n",
        "\n",
        "#CLUSTERING EPOCH 4\n",
        "axs[1, 2].set_title('Iteration 4')\n",
        "assignPointsToCluster(clusters, X)\n",
        "plotclusters(clusters, axs[1, 2])\n",
        "updateCluster(clusters)\n",
        "\n",
        "# Hide x labels and tick labels for top plots and y ticks for right plots.\n",
        "for ax in axs.flat:\n",
        "    ax.label_outer()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1080x720 with 6 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HqWdqALtALKg"
      },
      "source": [
        "Let us now try the same thing with different number of clusters. We will also see how initialization matters."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qDwkJxaP_BVA",
        "outputId": "46f092b0-6294-43c9-ffc9-bdc7dce2d4b9"
      },
      "source": [
        "# Generating Synthetic Data\n",
        "\n",
        "k=4\n",
        "color=[\"darkturquoise\",\"darkorange\",\"teal\",\"darkviolet\",\"tomato\", \"yellowgreen\",\"hotpink\",\"gold\"]\n",
        "\n",
        "X,_=make_blobs(n_samples=500, n_features=2, centers=k, random_state=10)\n",
        "print(\"Shape = \" + str(X.shape))\n",
        "\n",
        "print(\"Sample:\")\n",
        "print(X[:7])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Shape = (500, 2)\n",
            "Sample:\n",
            "[[ -1.31898446  -6.47826668]\n",
            " [  3.87910747  -8.2401545 ]\n",
            " [ -0.49239887  -5.28550826]\n",
            " [ -1.11543839  -4.55232113]\n",
            " [  5.14041086 -10.44771931]\n",
            " [  6.55519802 -10.28277104]\n",
            " [  1.40404168  -6.43997659]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 607
        },
        "id": "2_HmX5BaAfjq",
        "outputId": "4789d39f-3585-4bf7-8bd9-41d880ec8962"
      },
      "source": [
        "#Plotting the initial dataset\n",
        "fig, axs = plt.subplots(2, 3)\n",
        "fig.set_size_inches(15, 10)\n",
        "axs[0, 0].scatter(X[:,0],X[:,1], s = 2, c = 'black')\n",
        "axs[0, 0].set_title('Dataset')\n",
        "\n",
        "## Change initialization here to 'np.random.seed(0)'\n",
        "np.random.seed(3)\n",
        "initializeClusterCentroids()\n",
        "\n",
        "#Now, lets plot the centroids it has initalized\n",
        "axs[0, 1].set_title('Centroid Initialization')\n",
        "axs[0, 1].scatter(X[:, 0], X[:, 1], s = 2, c = 'black')\n",
        "for i in range(k):#for all the clusters\n",
        "    center = clusters[i]['center'] #its cluster's center\n",
        "    axs[0, 1].scatter(center[0], center[1], c=clusters[i]['color'], s=250, marker=\"o\")\n",
        "\n",
        "#CLUSTERING EPOCH 1\n",
        "axs[0, 2].set_title('Iteration 1')\n",
        "assignPointsToCluster(clusters, X)\n",
        "plotclusters(clusters, axs[0, 2])\n",
        "updateCluster(clusters)\n",
        "\n",
        "#CLUSTERING EPOCH 2\n",
        "axs[1, 0].set_title('Iteration 2')\n",
        "assignPointsToCluster(clusters, X)\n",
        "plotclusters(clusters, axs[1, 0])\n",
        "updateCluster(clusters)\n",
        "\n",
        "#CLUSTERING EPOCH 3\n",
        "axs[1, 1].set_title('Iteration 3')\n",
        "assignPointsToCluster(clusters, X)\n",
        "plotclusters(clusters, axs[1, 1])\n",
        "updateCluster(clusters)\n",
        "\n",
        "#CLUSTERING EPOCH 4\n",
        "axs[1, 2].set_title('Iteration 4')\n",
        "assignPointsToCluster(clusters, X)\n",
        "plotclusters(clusters, axs[1, 2])\n",
        "updateCluster(clusters)\n",
        "\n",
        "# Hide x labels and tick labels for top plots and y ticks for right plots.\n",
        "for ax in axs.flat:\n",
        "    ax.label_outer()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1080x720 with 6 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nlqe_wvnAyvp"
      },
      "source": [
        "**As you can see, changing the random seed and hence changing the initialization has a large effect on the performance of KMeans.** "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uVyJPKobClt8"
      },
      "source": [
        "Hence we can run our K-Means Algorithm by calling the following function with appropriate X (dataset)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3PHM6J-lAg6E"
      },
      "source": [
        "from copy import deepcopy\n",
        "\n",
        "def run_kmeans(k, X):\n",
        "  initializeClusterCentroids()\n",
