7_K_MeansClustering.ipynb

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  "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/Harsha-070/FMML_IIITH/blob/main/7_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 Ganesh Chandan\n",
        "\n",
        "kanakala.ganesh@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": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PGIO_edJ4uhB",
        "outputId": "b41091f7-7f68-4c38-9f93-4ed93fa5178e"
      },
      "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": 2,
      "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": 3,
      "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": 4,
      "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": 853
        },
        "id": "gcTPXjLe-7nC",
        "outputId": "82b0dc02-1a40-4a0d-9576-06a953d501cf"
      },
      "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": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x1000 with 6 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "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": "3a48b5dc-fbb1-47c3-d1f1-1102bd074c52"
      },
      "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": 6,
      "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": 853
        },
        "id": "2_HmX5BaAfjq",
        "outputId": "90000463-c976-406b-a77d-a7ce61eabe36"
      },
      "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": 7,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x1000 with 6 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "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": 8,
      "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": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 129
        },
        "id": "hP0Isa2gD7n3",
        "outputId": "0fe71961-71b9-4d82-8d48-95233aa50b21"
      },
      "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": 10,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.10/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": 661
        },
        "id": "xHll4yqNFCSn",
        "outputId": "4bf594c3-1e22-4971-ffe5-9d42b4567461"
      },
      "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": 11,
      "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 800x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "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": "052ae8bb-da62-4c8e-8346-f2b024cc840f"
      },
      "source": [
        "# importing the dataset\n",
        "from sklearn.datasets import load_digits\n",
        "\n",
        "digits = load_digits()\n",
        "digits.data.shape"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(1797, 64)"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xUBgYLeN9Sa-",
        "outputId": "6648f381-4ffe-476f-df9e-e26808fe2095"
      },
      "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": 13,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.10/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": [