        "  assignPointsToCluster(clusters, X)\n",
        "  while (True):\n",
        "    prev_clusters = deepcopy(clusters)\n",
        "    updateCluster(clusters)\n",
        "    assignPointsToCluster(clusters, X)\n",
        "    if prev_clusters == clusters:\n",
        "      break\n",
        "  return clusters"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PUxLYV43D99i"
      },
      "source": [
        "### Kmeans in scikit-learn"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YVCkiXmdEcNg"
      },
      "source": [
        "Even though implementation of KMeans is easy, using libraries like sklearn allows our code to  be much simpler and faster. The next two cells show how to use it."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WT-WZDaikBD1"
      },
      "source": [
        "Check out all functionalities at https://scikit-learn.org/stable/modules/generated/sklearn.cluster.KMeans.html"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# importing Kmeans from scikit-learn\n",
        "from sklearn.cluster import KMeans"
      ],
      "metadata": {
        "id": "6v60U4zKUODb"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 129
        },
        "id": "hP0Isa2gD7n3",
        "outputId": "491b681b-8888-4519-84a3-af18958b8248"
      },
      "source": [
        "kmeans_demo = KMeans(n_clusters=5) #random centroid intialization\n",
        "#kmeans_demo = KMeans() #What if we dont initialize the number of clusters?\n",
        "#kmeans_demo = KMeans(n_clusters=5, init='k-means++') #Does smart centroid initialization help?\n",
        "\n",
        "#Let us fit our synthetic datapoints into the kmeans object\n",
        "kmeans_demo.fit(X)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.9/dist-packages/sklearn/cluster/_kmeans.py:870: FutureWarning: The default value of `n_init` will change from 10 to 'auto' in 1.4. Set the value of `n_init` explicitly to suppress the warning\n",
            "  warnings.warn(\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "KMeans(n_clusters=5)"
            ],
            "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>KMeans(n_clusters=5)</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\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">KMeans</label><div class=\"sk-toggleable__content\"><pre>KMeans(n_clusters=5)</pre></div></div></div></div></div>"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 513
        },
        "id": "xHll4yqNFCSn",
        "outputId": "66c95fe6-cf6a-4ecf-95ed-e043f686fc0e"
      },
      "source": [
        "#Lets inspect the clustering model\n",
        "print(\"ITERATIONS TO CONVERGE = \" + str(kmeans_demo.n_iter_))\n",
        "print(\"CLUSTER CENTROIDS = \")\n",
        "print(str(kmeans_demo.cluster_centers_))\n",
        "print()\n",
        "\n",
        "#using the colours we defined for the clusters at the start\n",
        "colors_toplot = []\n",
        "for label in kmeans_demo.labels_:\n",
        "  colors_toplot.append(color[label])\n",
        "\n",
        "plt.scatter(X[:,0], X[:, 1], c = colors_toplot, s=2)\n",
        "plt.scatter(kmeans_demo.cluster_centers_[:,0], kmeans_demo.cluster_centers_[:,1], c = 'black', s=250, marker = \"o\")\n",
        "plt.gcf().set_size_inches(8,6)\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "ITERATIONS TO CONVERGE = 5\n",
            "CLUSTER CENTROIDS = \n",
            "[[-6.20071147  5.13256421]\n",
            " [-0.06527291 -5.46786296]\n",
            " [ 1.99346069  5.33677989]\n",
            " [ 5.49063417 -9.5824711 ]\n",
            " [ 3.45413067  4.59073007]]\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x432 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eBe2HWoNFWTO"
      },
      "source": [
        "### KMeans on Digits Dataset (KMeans for labelling)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fhekZruK9KNr"
      },
      "source": [
        "Here we will attempt to use k-means to try to identify similar digits without using the original label information; this might be similar to a first step in extracting meaning from a new dataset about which you don't have any a priori label information."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "L4yV9wx9FVun",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "cb58ac58-8a4b-4671-b1af-521d784c851a"
      },
      "source": [
        "# importing the dataset\n",
        "from sklearn.datasets import load_digits\n",
        "\n",
        "digits = load_digits()\n",