              "(10, 64)"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 268
        },
        "id": "lSVbUHUi9n18",
        "outputId": "d0bfe611-3b64-4c9b-d619-ece4a7e07d0d"
      },
      "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": 14,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x300 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": 15,
      "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": "5941b1e3-7576-4faa-ced5-125831a5ba9a"
      },
      "source": [
        "from sklearn.metrics import accuracy_score\n",
        "accuracy_score(digits.target, labels)"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.7935447968836951"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ]
    },
    {
      "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": 458
        },
        "id": "1idrQbsg-OQZ",
        "outputId": "c1792a14-b111-49e4-efaf-96b935afa3cd"
      },
      "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": 17,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 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": 18,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "wJWkYsYtA9Bi",
        "outputId": "7912dbfb-78fc-41a6-995d-bdd06112bfe2"
      },
      "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": 19,
      "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"
            ],
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              "      <th>0</th>\n",
              "      <td>5.1</td>\n",
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            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "df",
              "summary": "{\n  \"name\": \"df\",\n  \"rows\": 150,\n  \"fields\": [\n    {\n      \"column\": \"sepal_length\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.828066127977863,\n        \"min\": 4.3,\n        \"max\": 7.9,\n        \"samples\": [\n          6.2,\n          4.5,\n          5.6\n        ],\n        \"num_unique_values\": 35,\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"sepal_width\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.4358662849366982,\n        \"min\": 2.0,\n        \"max\": 4.4,\n        \"samples\": [\n          2.3,\n          4.0,\n          3.5\n        ],\n        \"num_unique_values\": 23,\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"petal_length\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 1.7652982332594662,\n        \"min\": 1.0,\n        \"max\": 6.9,\n        \"samples\": [\n          6.7,\n          3.8,\n          3.7\n        ],\n        \"num_unique_values\": 43,\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"petal_width\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.7622376689603465,\n        \"min\": 0.1,\n        \"max\": 2.5,\n        \"samples\": [\n          0.2,\n          1.2,\n          1.3\n        ],\n        \"num_unique_values\": 22,\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "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": "f1ca4447-fa81-4c9a-d714-94f0c021b1ea"