        "digits.data.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(1797, 64)"
            ]
          },
          "metadata": {},
          "execution_count": 37
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xUBgYLeN9Sa-",
        "outputId": "68d31326-7ce3-4339-bf9d-3c57f2fb6067"
      },
      "source": [
        "# importing Kmeans from scikit-learn\n",
        "from sklearn.cluster import KMeans\n",
        "\n",
        "# Perform KMeans\n",
        "kmeans = KMeans(n_clusters=10, random_state=0)\n",
        "clusters = kmeans.fit_predict(digits.data)\n",
        "kmeans.cluster_centers_.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(10, 64)"
            ]
          },
          "metadata": {},
          "execution_count": 45
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 197
        },
        "id": "lSVbUHUi9n18",
        "outputId": "47f9711a-c8d8-4da4-8f90-2237ca272339"
      },
      "source": [
        "# We can now see how the centers of the clusters formed are\n",
        "\n",
        "fig, ax = plt.subplots(2, 5, figsize=(8, 3))\n",
        "centers = kmeans.cluster_centers_.reshape(10, 8, 8)\n",
        "for axi, center in zip(ax.flat, centers):\n",
        "    axi.set(xticks=[], yticks=[])\n",
        "    axi.imshow(center, interpolation='nearest', cmap=plt.cm.binary)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x216 with 10 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iAMCCXBR-ARJ"
      },
      "source": [
        "Because k-means knows nothing about the identity of the cluster, the 0–9 labels may be permuted. We can fix this by matching each learned cluster label with the true labels found in them:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_E4d3Jkc-BMY"
      },
      "source": [
        "from scipy.stats import mode\n",
        "\n",
        "labels = np.zeros_like(clusters)\n",
        "for i in range(10):\n",
        "    mask = (clusters == i)\n",
        "    labels[mask] = mode(digits.target[mask])[0]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0c2izOVb-Ezq"
      },
      "source": [
        "Now we can check how accurate our unsupervised clustering was in finding similar digits within the data:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SZ2HJXhT-IJn",
        "outputId": "9f975bad-d62b-488e-94c6-f5fc8de776da"
      },
      "source": [
        "from sklearn.metrics import accuracy_score\n",
        "accuracy_score(digits.target, labels)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.7935447968836951"
            ]
          },
          "metadata": {},
          "execution_count": 47
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dwjdViYU-QRE"
      },
      "source": [
        "**Hence clustering algorithms like KMeans are highly effective for identifying labels for groups apriori and even a simple KMeans acheives a ~80% accuracy on digit classification.**\n",
        "\n",
        "The confusion matrix for this looks like:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        },
        "id": "1idrQbsg-OQZ",
        "outputId": "aa26153a-36f2-4346-9dfd-91060085eb3a"
      },
      "source": [
        "from sklearn.metrics import confusion_matrix\n",
        "import seaborn as sns; sns.set()\n",
        "\n",
        "mat = confusion_matrix(digits.target, labels)\n",
        "sns.heatmap(mat.T, square=True, annot=True, fmt='d', cbar=False,\n",
        "            xticklabels=digits.target_names,\n",
        "            yticklabels=digits.target_names)\n",
        "plt.xlabel('true label')\n",
        "plt.ylabel('predicted label');"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MV0GTurvFkji"
      },
      "source": [
        "### KMeans on Iris Dataset (Elbow Method)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eNrXyKIjAp2L"
      },
      "source": [
        "We will perform KMeans on the famous Iris Dataset which has four features: sepal length, sepal width, petal length, and petal width. The fifth column is for species, which holds the value for these types of plants."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JOcJbmeaFFhF"
      },
      "source": [
        "#Importing the neccesary libraries\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn.cluster import KMeans\n",
        "\n",
        "from sklearn import datasets\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "wJWkYsYtA9Bi",
        "outputId": "42eadf01-9124-475b-9267-c56c664d489a"
      },
      "source": [
        "#import the dataset\n",
        "iris = datasets.load_iris()\n",
        "df = pd.DataFrame(iris.data, columns=['sepal_length', 'sepal_width', 'petal_length', 'petal_width'])\n",
        "x = df.iloc[:, [0,1,2,3]].values\n",
        "df.head(5)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "   sepal_length  sepal_width  petal_length  petal_width\n",
              "0           5.1          3.5           1.4          0.2\n",
              "1           4.9          3.0           1.4          0.2\n",
              "2           4.7          3.2           1.3          0.2\n",
              "3           4.6          3.1           1.5          0.2\n",
              "4           5.0          3.6           1.4          0.2"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-7381fc01-b704-4bf0-817a-2ca4a92e4d91\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <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>sepal_length</th>\n",
              "      <th>sepal_width</th>\n",
              "      <th>petal_length</th>\n",
              "      <th>petal_width</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>5.1</td>\n",
              "      <td>3.5</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>4.9</td>\n",
              "      <td>3.0</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>4.7</td>\n",
              "      <td>3.2</td>\n",
              "      <td>1.3</td>\n",
              "      <td>0.2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>4.6</td>\n",
              "      <td>3.1</td>\n",
              "      <td>1.5</td>\n",
              "      <td>0.2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>5.0</td>\n",
              "      <td>3.6</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.2</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-7381fc01-b704-4bf0-817a-2ca4a92e4d91')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-7381fc01-b704-4bf0-817a-2ca4a92e4d91 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-7381fc01-b704-4bf0-817a-2ca4a92e4d91');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 50
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZQAJZu30D9yx"
      },
      "source": [
        "Let us start with assigning the initial number of clusters as k=5."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zZKt6zzmD1e6",
        "outputId": "2fa4595d-34f4-4605-9afa-4fb7e649020c"
      },
      "source": [
        "kmeans5 = KMeans(n_clusters=5)\n",
        "y_kmeans5 = kmeans5.fit_predict(x)\n",
        "print(y_kmeans5)\n",
        "\n",
        "kmeans5.cluster_centers_"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
            " 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 3 0 0 0 3 0 3 3 0 3 0 3 0 0 3 0 3 0 3 0 0\n",
            " 0 0 0 0 0 3 3 3 3 0 3 0 0 0 3 3 3 0 3 3 3 3 3 0 3 3 4 0 2 4 4 2 3 2 4 2 4\n",
            " 4 4 0 4 4 4 2 2 0 4 0 2 0 4 2 0 0 4 2 2 2 4 0 0 2 4 4 0 4 4 4 0 4 4 4 0 4\n",
            " 4 0]\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[6.20769231, 2.85384615, 4.74615385, 1.56410256],\n",
              "       [5.006     , 3.428     , 1.462     , 0.246     ],\n",
              "       [7.475     , 3.125     , 6.3       , 2.05      ],\n",
              "       [5.508     , 2.6       , 3.908     , 1.204     ],\n",
              "       [6.52916667, 3.05833333, 5.50833333, 2.1625    ]])"
            ]
          },
          "metadata": {},
          "execution_count": 51
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xL3AAUdCEGsA"
      },
      "source": [
        "How do we choose the optimal number of clusters? There’s a method called the Elbow method, which is designed to help find the optimal number of clusters in a dataset. So let’s use this method to calculate the optimum value of k. To implement the Elbow method, we need to create some Python code (shown below), and we’ll plot a graph between the number of clusters and the corresponding error value.\n",
        "\n",
        "This graph generally ends up shaped like an elbow, hence its name:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "8VSBRjiLEQ7V",
        "outputId": "82d3732f-7670-422f-f9ea-85ced83edf13"
      },
      "source": [
        "Error =[]\n",
        "for i in range(1, 11):\n",
        "    kmeans = KMeans(n_clusters = i).fit(x)\n",
        "    kmeans.fit(x)\n",
        "    Error.append(kmeans.inertia_)\n",
        "    \n",
        "plt.plot(range(1, 11), Error)\n",