      },
      "source": [
        "kmeans5 = KMeans(n_clusters=5)\n",
        "y_kmeans5 = kmeans5.fit_predict(x)\n",
        "print(y_kmeans5)\n",
        "\n",
        "kmeans5.cluster_centers_"
      ],
      "execution_count": 20,
      "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": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.10/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": [
              "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": 20
        }
      ]
    },
    {
      "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": 1000
        },
        "id": "8VSBRjiLEQ7V",
        "outputId": "710e8695-7b2a-400d-f60f-34e48eb395d9"
      },
      "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": 21,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.10/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",
            "/usr/local/lib/python3.10/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",
            "/usr/local/lib/python3.10/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",
            "/usr/local/lib/python3.10/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",
            "/usr/local/lib/python3.10/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",
            "/usr/local/lib/python3.10/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",
            "/usr/local/lib/python3.10/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",
            "/usr/local/lib/python3.10/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",
            "/usr/local/lib/python3.10/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",
            "/usr/local/lib/python3.10/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",
            "/usr/local/lib/python3.10/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",
            "/usr/local/lib/python3.10/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",
            "/usr/local/lib/python3.10/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",
            "/usr/local/lib/python3.10/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",
            "/usr/local/lib/python3.10/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",
            "/usr/local/lib/python3.10/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",
            "/usr/local/lib/python3.10/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",
            "/usr/local/lib/python3.10/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",
            "/usr/local/lib/python3.10/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",