        "plt.title('Elbow method')\n",
        "plt.xlabel('No of clusters')\n",
        "plt.ylabel('Error')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAEWCAYAAACJ0YulAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAgAElEQVR4nO3deZRc5X3m8e9TvWppdYHUElJ3McIgwCzuhig2eMGOGRxwHMM4tuPJYnDIkIyJh5DFIXPmZDyb45lkjE3iIWGMbZEwXmKbAdtMbCwv2B4bjzBCIDBBFotaawuk1trq7Td/3Ldb1U1rpatvVdfzOadO3fveW3V/XTrqp+99632vIgIzMzOAQt4FmJlZ9XAomJnZOIeCmZmNcyiYmdk4h4KZmY1zKJiZ2TiHgs0qkq6T9P2y9ZB0Vp41TSdJH5L099P0XhM+KzNwKFgNkvSspIOS9pU9/jrvuqabpDdJ6s27DqsvjXkXYHaSfjkivpl3EWazjc8UrB68VdJGSTsl/YWkAoCkgqR/J+k5STsk3SWpPW1bJekP03Jnugx1Y1o/U9KLY+9TLl2S+YGkWyXtTsd9bWrflI5zbdn+LZL+UtLzkrZL+htJcyTNA/4PsKzsbGhZellzqnWvpPWSVpa93yslfScde72kt5dtWyjpPkl7JP0YOHP6P2qrdQ4Fqwf/AlgJXAxcDfxWar8uPX4BeAUwHxi7DPVd4E1p+Y3ARuCysvXvRcToEY73GmAdsBD4X8DngJ8HzgJ+A/hrSfPTvh8BzgZ60vZO4M8iYj9wFbAlIuanx5b0mren9ywC943VLKkJ+ArwDWAx8AHgbknnpNd9AhgAlqbPYOxzMDssIvzwo6YewLPAPmB32eNfpW3XAd8v2zeAK8vW3w+sTsurgfeXbTsHGCK7rHomsIvsD6e/AX4H6E37rQL+4Ai1XQc8XbZ+YaphSVnbC2QhIGA/cGbZtkuBZ9Lym8aOWbb9Q8A3y9bPAw6m5TcA24BC2fbPptc0pJ/t3LJtHy7/rPzwIyLcp2A165o4/j6FTWXLzwFjl2GWpfXybY1kv8B/Jmk/2S/vNwD/Cbg+/dX9RuC2oxxve9nyQYCImNw2H+gA5gIPSxrbJrJf4EezrWz5ANAqqTH9PJti4hnMc2RnHx3pZ5v8WZhN4MtHVg9KZcunA2OXYbYA/2zStmEO/1L/LvBOoDkiNqf1a4FTgLXTUNdOsoA4PyKK6dEeEWOXlk50CuMtQGlSX8fpwGagj+xnm/xZmE3gULB68MeSTpFUAm4CPp/aPwvcLOmMdI3/w8DnI2I4bf8u8HvAg2n9O2n9+xEx8nKLSn/R/0/gVkmLYbxT+xfTLtuBhWOd38fhIbIzhw9KapL0JuCXgc+ler8MfEjSXEnnkQWc2QQOBatVX5k0TuGeo+x7L/Aw2V/3XwPuTO2fAv6O7Jf+M2SdsB8oe913gTYOh8L3yS73PMj0+RNgA/AjSXuAb5L1bRARPyULro3p20TLjvw2EBGDZCFwFdlZyP8A3pveB7JAm092+ekzwKen8eewWUIRvsmOmZllfKZgZmbjHApmZjbOoWBmZuMcCmZmNq6mB68tWrQoli9fnncZZmY15eGHH94ZER1TbatYKKSRn58va3oF8GfAXal9Odl0Be+OiF3KhnR+HHgr2Xetr4uInxztGMuXL2fNmjXTX7yZ2Swm6Yij2St2+SginoqInojoAX6O7Bf9PcAtZHPPrCCbe+aW9JKrgBXpcQNwe6VqMzOzqc1Un8LlwM8i4jmyWSpXpfZVwDVp+Wrgrsj8CChKWjpD9ZmZGTMXCu8hG5kJ2WRjW9PyNmBJWu5k4mRdvanNzMxmSMVDQVIz2fzv/zB5W2TDqU9oSLWkGyStkbSmr69vmqo0MzOYmTOFq4CflE0dvH3sslB63pHaNzNxBseu1DZBRNwRESsjYmVHx5Sd52ZmdpJmIhT+JYcvHUF2p6ix2RmvJZusbKz9vcpcAvSXXWYyM7MZUNFxCuk+s1eQ3bVqzEeAL0i6nuwmH+9O7feTfR11A9k3ld5XydrMzOylKhoKkd1nduGkthfIvo00ed8AbqxkPWPWPPsiq3+6gw/+4jmU3fHKzKzu1eU0F+u37OH27/yMrf0DeZdiZlZV6jIUuktFAB7dtDvnSszMqktdhsIrl7bR1CDW9joUzMzK1WUotDQ2cN7SBT5TMDObpC5DAaCnVOSx3n5GRn07UjOzMXUbCt2lIvsHR9iwY1/epZiZVY26DgVwZ7OZWbm6DYUzFs6jrbXRnc1mZmXqNhQKBdFTKrL2eYeCmdmYug0FgO6uIk9t38vBwZG8SzEzqwr1HQqlIiOjwfot/XmXYmZWFeo8FNoBWOvOZjMzoM5DYXFbK53FOTza6zMFMzOo81CA7Gxh7aZdeZdhZlYVHApdRTa9eJAX9h3KuxQzs9w5FNIgtnW+hGRm5lC4sLOdgtzZbGYGDgXmtTRy9pI2h4KZGQ4FIOtXeLR3N9kdQc3M6pdDgaxfYfeBIZ5/8UDepZiZ5cqhgAexmZmNcSgA5yxpo7Wp4FAws7pX0VCQVJT0RUk/lfSkpEslnSrpAUlPp+dT0r6SdJukDZLWSbq4krWVa2wocGFnu++tYGZ1r9JnCh8H/jEizgW6gSeBW4DVEbECWJ3WAa4CVqTHDcDtFa5tgu6uIo9v2cPQyOhMHtbMrKpULBQktQOXAXcCRMRgROwGrgZWpd1WAdek5auBuyLzI6AoaWml6pusu1RkcHiUp7btnalDmplVnUqeKZwB9AGflvSIpE9KmgcsiYitaZ9twJK03AlsKnt9b2qbQNINktZIWtPX1zdtxfakkc3uVzCzelbJUGgELgZuj4iLgP0cvlQEQGQDA05ocEBE3BERKyNiZUdHx7QV23XKHBbOa3YomFldq2Qo9AK9EfFQWv8iWUhsH7sslJ53pO2bgVLZ67tS24yQRHep6M5mM6trFQuFiNgGbJJ0Tmq6HHgCuA+4NrVdC9yblu8D3pu+hXQJ0F92mWlGdHcV2dC3j70DQzN5WDOzqtFY4ff/AHC3pGZgI/A+siD6gqTrgeeAd6d97wfeCmwADqR9Z1TP6UUi4LHN/bz2zEUzfXgzs9xVNBQiYi2wcopNl0+xbwA3VrKeY+nuOjyy2aFgZvXII5rLFOc2s3zhXPcrmFndcihMknU2+4Y7ZlafHAqTdHcV2bZngG39A3mXYmY24xwKk/Sc7kFsZla/HAqTnLd0AY0F8WivQ8HM6o9DYZLWpgZeuXSBO5vNrC45FKbQXWpnXW8/o6O+PaeZ1ReHwhR6Sqew79AwG3fuy7sUM7MZ5VCYQk+6Pecjz/sSkpnVF4fCFF6xaD7zWxrd2WxmdcehMIVCQbyqq92D2Mys7jgUjqCnVOTJrXsYGBrJuxQzsxnjUDiC7lKR4dFg/ZY9eZdiZjZjHApHMHZ7To9XMLN64lA4giULWjltQas7m82srjgUjqK71O4zBTOrKw6Fo+gpncKzLxxg1/7BvEsxM5sRDoWj6E6D2HwJyczqhUPhKC7sbEfC4xXMrG44FI6irbWJszrm+0zBzOqGQ+EYekpFHt20mwjPmGpms19FQ0HSs5Iek7RW0prUdqqkByQ9nZ5PSe2SdJukDZLWSbq4krUdr+5SkRf2D9K762DepZiZVdxMnCn8QkT0RMTKtH4LsDoiVgCr0zrAVcCK9LgBuH0GajumsUFsvj2nmdWDPC4fXQ2sSsurgGvK2u+KzI+AoqSlOdQ3wTmntdHSWPB4BTOrC5UOhQC+IelhSTektiURsTUtbwOWpOVOYFPZa3tT2wSSbpC0RtKavr6+StU9rqmhwAWd7e5sNrO6UOlQeH1EXEx2aehGSZeVb4ys9/aEenAj4o6IWBkRKzs6Oqax1CPr7iry2OZ+hkZGZ+R4ZmZ5qWgoRMTm9LwDuAd4NbB97LJQet6Rdt8MlMpe3pXactddamdgaJR/2r4371LMzCqqYqEgaZ6ktrFl4C3A48B9wLVpt2uBe9PyfcB707eQLgH6yy4z5erwjKkexGZms1tjBd97CXCPpLHj/K+I+EdJ/w/4gqTrgeeAd6f97wfeCmwADgDvq2BtJ+T0U+dyytwmHt20m197zel5l2NmVjEVC4WI2Ah0T9H+AnD5FO0B3Fipel4OSXSXiv5aqpnNeh7RfJy6u4r804697Ds0nHcpZmYV41A4Tj2lIhHw+Gb3K5jZ7OVQOE6v6krTaPsSkpnNYg6F47RwfgunnzrXg9jMbFZzKJyA7lKRtc87FMxs9nIonIDurna29A+wY89A3qWYmVWEQ+EEjA9i63Vns5nNTg6FE3BBZzsNBbmz2cxmLYfCCWhtauDc09o8iM3MZi2HwgnqLhV5tHc3o6O+PaeZzT4OhRPU01Vk78Awz7ywP+9SzMymnUPhBPWcPjZjqi8hmdns41A4QWd2zGdec4P7FcxsVnIonKCGgriwq91nCmY2KzkUTkJ3qcgTW/dwaHgk71LMzKaVQ+EkXFQqMjQSPLnVt+c0s9nFoXASukvubDaz2cmhcBJOW9DK4rYWdzab2azjUDgJY7fn9JmCmc02DoWT1FMqsnHnfvoPDOVdipnZtHEonKSxGVPXbfbZgpnNHhUPBUkNkh6R9NW0foakhyRtkPR5Sc2pvSWtb0jbl1e6tpfjwnR7Tt90x8xmk5k4U7gJeLJs/b8Ct0bEWcAu4PrUfj2wK7XfmvarWgtamzizY55vz2lms0pFQ0FSF/BLwCfTuoA3A19Mu6wCrknLV6d10vbL0/5Vq7tUZO2mfiI8Y6qZzQ6VPlP4GPBBYDStLwR2R8RwWu8FOtNyJ7AJIG3vT/tPIOkGSWskrenr66tk7cd0UanIzn2H2NLv23Oa2exQsVCQ9DZgR0Q8PJ3vGxF3RMTKiFjZ0dExnW99wsYGsblfwcxmi0qeKbwOeLukZ4HPkV02+jhQlNSY9ukCNqflzUAJIG1vB16oYH0v27mnLaC5oeB+BTObNSoWChHxpxHRFRHLgfcA34qIXwe+Dbwz7XYtcG9avi+tk7Z/K6r8Yn1zY4Hzli3wyGYzmzWOGQqSCpJeO43H/BPgDyRtIOszuDO13wksTO1/ANwyjcesmJ5Skcd6+xkeGT32zmZmVe6YoRARo8AnXs5BIuI7EfG2tLwxIl4dEWdFxLsi4lBqH0jrZ6XtG1/OMWdKT6nIwaERNvTty7sUM7OX7XgvH62W9CvV/hXRPLiz2cxmk+MNhd8B/gEYlLRH0l5JeypYV81YvnAuC1ob3dlsZrNC47F3gYhoq3QhtWpsxtS1m/rzLsXM7GU77m8fSXq7pL9Mj7dVsqhac1GpyD9t38uBweFj72xmVsWOKxQkfYRsDqMn0uMmSX9eycJqSXepyMho8PhmX1Ezs9p2vGcKbwWuiIhPRcSngCvJ5jQy4FVdvj2nmc0OJzJ4rVi23D7dhdSyjrYWOotzWOvOZjOrccfV0Qx8GHhE0rcBAZdRI4PLZkrP6b49p5nVvuMa0Uw2y+klwJeBLwGXRsTnK1xbTenpKtK76yA79x3KuxQzs5N2vCOaPxgRWyPivvTYNgO11ZSxQWw+WzCzWna8fQrflPRHkkqSTh17VLSyGnNB5wIaCnIomFlNO94+hV9NzzeWtQXwiuktp3bNbW7k7CVtrO31IDYzq13HDIXUp3CL+xCOrafUzv2PbSMi8DRRZlaLjrdP4Y9noJaa191VpP/gEM++cCDvUszMTor7FKaRO5vNrNa5T2Eanb2kjbnNDazdtJtrLurMuxwzsxN2vLOknlHpQmaDhoK4oLPd02ibWc066uUjSR8sW37XpG0frlRRtaynVGT9lj0MDvv2nGZWe47Vp/CesuU/nbTtymmuZVbo7ioyODzKT7d5xlQzqz3HCgUdYXmqdQO6S9lcge5sNrNadKxQiCMsT7VuQGdxDovmt/hObGZWk44VCt1j92QGXpWWx9YvPNoLJbVK+rGkRyWtl/QfUvsZkh6StEHS5yU1p/aWtL4hbV8+DT/fjJNET6mdtZt25V2KmdkJO2ooRERDRCyIiLaIaEzLY+tNx3jvQ8CbI6Ib6AGulHQJ8F+BWyPiLGAXcH3a/3pgV2q/Ne1Xk7q7ivysbz97BobyLsXM7IScyE12Tkhk9qXVpvQI4M3AF1P7KuCatHx1Widtv1w1OlfE2CC2xzwPkpnVmIqFAoCkBklrgR3AA8DPgN0RMXaH+15gbJRXJ7AJIG3vBxZO8Z43SFojaU1fX18lyz9p3en2nGvd2WxmNaaioRARIxHRA3QBrwbOnYb3vCMiVkbEyo6OjpddYyW0z23iFYvm+RtIZlZzKhoKYyJiN/Bt4FKgKGlsJHUXsDktbwZKAGl7O/DCTNRXCd2lIms37SbCX9Iys9pRsVCQ1CGpmJbnAFcAT5KFwzvTbtcC96bl+9I6afu3ooZ/o3Z3tbNj7yG27RnIuxQzs+N2vBPinYylwCpJDWTh84WI+KqkJ4DPSfrPwCPAnWn/O4G/k7QBeJGJo6lrTs/ppwDZILal7XNyrsbM7PhULBQiYh1w0RTtG8n6Fya3DwDvmtxeq165tI2mBrF2Uz9XXrA073LMzI7LjPQp1KOWxgbOW7rAg9jMrKY4FCqou1Tksd5+RkZrtmvEzOqMQ6GCekpF9g+O8LO+fcfe2cysCjgUKmhsZLMHsZlZrXAoVNAZC+fR1troUDCzmuFQqKBCQXR3FT2y2cxqhkOhwrpL7fx0214GhkbyLsXM7JgcChXWUzqFkdFg/RbPmGpm1c+hUGHdXdntOX0nNjOrBQ6FClu8oJVl7a3ubDazmuBQmAHdJXc2m1ltcCjMgJ5SkedfPMCL+wfzLsXM7KgcCjNgbBDbo70+WzCz6uZQmAEXdrZTEKx93qFgZtXNoTAD5rU0smJxm88UzKzqORRmSE/qbK7hm8mZWR1wKMyQ7lKRXQeG2PTiwbxLMTM7IofCDOkuZYPYHvFNd8ysijkUZsjZS9pobSrwqEc2m1kVcyjMkKaGAhcsa3dns5lVNYfCDOopFXl8cz9DI6N5l2JmNqWKhYKkkqRvS3pC0npJN6X2UyU9IOnp9HxKapek2yRtkLRO0sWVqi0v3aUih4ZHeWrb3rxLMTObUiXPFIaBP4yI84BLgBslnQfcAqyOiBXA6rQOcBWwIj1uAG6vYG256PHtOc2sylUsFCJia0T8JC3vBZ4EOoGrgVVpt1XANWn5auCuyPwIKEpaWqn68tB1yhxOndfsyfHMrGrNSJ+CpOXARcBDwJKI2Jo2bQOWpOVOYFPZy3pT26whKRvE5s5mM6tSFQ8FSfOBLwG/HxF7yrdFNrz3hIb4SrpB0hpJa/r6+qax0pnR3VXk6R372HdoOO9SzMxeoqKhIKmJLBDujogvp+btY5eF0vOO1L4ZKJW9vCu1TRARd0TEyohY2dHRUbniK6S71E4ErPPZgplVoUp++0jAncCTEfHRsk33Adem5WuBe8va35u+hXQJ0F92mWnW6O5K02h7EJuZVaHGCr7364DfBB6TtDa1/VvgI8AXJF0PPAe8O227H3grsAE4ALyvgrXl5pR5zSxfONedzWZWlSoWChHxfUBH2Hz5FPsHcGOl6qkm3aUiP37mxbzLMDN7CY9ozkF3V5Gt/QNs3zOQdylmZhM4FHLQ7UFsZlalHAo5OH/ZAhoLcr+CmVUdh0IOWpsaeOXSBR7EZmZVx6GQk+5SO+s29TM66ttzmln1cCjkpLuryN5Dw2zcuS/vUszMxjkUcnJ4xlQPYjOz6uFQyMmZHfOZ39LozmYzqyoOhZwUCuJVXe18+6kdPLtzf97lmJkBDoVc/c4bz6T/4BBXfvxBPvm9jYy409nMcuZQyNEbz+7ggZvfyOvOXMR//tqTvPNv/i9Pb/etOs0sPw6FnJ3W3sonr13Jx9/TwzM79/NLt32fT3x7A0Mjo3mXZmZ1yKFQBSRxdU8nD9z8Rq44bwl/8fWnuOYTP2D9Fn8zycxmlkOhinS0tfCJX7+Y23/9YrbvOcTVf/0DPvqNpzg0PJJ3aWZWJxwKVeiqC5fyzT+4jLf3LOO2b23gl//q+548z8xmhEOhShXnNvPRd/fw6et+nr0Dw7zjf/yAP7//SQaGfNZgZpXjUKhyv3DuYr5+82X86s+fzt8+uJGrPv4936DHzCrGoVADFrQ28efvuJC7f/s1DI+O8u6//SH//t7H2X9oOO/SzGyWcSjUkNedtYh/vOkyrnvtcu760XP84sce5PtP78y7LDObRRwKNWZeSyMfevv5/MPvXEpzQ4HfuPMhbvnSOvYMDOVdmpnNAg6FGrVy+ancf9Mb+N03nskX1mziLR99kNVPbs+7LDOrcQ6FGtba1MAtV53LPe9/He1zmrh+1Rp+/3OPsGv/YN6lmVmNqlgoSPqUpB2SHi9rO1XSA5KeTs+npHZJuk3SBknrJF1cqbpmo+5Ska984PXcdPkKvrpuK1fc+l3uf2xr3mWZWQ2q5JnCZ4ArJ7XdAqyOiBXA6rQOcBWwIj1uAG6vYF2zUnNjgZuvOJuvfOD1LG2fw/vv/gn/+u8fpm/vobxLM7MaUrFQiIgHgclfqL8aWJWWVwHXlLXfFZkfAUVJSytV22z2yqULuOf9r+VPrjyX1T/dwRW3fpd7HuklwtNym9mxzXSfwpKIGLuusQ1YkpY7gU1l+/WmtpeQdIOkNZLW9PX1Va7SGtbYUOBfv+lM7v83b+AVi+Zx8+cf5fpVa9jafzDv0sysyuXW0RzZn64n/OdrRNwRESsjYmVHR0cFKps9zlo8n3/43dfyZ287jx/+7AXe8tEH+dyPn/dZg5kd0UyHwvaxy0LpeUdq3wyUyvbrSm32MjUUxG+9/gy+/vuXcUFnO7d8+TF+486H2PTigbxLM7MqNNOhcB9wbVq+Fri3rP296VtIlwD9ZZeZbBqcvnAud//2a/jwv7iQRzf185ZbH+QzP3iGUd8C1MzKVPIrqZ8FfgicI6lX0vXAR4ArJD0N/PO0DnA/sBHYAPxP4P2VqqueFQri115zOt+4+TJe84pT+dBXnuBX7/ghG/v25V2amVUJ1fL15ZUrV8aaNWvyLqMmRQRf/slm/uNXn2BgaIR3XNzJhZ1FLuhcwNlL2mhtasi7RDOrEEkPR8TKqbY1znQxVh0k8Ss/18Ubzl7Ef/nak3x13VY+++PsC2CNBXHW4vmcv6yd85ct4PxlCzhv2QLaWptyrtrMKs1nCgZkZw69uw7y+OZ+1m/Zw/ot/Ty+Zc+EwW/LF87NgqJzwXhgLJrfkmPVZnYyfKZgxySJ0qlzKZ06l6suPDxucMfegSwkUlis27ybr5VNoXHagtbxs4nzO7Og6CzOQVIeP4aZvUwOBTuqxW2tLD6nlV84Z/F4W//BIZ5IZxNjZxXffmoHY19kKs5tSkFx+PLTGYvm01BwUJhVO4eCnbD2OU1ceuZCLj1z4XjbwcERfrptz3hIrN+yh8/84FkGR0YBmNPUwCuXtnH+snYuSJefViyZT0ujO7TNqon7FKxihkZG2bBjH+u37OHxzf08sWUPT2zdw750G9GmBrFicduEy0+nnzqXhfOaaWzwrO5mlXK0PgWHgs2o0dHguRcPjJ9NjIXFC2X3gJBg4bxmOtpaWdzWQkdbC4vTo6OtlcULWuiY38LiBS3MbfbJrtmJckezVY1CQZyxaB5nLJrH2161DMi++bR9zyGe2NrPlt0D7Nh7iL69A/TtPcSOvYd4attedu47xPAUo6/ntzTSURYc2XNZmKQAOWVuMwX3aZgdk0PBcieJ09pbOa299Yj7jI4Guw4M0rfvEDv2HErBcYgdewfGl9dv2cOOPQPsHxx5yesbC5oUHq2TzkBaWLyglUXzm93PYXXNoWA1oVAQC+e3sHB+C+eedvR99x8aHj/LmBwcO/YeonfXQdZu2s0L+weZ6uppcW4TxTlNtM9pYkF6nrw8+bFgThNtLY0+G7Ga51CwWWdeSyPzWhpZvmjeUfcbGhnlxf2D6cxjYEKQ7D44RH969O46OL48cpQJBAuCttapAqPxqIHSPqeJttYmf2XXqoJDwepWU0OBJQtaWbKgFWg/5v4RwYHBkfGAKH/smaKt/+AQW/oPjm8bGjn6lzraWhsPB0lrFiZzmxtpbWpgTlMDc5oLzGlqyNabGw4vT2qb09RAa9p3TlODv8llJ8ShYHacJI2fhSwrzjmh10YEA0OjUwbHkYLlmZ37OTg0wsHBUQaGRjgwOMzJzHTe1CBaywIkC40G5jSl4GietG1yW3kYNTUwt7mROc2Fsu0NtDY2+NLZLOFQMJsBkrK/5JsbjtqhfjQRwdBIcHBohENDI1lgDI1wcDB7HkgBMtY+MJjahsq3j62PMjA4ws59g+PbxrYfGBqZsq/lWFoaCxPPVlJgzJ0UOkcMnObD2+e85MyngeaGAk0NBV9mqzCHglmNkERzo2huLMCcys1YGxEMjowykALmwOAwA0OjUwTLSDqDydoGpgqpoRH2Hxpm577Bia8dHBkf7X6iJGgqFGhsEI0F0ZTCorEhW24siMaGAk1p++Hlw89T75ueJywXxo/R2KDx4zYUsn2y58OvaUjLY+2T9yvf3lQo0NAwcb+CyH3eMIeCmU0giZbGBloaG2incuEzPDLKwPDolIEydqZTfjZ0aHiUoZFRhkeCodHseXhklKHR7DlrT20jwXDaZ2hklIGhUYZHhie2j2+fuO/waBz1CwWVdjgkxkJk6vC56fIV/HL3suk//rS/o5nZcWhsKDC/ocD8lur7NTQ6GgyPZmExlMJneDQLjZG0bWSK9eGR9Dw6qX00GBkLsrH1sgB6yX6jwchIefto2Xtnz8W5lQns6vvXMDPLWaEgmguiecZvY5+/+vuJzczsiBwKZmY2zqFgZmbjqioUJF0p6SlJGyTdknc9Zmb1pmpCQVID8AngKuA84F9KOi/fqszM6kvVhALwamBDRGyMiEHgc8DVOddkZlZXqikUOoFNZeu9qW0CSTdIWiNpTV9f34wVZ2ZWD6opFI5LRNwRESsjYmVHR0fe5ZiZzSrVNHhtM1AqW+9KbUf08MMP75T0XEWrqm81wwgAAAXxSURBVLxFwM68i6gi/jwO82cxkT+PiV7O5/HPjrRBcTLTIVaApEbgn4DLycLg/wG/FhHrcy2swiStOdINtOuRP4/D/FlM5M9jokp9HlVzphARw5J+D/g60AB8arYHgplZtamaUACIiPuB+/Ouw8ysXtVcR/MsdEfeBVQZfx6H+bOYyJ/HRBX5PKqmT8HMzPLnMwUzMxvnUDAzs3EOhZxIKkn6tqQnJK2XdFPeNeVNUoOkRyR9Ne9a8iapKOmLkn4q6UlJl+ZdU54k3Zz+nzwu6bOSWvOuaaZI+pSkHZIeL2s7VdIDkp5Oz6dM1/EcCvkZBv4wIs4DLgFu9ASA3AQ8mXcRVeLjwD9GxLlAN3X8uUjqBP4NsDIiLiD7yvp78q1qRn0GuHJS2y3A6ohYAaxO69PCoZCTiNgaET9Jy3vJ/tO/ZK6neiGpC/gl4JN515I3Se3AZcCdABExGBG7860qd43AnDTIdS6wJed6ZkxEPAi8OKn5amBVWl4FXDNdx3MoVAFJy4GLgIfyrSRXHwM+CIzmXUgVOAPoAz6dLqd9UtK8vIvKS0RsBv4SeB7YCvRHxDfyrSp3SyJia1reBiyZrjd2KORM0nzgS8DvR8SevOvJg6S3ATsi4uG8a6kSjcDFwO0RcRGwn2m8PFBr0vXyq8nCchkwT9Jv5FtV9YhsXMG0jS1wKORIUhNZINwdEV/Ou54cvQ54u6Rnye6j8WZJf59vSbnqBXojYuzM8YtkIVGv/jnwTET0RcQQ8GXgtTnXlLftkpYCpOcd0/XGDoWcSBLZNeMnI+KjedeTp4j404joiojlZB2I34qIuv1LMCK2AZsknZOaLgeeyLGkvD0PXCJpbvp/czl13PGe3Adcm5avBe6drjd2KOTndcBvkv1VvDY93pp3UVY1PgDcLWkd0AN8OOd6cpPOmL4I/AR4jOz3Vt1MeSHps8APgXMk9Uq6HvgIcIWkp8nOpD4ybcfzNBdmZjbGZwpmZjbOoWBmZuMcCmZmNs6hYGZm4xwKZmY2zqFgs46kkPTfy9b/SNKHpuF9WyR9M319+FePY//l5TNbnuCxrpO07GRea/ZyOBRsNjoEvEPSoml+34sAIqInIj4/ze892XVkUzoctzRZnNnL4lCw2WiYbHDTzZM3pL/evyVpnaTVkk6fYp9TJf3vtM+PJL1K0mLg74GfT2cKZ056zVnpLOJRST+ZYvt1kv66bP2rkt6U7iHxmXSfgMfSfQPeCawkG7y2VtIcST8n6buSHpb09bIpDr4j6WOS1gA3SXpXeq9HJT04DZ+l1Rn/ZWGz1SeAdZL+26T2vwJWRcQqSb8F3MZLpx3+D8AjEXGNpDcDd0VEj6TfBv4oIt42xfHuBj4SEfekG8AUgMXHUWcP0JnuE4CkYkTslvR76Vhr0hxZfwVcHRF96dLVfwF+K71Hc0SsTK9/DPjFiNgsqXgcxzebwKFgs1JE7JF0F9nNWQ6WbboUeEda/jtgcmgAvB74lfQ+35K0UNKCIx1LUhvZL/Z70msGUvvxlLoReIWkvwK+Bkw1JfQ5wAXAA+k9G8imkB5TfinrB8BnJH2BbOI4sxPiy0c2m30MuB6ohnsRDDPx/1srQETsIruz2neA32XqmwwJWJ/6Mnoi4sKIeEvZ9v1jCxHxu8C/A0rAw5IWTutPYbOeQ8FmrYh4EfgCWTCM+b8cvpXjrwPfm+Kl30vbkPQmYOfR7nWR7pzXK+ma9JoWSXMn7fYs0COpIKkEvDrtuwgoRMSXyH6Zj02RvRdoS8tPAR1K92mW1CTp/KlqkXRmRDwUEX9GdqOe0pHqNpuKLx/ZbPffgd8rW/8A2R3N/pjsl+b7pnjNh4BPpRlKD3B4iuKj+U3gbyX9R2AIeBcT7yL3A+AZsimwnySb8ROyW7B+WtLYH2h/mp4/A/yNpINkl7zeCdyWbtXZSHYWtH6KOv5C0gqys4vVwKPHUbvZOM+SamZm43z5yMzMxjkUzMxsnEPBzMzGORTMzGycQ8HMzMY5FMzMbJxDwczMxv1/X2Um0ryRjQ4AAAAASUVORK5CYII=\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vEhXXxe6Em4E"
      },
      "source": [
        "The output graph of the Elbow method shows that the shape of elbow is approximately formed at k=3. The optimal value of k is between 2 and 4, as the elbow-like shape is formed at k=3 in the above graph."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GTpdV03VE79J",
        "outputId": "5bd81f78-c6d4-4ad4-9618-a1a600c29184"
      },
      "source": [
        "kmeans3 = KMeans(n_clusters=3)\n",
        "y_kmeans3 = kmeans3.fit_predict(x)\n",
        "print(y_kmeans3)\n",
        "\n",
        "kmeans3.cluster_centers_"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
            " 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
            " 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 2 2 2 0 2 2 2 2\n",
            " 2 2 0 0 2 2 2 2 0 2 0 2 0 2 2 0 0 2 2 2 2 2 0 2 2 2 2 0 2 2 2 0 2 2 2 0 2\n",
            " 2 0]\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[5.9016129 , 2.7483871 , 4.39354839, 1.43387097],\n",
              "       [5.006     , 3.428     , 1.462     , 0.246     ],\n",
              "       [6.85      , 3.07368421, 5.74210526, 2.07105263]])"
            ]
          },
          "metadata": {},
          "execution_count": 35
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3_wPmjOSFP5y"
      },
      "source": [
        "We can now visualize the clustering in two dimensions instead of the original four."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        },
        "id": "GOPhGuicFBkV",
        "outputId": "75ab1284-fae6-4967-a357-489848c13d47"
      },
      "source": [
        "plt.scatter(x[:,0], x[:,1], c=y_kmeans3, cmap='rainbow')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f2c46500210>"
            ]
          },
          "metadata": {},
          "execution_count": 36
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WJz6aYt6RRRl"
      },
      "source": [
        "## Points to think about"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BFLzASTIRaNc"
      },
      "source": [
        "1. Is feature scaling essential for KMeans as it is for most ML algos?\n",
        "2. How can we prevent initialization variation in KMeans?\n",
        "3. What is the training and testing complexity of KMeans?"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**1st solution**\n",
        "\n",
        "Yes, feature scaling is essential for KMeans clustering algorithm. Since KMeans uses Euclidean Distance to form clusters, it is wise to scale the variables before calculating the distance1. Feature scaling is especially relevant in machine learning models that compute some sort of distance metric, like most clustering methods like KMeans"
      ],
      "metadata": {
        "id": "zFHkC82NdFdk"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**2nd solution**\n",
        "\n",
        "One way to avoid initialization sensitivity in KMeans is to repeat the algorithm again and again along with initializing the centroids followed by picking up the cluster which results in a small intracluster distance and large intercluster distance1. Another way is to use a deterministic divisive hierarchical method such as PCA-Part (Principal Components Analysis Partitioning) for initialization"
      ],
      "metadata": {
        "id": "gYQF19N7dksR"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**3rd solution**\n",
        "\n",
        "KMeans algorithm doesn’t have a training phase so it also doesn’t have a training phase time complexity1. The k-means problem is solved using either Lloyd’s or Elkan’s algorithm. The average complexity is given by O(knT), where n is the number of samples and T is the number of iterations. The worst-case complexity is given by O(n^(k+2/p)) with n = n_samples, p = n_features"
      ],
      "metadata": {
        "id": "uVZnmhpedv1F"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uZrTx2nHSSZn"
      },
      "source": [
        "## References and resources\n",
        "\n",
        "1. https://towardsdatascience.com/k-means-clustering-algorithm-applications-evaluation-methods-and-drawbacks-aa03e644b48a\n",
        "2. https://www.analyticsvidhya.com/blog/2019/08/comprehensive-guide-k-means-clustering/\n",
        "3. https://en.wikipedia.org/wiki/K-means_clustering\n",
        "4. https://jakevdp.github.io/PythonDataScienceHandbook/05.11-k-means.html\n",
        "5. https://heartbeat.fritz.ai/k-means-clustering-using-sklearn-and-python-4a054d67b187\n",
        "6. https://www.geeksforgeeks.org/k-means-clustering-introduction/\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "az5_vhJnWLzS"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}