            "/usr/local/lib/python3.10/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": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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TaFxsTUREJAWGIpmov66IiIiIWh5DkUxEh/sDYCgiIiKSCkORTNhHigrLqlFnskhcDRERUevDUCQTAb4a+Pt4QBCAghI+W42IiKilMRTJhEKh4GJrIiIiCTEUyUh0GNcVERERSYWhSEbsI0XnGIqIiIhaHEORjNhDUX5xJax83AcREVGLYiiSkbZtfKBWKVBrtOCCvlbqcoiIiFoVhiIZUauUaBfiCwDIK+IUGhERUUtiKJIZXoFGREQkDYYimYniFWhERESSYCiSmWg+A42IiEgSDEUyExVuC0UX9LWorjVJXA0REVHrwVAkM75eHgjWegLgaBEREVFLYiiSoahQTqERERG1NIYiGYoK52JrIiKilsZQJEPRfNwHERFRi2MokiH7vYoKSqpgsVolroaIiKh1YCiSodAgb3h6qGC2WFFYViN1OURERK0CQ5EMKRUKRIZdetwH72xNRETUIhiKZEq8szWfgUZERNQiGIpkKop3tiYiImpRDEUyxcd9EBERtSyGIpmKDPWDAoC+ygh9lVHqcoiIiNweQ5FMeWpUCAvyBsDF1kRERC2BoUjGuK6IiIio5TAUyRgf90FERNRyGIpkTBwp4mX5REREzY6hSMbsV6D9XloNk9kicTVERETuTZahaOfOnXjwwQeRmJiIlJQUTJw4EbW1teL+r776CsOGDUNiYiIGDx6M7du3Ox3DaDTitddeQ79+/ZCUlIRx48ZBp9O15Gk0WpC/J3y91LAKAs5fqJa6HCIiIrcmu1C0Zs0avPLKK8jIyMC6devw8ssvIzIyEhaLbaTk0KFDmDJlCpKSkpCZmYn09HS8+OKL2LNnj8NxFi9ejK1bt2LGjBlYsWIFjEYjnnzySVRUuM6VXAqFQpxCO8cr0IiIiJqVWuoC6tPpdFi5ciVWr16Ne+65R9w+ePBg8ec1a9agW7duePnllwEAffr0QV5eHpYvX477778fAFBYWIht27bhpZdewiOPPAIASExMRP/+/bFp0yZMmjSpBc+qcaLC/PHruYtcV0RERNTMZDVStGPHDkRGRjoEovqMRiO+/fZbMfzYZWRk4PTp08jPzwcAHDhwAFar1aFdYGAg+vXrh+zs7OY7gWbAy/KJiIhahqxGin766SfEx8dj9erV+PDDD1FRUYGuXbvihRdeQPfu3XHu3DmYTCbExsY6vC8uLg6AbaQpMjISOp0Obdq0QUBAgFO7bdu2NbpOtbrlsmRMOy0AIK+kEiqVAgqFosU++2apVEqH7yQ99om8sD/khf0hL3LoD1mFopKSEhw7dgwnT57ESy+9BG9vb/z973/H+PHjsXfvXuj1egCAVqt1eJ/9tX2/wWCAv7+/0/G1Wq3Y5lYplQoEBfk26hg3w8/fCyqlAtW1ZpgVSoQF+bTYZ98qrdZb6hLoCuwTeWF/yAv7Q16k7A9ZhSJBEFBdXY23334bHTt2BAB0794dAwYMwIYNG5CamipxhYDVKsBgaNkrwdqF+CKvuBI/nyxGj/jQFv3sm6FSKaHVesNgqIHFYpW6HAL7RG7YH/LC/pCX5uwPrda7QSNQsgpFWq0WgYGBYiACbGuBOnfujFOnTmHIkCEA4HQFmcFgAABxukyr1aKy0nkNjsFgcJpSuxVmc8v+4YkMtYWiM78b0C22TYt+9q2wWKwt/jui62OfyAv7Q17YH/IiZX/IaiK1Q4cO19xXV1eH6OhoeHh4ON1vyP7avtYoNjYWFy5ccJoq0+l0TuuRXEFUGB/3QURE1NxkFYr69++Pixcv4sSJE+K28vJy/PLLL+jSpQs0Gg1SUlLw73//2+F9WVlZiIuLQ2RkJAAgNTUVSqUSe/fuFdvo9XocOHAAaWlpLXMyTSgqnI/7ICIiam6ymj4bOHAgEhMTMW3aNMyYMQOenp5Yu3YtNBoNRo0aBQB45plnMHbsWCxcuBDp6en49ttvsWvXLrz11lvicdq2bYtHHnkEr7/+OpRKJcLDw/HOO+/A398fI0eOlOr0bpn9svziizWoqTPD21NW3UZEROQWZPW3q1KpxNq1a7FkyRIsWLAAJpMJvXr1wsaNGxEaaltg3KtXL6xYsQLLli3Dtm3b0K5dOyxevBjp6ekOx5o3bx58fX2xdOlSVFVVoUePHli/fv1Vr0qTO62PBgF+GugrjSgoqUKHyMaviyIiIiJHCkEQBKmLcCUWixVlZVUt/rlvbfkJP+tKMWZQPPr3iGzxz28ItVqJoCBflJdXcdGiTLBP5IX9IS/sD3lpzv4IDvZt0NVnslpTRNd2+RloXFdERETUHBiKXAQf90FERNS8GIpcRPSlK9DySyphtXLGk4iIqKkxFLmI8CAfaNRKGE1WFF+skbocIiIit8NQ5CKUSgUiQm3PXDtXVHGD1kRERHSzGIpcCNcVERERNR+GIhfCx30QERE1H4YiF8KRIiIioubDUORC7KGovKIOlTUmiashIiJyLwxFLsTbU42QAC8AQB4XWxMRETUphiIXEx3OdUVERETNgaHIxfBxH0RERM2DocjFcLE1ERFR82AocjH2UHT+QhXMFj7VmYiIqKkwFLmYkAAveHuqYLEK+L20WupyiIiI3AZDkYtRKBSICr20rohXoBERETUZhiIXxDtbExERNT2GIhcUFc7F1kRERE2NocgF1b8CTRAEiashIiJyDwxFLigixBcKBVBZY8LFSqPU5RAREbkFhiIXpPFQoW2wDwAgr5iLrYmIiJoCQ5GL4uM+iIiImhZDkYsSH/dRxFBERETUFBiKXBQf90FERNS0GIpclD0UFZVXo85kkbgaIiIi18dQ5KICfDXQ+nhAEICCkiqpyyEiInJ5DEUuSqFQXF5XxCvQiIiIGo2hyIXxcR9ERERNh6HIhfFxH0RERE2HociF2afP8osrYeXjPoiIiBqFociFtQ32gVqlQK3RggsXa6Quh4iIyKUxFLkwtUqJdiG+ADiFRkRE1FgMRS4umoutiYiImgRDkYvjna2JiIiaBkORi+Mz0IiIiJoGQ5GLs1+WX2qoRXWtSeJqiIiIXBdDkYvz9fJAG60nAE6hERERNQZDkRuw39n6HEMRERHRLZNVKNqxYwcSEhKcvt544w2Hdlu3bsXgwYORmJiIYcOGYd++fU7HqqiowNy5c9G7d28kJydj2rRpKC4ubqlTaVGRXGxNRETUaGqpC7iad999F/7+/uLr8PBw8efdu3dj/vz5mDx5Mvr06YOsrCxMmTIFGzduRFJSkthu+vTpOHXqFBYuXAhPT08sW7YMkyZNwvbt26FWy/K0b1k0QxEREVGjyTIddOnSBcHBwVfdt3z5cgwZMgTTp08HAPTp0wcnT57EqlWrkJmZCQD48ccfceDAAaxbtw6pqakAgJiYGGRkZGDv3r3IyMhokfNoKfbF1gUlVbBYrVApZTUASERE5BJc6m/PvLw8nDlzBunp6Q7bMzIykJOTA6PRCADIzs6GVqtFv379xDaxsbHo1KkTsrOzW7TmlhAa6A1PjQpmixWFpdVSl0NEROSSZDlSNHToUJSXl6Ndu3b4v//7P0ycOBEqlQo6nQ6AbdSnvri4OJhMJuTl5SEuLg46nQ4xMTFQKBQO7WJjY8VjNIZaLb8sGRXmh1P5ehSUVuP227SS1KBSKR2+k/TYJ/LC/pAX9oe8yKE/ZBWKQkNDMXXqVHTv3h0KhQJfffUVli1bhqKiIixYsAB6vR4AoNU6/qVvf23fbzAYHNYk2QUEBODYsWONqlGpVCAoyLdRx2gOd0QH4VS+HiX6Wsnr02q9Jf18csY+kRf2h7ywP+RFyv6QVSi6++67cffdd4uvU1NT4enpiffffx+TJ0+WsLLLrFYBBoP8pqjCA7wAACfPlqO8vEqSGlQqJbRabxgMNbBYrJLUQI7YJ/LC/pAX9oe8NGd/aLXeDRqBklUoupr09HT84x//wIkTJxAQEADAdrl9aGio2MZgMACAuF+r1aKwsNDpWHq9XmzTGGaz/P7wRITYRofOFlVIXp/FYpW8BnLEPpEX9oe8sD/kRcr+cKmJ1NjYWABwWhek0+ng4eGBqKgosV1ubi4EQXBol5ubKx7D3USG+kEBwFBlhL7KKHU5RERELkf2oSgrKwsqlQqdO3dGVFQU2rdvjz179ji16du3LzQaDQAgLS0Ner0eOTk5Ypvc3FwcP34caWlpLVp/S/HUqBAW7AMAyCuukLgaIiIi1yOr6bMJEyYgJSUFCQkJAIAvv/wSW7ZswdixY8XpsqlTp2LmzJmIjo5GSkoKsrKycPToUWzYsEE8TnJyMlJTUzF37lzMnj0bnp6eeOutt5CQkIBBgwZJcm4tISrMD0Vl1cgrqkTXmDZSl0NERORSZBWKYmJisH37dhQWFsJqtaJ9+/aYO3cuxowZI7YZOnQoampqkJmZibVr1yImJgYrV65EcnKyw7GWLVuGJUuWYMGCBTCbzUhNTcW8efPc7m7W9UWF+eHQr8W8szUREdEtUAhXLryh67JYrCgrk+bqrhs5cuoClm87iogQX7wyMaXFP1+tViIoyBfl5VVctCgT7BN5YX/IC/tDXpqzP4KDfRt09Zns1xRRw9mfgfZ7aTVMZovE1RAREbkWhiI3EuTvCV8vNayCgIIL8hzNIiIikiuGIjeiUCgQdWm0KK+I64qIiIhuBkORm4kOtz3ehIutiYiIbg5DkZsRR4oYioiIiG4KQ5GbsYeic8WVTnf0JiIiomtjKHIzt7XxhUqpQE2dGaWGWqnLISIichkMRW7GQ63EbW1sD4flFBoREVHDMRS5Ia4rIiIiunkMRW6Il+UTERHdPIYiNxQVzpEiIiKim8VQ5IbsI0XFF2tQU2eWuBoiIiLXwFDkhrQ+GgT6aQAA+SUcLSIiImoIhiI3FRXGO1sTERHdDIYiNxXNdUVEREQ3haHITfGyfCIiopvDUOSm7KEov7gSVisf90FERHQjDEVuKjzIBxq1EkazFUXl1VKXQ0REJHsMRW5KqVQgIpRTaERERA3FUOTGuK6IiIio4RiK3BhDERERUcMxFLkxhiIiIqKGYyhyY/ZQVF5Rh4pqo8TVEBERyRtDkRvz9lQjNNALAEeLiIiIboShyM3xcR9EREQNw1Dk5riuiIiIqGEYitxcNEMRERFRgzAUuTn7SNH5C1UwW6wSV0NERCRfDEVurk2AF7w91bBYBZy/UCV1OURERLLFUOTmFAoF1xURERE1AENRK8BQREREdGMMRa0AQxEREdGNMRS1AvVDkSAIEldDREQkTwxFrUBEiC+UCgUqa0y4WMnHfRAREV0NQ1EroPFQoW0bHwBAXnGFxNUQERHJE0NRK2GfQjtXxHVFREREV8NQ1EpwsTUREdH1MRS1EnzcBxER0fXJNhRVVVUhLS0NCQkJ+Pnnnx32bd26FYMHD0ZiYiKGDRuGffv2Ob2/oqICc+fORe/evZGcnIxp06ahuLi4pcqXHftIUVFZNeqMFomrISIikh/ZhqLVq1fDYnH+y3v37t2YP38+0tPTkZmZiaSkJEyZMgVHjhxxaDd9+nQcPHgQCxcuxBtvvIHc3FxMmjQJZrO5hc5AXgL8PKH18YAAIP8CR4uIiIiuJMtQdPr0aXz00UeYOnWq077ly5djyJAhmD59Ovr06YOXX34ZiYmJWLVqldjmxx9/xIEDB/DXv/4VGRkZuPfee/H222/jf//7H/bu3duSpyIrUeH+ADiFRkREdDWyDEWLFy/GyJEjERMT47A9Ly8PZ86cQXp6usP2jIwM5OTkwGi03YMnOzsbWq0W/fr1E9vExsaiU6dOyM7Obv4TkCkutiYiIro22YWiPXv24OTJk/jTn/7ktE+n0wGAU1iKi4uDyWRCXl6e2C4mJgYKhcKhXWxsrHiM1kgMRbwsn4iIyIla6gLqq6mpwauvvooZM2bAz8/Pab9erwcAaLVah+321/b9BoMB/v7+Tu8PCAjAsWPHGl2nWi27LNkgMbfZfk/5JZVQqhRQXhEaG0ulUjp8J+mxT+SF/SEv7A95kUN/yCoUrVmzBm3atMHDDz8sdSnXpFQqEBTkK3UZt8Rf6w0PtRK1RguMVgVuC2me89BqvZvluHTr2Cfywv6QF/aHvEjZH7IJRQUFBfjHP/6BVatWoaLC9iiK6upq8XtVVRUCAgIA2C63Dw0NFd9rMBgAQNyv1WpRWFjo9Bl6vV5sc6usVgEGQ3WjjiGliBBfnCmswM+/FcNLFdakx1aplNBqvWEw1MBisTbpsenWsE/khf0hL+wPeWnO/tBqvRs0AiWbUJSfnw+TyYSnnnrKad/YsWPRvXt3LF26FIBtzVBsbKy4X6fTwcPDA1FRUQBsa4dycnIgCILDuqLc3FzEx8c3ulaz2XX/8ESG+uFMYQXOnDcguUNIs3yGxWJ16d+RO2KfyAv7Q17YH/IiZX/IJhR16tQJH3zwgcO2EydOYMmSJVi0aBESExMRFRWF9u3bY8+ePRg4cKDYLisrC3379oVGowEApKWlYfXq1cjJycFdd90FwBaIjh8/jokTJ7bcSckQr0AjIiK6OtmEIq1Wi5SUlKvu69KlC7p06QIAmDp1KmbOnIno6GikpKQgKysLR48exYYNG8T2ycnJSE1Nxdy5czF79mx4enrirbfeQkJCAgYNGtQi5yNX0eEMRURERFcjm1DUUEOHDkVNTQ0yMzOxdu1axMTEYOXKlUhOTnZot2zZMixZsgQLFiyA2WxGamoq5s2bB7Xa5U65SUVeGikqNdSiqtYEXy8PiSsiIiKSB4UgCMKtvLGurg6bN29Gp06dcOeddzZ1XbJlsVhRVlYldRmN8pfVB1FqqMPsUclIiA5qsuOq1UoEBfmivLyK8/MywT6RF/aHvLA/5KU5+yM42LdBC61v+WYAnp6e4jPFyLVEhdnu4XSOU2hERESiRt0h6Y477kBBQUFT1UIthIutiYiInDUqFM2YMQObNm3CN99801T1UAvg4z6IiIicNWrV8YYNGxAYGIgJEyYgMjISkZGR8PT0dGijUCiwZs2aRhVJTSvq0hVoBReqYLFaoVLyFvdERESNCkUnT54EANx2222wWCw4e/asU5srH8pK0gsN9IanRoU6owWFpdWICHV+zhwREVFr06hQ9NVXXzVVHdSClAoFokL9cKpAj7ziSoYiIiIiNHJNEbku+7oiXoFGRERk0yR3Mvzuu+/wn//8B+fPnwcAtGvXDn/4wx/Qu3fvpjg8NQNegUZEROSoUaHIaDTi+eefxxdffAFBEKDVagHYnlq/fv163HfffVi6dCk8PHjXZLmJ4uM+iIiIHDRq+mzVqlX4/PPPMW7cOBw4cADfffcdvvvuOxw8eBDjx4/H3r17sWrVqqaqlZpQZIgfFAAMVUboK+ukLoeIiEhyjQpF//rXvzBixAjMmjULISEh4vY2bdrgL3/5Cx588EH885//bHSR1PQ8NSqEBfsA4GgRERER0MhQVFJSgm7dul1zf7du3VBSUtKYj6BmxHVFRERElzUqFLVt2xbffffdNfd///33aNu2bWM+gppRNEMRERGRqFGh6MEHH8Rnn32GBQsWQKfTwWKxwGq1QqfT4aWXXsKePXswYsSIpqqVmhgvyyciIrqsUVefTZ48GXl5ediyZQu2bt0K5aXHRVitVgiCgBEjRmDy5MlNUig1PXsoKiythslsgYdaJXFFRERE0mlUKFKpVHj11Vfx5JNPIjs7GwUFBQCAiIgIpKWloWPHjk1SJDWPIH9P+Hl7oLLGhIILVWjfVit1SURERJK55VBUU1ODxx9/HH/84x/x2GOPMQC5IIVCgagwP5w4W468okqGIiIiatVueU2Rt7c38vPz+cBXF8d1RURERDaNWmh9991348CBA01VC0mAl+UTERHZNCoUPfvsszhz5gz+8pe/4NChQygqKsLFixedvki+6ociQRAkroaIiEg6jVpoPWTIEADAqVOnsGvXrmu2O3HiRGM+hppRuxBfqJQK1NSZUWqoRUiAt9QlERERSaJRoehPf/oT1xS5OLVKidva+CK/pBJ5RZUMRURE1GrdcigymUy47777EBgYyLtWu7ioMD9bKCquRHJ8qNTlEBERSeKW1xQplUo8/PDD2Lt3b1PWQxKIDudiayIiolsORSqVCu3atYPRaGzKekgCly/Lr5C4EiIiIuk06uqz0aNHY8uWLbzCzMXZQ1HJxVrU1JklroaIiEgajVpobbVaodFocN9992Hw4MGIiIiAl5eXQxuFQoEnn3yyMR9DzczfR4Mgf0+UV9Qhv6QSd0QGSl0SERFRi2tUKHrttdfEn7dt23bVNgxFriEqzA/lFXXIK2YoIiKi1qlRoejLL79sqjpIYlFhfjh6uhTnirjYmoiIWqebDkVHjx5FdHQ0AgMDERERcd22+fn5OHTo0A3bkfT4uA8iImrtbnqh9aOPPoqvv/5afH3x4kV0794d3333nVPbH374AS+88ELjKqQWYQ9FBSWVsFr5uA8iImp9bjoUXfl8LEEQUFdXB4vF0mRFUcsLD/KBRq2E0WxFUXm11OUQERG1uEZdkk/uQ6lUICKUU2hERNR6MRSRiOuKiIioNWMoIhEf90FERK3ZLV2SX1BQgF9++QUAUFFhezTE2bNnodVqHdrl5+c3sjxqSRwpIiKi1uyWQtHbb7+Nt99+22HbokWLnNoJggCFQnFrlVGLi7y0pqi8og4V1Ub4+2gkroiIiKjl3HQoWrJkSXPUQTLg7alGaKAXSi7WIq+4Ep3bB0tdEhERUYu56VA0YsSI5qiDZCI6zJ+hiIiIWiVZLbTev38/Ro8ejT59+qBr16649957sWTJEnHdkt1XX32FYcOGITExEYMHD8b27dudjmU0GvHaa6+hX79+SEpKwrhx46DT6VrqVFyWfV0RH/dBREStjaxC0cWLF9GtWzcsWrQI69atw7hx4/DJJ5/gueeeE9scOnQIU6ZMQVJSEjIzM5Geno4XX3wRe/bscTjW4sWLsXXrVsyYMQMrVqyA0WjEk08+6RSwyBEXWxMRUWvVqAfCNrXhw4c7vE5JSYFGo8H8+fNRVFSE8PBwrFmzBt26dcPLL78MAOjTpw/y8vKwfPly3H///QCAwsJCbNu2DS+99BIeeeQRAEBiYiL69++PTZs2YdKkSS17Yi4k6tJl+b+XVsFssUKtklVuJiIiajay/xsvMDAQAGAymWA0GvHtt9+K4ccuIyMDp0+fFm8BcODAAVitVod2gYGB6NevH7Kzs1usdlfURusFH081LFYB5y9USV0OERFRi5HVSJGdxWKB2WzGqVOnsGrVKgwYMACRkZE4deoUTCYTYmNjHdrHxcUBAHQ6HSIjI6HT6dCmTRsEBAQ4tdu2bVuj61OrZZ8lGyUq3A//O3cRBReqEBsRcOM3XKK6NKqk4uiSbLBP5IX9IS/sD3mRQ3/IMhT1798fRUVFAIC7774bS5cuBQDo9XoAcLpJpP21fb/BYIC/v7/TcbVardjmVimVCgQF+TbqGHJ3R3QQ/nfuIor1dbd0rlqtdzNURY3BPpEX9oe8sD/kRcr+kGUoWrt2LWpqanDq1CmsWbMGkydPxvr166UuCwBgtQowGNz7KfLhgV4AgN/OlaG8vOFTaCqVElqtNwyGGlgs1uYqj24C+0Re2B/ywv6Ql+bsD63Wu0EjULIMRR07dgQAJCcnIzExEcOHD8fnn3+ODh06AIDTFWQGgwEAxOkyrVaLykrnq6cMBoPTlNqtMJvd+w9PRIhtdOhcUSVMJstN35XcYrG6/e/I1bBP5IX9IS/sD3mRsj9kP5GakJAADw8PnDt3DtHR0fDw8HC635D9tX2tUWxsLC5cuOA0VabT6ZzWI5GziBBfKBUKVNaYUF5RJ3U5RERELUL2oeinn36CyWRCZGQkNBoNUlJS8O9//9uhTVZWFuLi4hAZGQkASE1NhVKpxN69e8U2er0eBw4cQFpaWovW74o81Cq0beMDgPcrIiKi1kNW02dTpkxB165dkZCQAC8vL/z6669Yt24dEhISMHDgQADAM888g7Fjx2LhwoVIT0/Ht99+i127duGtt94Sj9O2bVs88sgjeP3116FUKhEeHo533nkH/v7+GDlypFSn51Kiw/xw/kIV8oor0b1DiNTlEBERNTtZhaJu3bohKysLa9euhSAIiIiIwB//+EdMmDABGo3tie29evXCihUrsGzZMmzbtg3t2rXD4sWLkZ6e7nCsefPmwdfXF0uXLkVVVRV69OiB9evXX/WqNHIWFeaH/x4vwjmOFBERUSuhEARBkLoIV2KxWFFW5v43NTymK8WbW35CeLAPljzVp0HvUauVCAryRXl5FRctygT7RF7YH/LC/pCX5uyP4GDfBl19Jvs1RSSNqHDbiFpxWTXqjBaJqyEiImp+DEV0VQG+Gmh9NRAA5F/gFBoREbk/hiK6pqgw28Nh84oYioiIyP0xFNE1iaGIi62JiKgVYCiia4pmKCIiolaEoYiuSRwpKqmElRcpEhGRm2Moomtq28YHapUSdUYLSi7WSF0OERFRs2IoomtSKZXiw2G52JqIiNwdQxFdV1Q41xUREVHrwFBE18Ur0IiIqLVgKKLrunwFWoXElRARETUvhiK6rshLoajUUIeqWpPE1RARETUfhiK6Ll8vD7TRegEA8jmFRkREboyhiG7Ivq7oHK9AIyIiN8ZQRDfExdZERNQaMBTRDUXzsnwiImoFGIrohuwjRQUXqmC2WCWuhoiIqHkwFNENhQR6w1OjgtliRWFZtdTlEBERNQuGIrohpUKBqFBOoRERkXtjKKIG4eM+iIjI3TEUUYPwCjQiInJ3DEXUIGIoKuLjPoiIyD0xFFGDRIb4QQHAUG2CvrJO6nKIiIiaHEMRNYinRoXwYB8AnEIjIiL3xFBEDSY+7oOhiIiI3BBDETUYF1sTEZE7YyiiBuPjPoiIyJ0xFFGDRYX5AwAKS6thNFkkroaIiKhpMRRRgwX6aeDn7QGrIKDgQpXU5RARETUphiJqMIVCwXVFRETkthiK6KYwFBERkbtiKKKbwlBERETuiqGIbkr9UCQIgsTVEBERNR2GIrop7UJ8oVIqUFNnRqm+VupyiIiImgxDEd0UtUqJdiG+ADiFRkRE7oWhiG4a1xUREZE7Yiiim8ZnoBERkTtiKKKbFi2OFFVIXAkREVHTkVUo+uyzz/DMM88gLS0NSUlJGD58OLZt2+Z0ldPWrVsxePBgJCYmYtiwYdi3b5/TsSoqKjB37lz07t0bycnJmDZtGoqLi1vqVNxaVLjtcR8lF2tRU2eWuBoiIqKmIatQ9N5778Hb2xtz5szBmjVrkJaWhvnz52PVqlVim927d2P+/PlIT09HZmYmkpKSMGXKFBw5csThWNOnT8fBgwexcOFCvPHGG8jNzcWkSZNgNvMv8cby8/ZAkL8nAK4rIiIi96GWuoD61qxZg+DgYPF13759cfHiRaxfvx7PPvsslEolli9fjiFDhmD69OkAgD59+uDkyZNYtWoVMjMzAQA//vgjDhw4gHXr1iE1NRUAEBMTg4yMDOzduxcZGRktfm7uJirMD+UVdcgrrkR8VKDU5RARETWarEaK6gciu06dOqGyshLV1dXIy8vDmTNnkJ6e7tAmIyMDOTk5MBqNAIDs7GxotVr069dPbBMbG4tOnTohOzu7eU+ileAVaERE5G5kNVJ0NYcPH0Z4eDj8/Pxw+PBhALZRn/ri4uJgMpmQl5eHuLg46HQ6xMTEQKFQOLSLjY2FTqdrdE1qtayypCTa36YFAOSXVIq/D5XK8TtJj30iL+wPeWF/yIsc+kPWoejQoUPIysrC7NmzAQB6vR4AoNVqHdrZX9v3GwwG+Pv7Ox0vICAAx44da1RNSqUCQUG+jTqGO+h6RygAIL+kCtoAH6iUlwOoVustVVl0DewTeWF/yAv7Q16k7A/ZhqLCwkLMmDEDKSkpGDt2rNTliKxWAQZDtdRlSM5bpYBGrYTRZMGvp0tsj/9QKaHVesNgqIHFYpW6RALYJzLD/pAX9oe8NGd/aLXeDRqBkmUoMhgMmDRpEgIDA7FixQoolbYTCQgIAGC73D40NNShff39Wq0WhYWFTsfV6/Vim8Ywm/mHBwAiw/ygO2/Amd8NCAu8nOwtFit/RzLDPpEX9oe8sD/kRcr+kN1Eam1tLZ5++mlUVFTg3XffdZgGi42NBQCndUE6nQ4eHh6IiooS2+Xm5jrd3yg3N1c8BjUeF1sTEZE7kVUoMpvNmD59OnQ6Hd59912Eh4c77I+KikL79u2xZ88eh+1ZWVno27cvNBoNACAtLQ16vR45OTlim9zcXBw/fhxpaWnNfyKthPi4jyKGIiIicn2ymj5btGgR9u3bhzlz5qCystLhhoydO3eGRqPB1KlTMXPmTERHRyMlJQVZWVk4evQoNmzYILZNTk5Gamoq5s6di9mzZ8PT0xNvvfUWEhISMGjQIAnOzD1F8XEfRETkRmQVig4ePAgAePXVV532ffnll4iMjMTQoUNRU1ODzMxMrF27FjExMVi5ciWSk5Md2i9btgxLlizBggULYDabkZqainnz5kGtltUpu7TIUFsoulhphKHaiGCtl8QVERER3TqFcOXCG7oui8WKsrIqqcuQjTl/z0HxxRo8PzIJ3TuEICjIF+XlVVy0KBNqtZJ9IiPsD3lhf8hLc/ZHcLBvg64+k9WaInI94hQa1xUREZGLYyiiRokK5xVoRETkHhiKqFF4WT4REbkLhiJqFHso+r20CibOyRMRkQtjKKJGaaP1go+nGhargPMXuACdiIhcF0MRNYpCoah3E0fer4iIiFwXQxE1mhiKuK6IiIhcGEMRNZoYigo5UkRERK6LoYgazX5Z/rniSqeH8BIREbkKhiJqtIgQXygVClTVmFCqr5W6HCIiolvCUESN5qFW4bY2PgCA3PN6iashIiK6NQxF1CTs64p0DEVEROSiGIqoSdjXFeWeN0hcCRER0a1hKKImYR8pOsORIiIiclEMRdQkosL8AQDnL1ShzmiRuBoiIqKbx1BETSLAV4MAXw0EgQ+HJSIi18RQRE0mOtw2WvTpAR2qak0SV0NERHRzGIqoyQzqHQW1SomfTpVi0frvkfs7F10TEZHrYCiiJtO9Qwhen5qK0EBvXNDX4m8fHsbnh/J4l2siInIJDEXUpO6ICsLLE3ujZ3woLFYBH3/xG1bvPIZqTqcREZHMMRRRk/P18sCzI7risYF3QKVU4PDJEix673ucKeR0GhERyRdDETULhUKB+3pF4YXRPRES4IWSi7bptC8P53M6jYiIZImhiJpVbDstXhp3J5LvCIHZImDj5yex5tNfUF1rlro0IiIiBwxF1Ox8vTww5aFEjLzXNp126NdivPze9zhbWCF1aURERCKGImoRCoUCg+6MwpzRPdBG64niizX464eHsO8HTqcREZE8MBRRi4prF4CXxvVGUgfbdNqHe0/inX/+gpo6TqcREZG0GIqoxfl5e2Dqw4l4dEAHqJQKfHfCNp12rojTaUREJB2GIpKEQqHA4N7RmP14DwRrPVFUXoPFHxzGf34s4HQaERFJgqGIJNUhIgALx/VGt7g2MFus+ODf/8Pafx3ndBoREbU4hiKSnJ+3B6Y90g1/7B8HpUKBb48X4eX3DyGvuFLq0oiIqBVhKCJZUCoUSE+5HbMfT0aQvyeKyqqx+INDyP7pPKfTiIioRTAUkazcERmIhePuRGJsG5jMVrz32a94d9dx1Bo5nUZERM2LoYhkx99Hg+f+2A0P3xMLpUKBnF+K8Mr7h5Bfwuk0IiJqPgxFJEtKhQJD+rbHrFHJCPTT4PfSaix+/xC+Pnpe6tKIiMhNMRSRrMVHBWLh+N7oGhMMo9mK9Vm/Yt2u46gzWqQujYiI3AxDEcme1keD6f/XHQ+lxUKhAA4eK8QrHxxCwYUqqUsjIiI3wlBELkGpUGDoXe0x67FkBPhpcP5CFV55/3sc/Pl3qUsjIiI3wVBELiUhOgiLxvVGl/ZBMJqsWLf7BP6x+wTqTJxOIyKixpFVKDp79iwWLFiA4cOHo3Pnzhg6dOhV223duhWDBw9GYmIihg0bhn379jm1qaiowNy5c9G7d28kJydj2rRpKC4ubu5ToBag9dVgxqNJGHF3DBQK4MDPv2Px+4dwntNpRETUCLIKRb/99hv279+P22+/HXFxcVdts3v3bsyfPx/p6enIzMxEUlISpkyZgiNHjji0mz59Og4ePIiFCxfijTfeQG5uLiZNmgSzmfe7cQdKhQIP9IvBzJHJCPDVoOBCFV55/xByjhVKXRoREbkohSCj2wVbrVYolbacNmfOHBw7dgy7du1yaDN48GB07doVS5cuFbeNHDkS/v7+yMzMBAD8+OOPGDlyJNatW4fU1FQAgE6nQ0ZGBt58801kZGTcco0WixVlZRyRuBq1WomgIF+Ul1fBbLa22Ofqq4xY+89fcOJsOQAgrfttGDUwHhoPVYvVIFdS9QldHftDXtgf8tKc/REc7AuV6sbjQLIaKbIHomvJy8vDmTNnkJ6e7rA9IyMDOTk5MBqNAIDs7GxotVr069dPbBMbG4tOnTohOzu76QsnSQX4avD8o0l4MDUGCgDZP/2OxR8cwu+lDK9ERNRwsgpFN6LT6QAAMTExDtvj4uJgMpmQl5cntouJiYFCoXBoFxsbKx6D3ItSqcCw1BjMHJkEra8G+SVVePm9Q/jvL5xOIyKihlFLXcDN0Ov1AACtVuuw3f7avt9gMMDf39/p/QEBATh27Fij61CrXSpLthj70GRDhiibS2KHECyelII1O4/hxNlyrP3XcfyWr8fjg1rndJoc+oQuY3/IC/tDXuTQHy4ViuRAqVQgKMhX6jJkTav1lvTzg4J8sWTK3di093/Y/MX/sO/HApwpqsCcsXeiXaifpLVJReo+IUfsD3lhf8iLlP3hUqEoICAAgO1y+9DQUHG7wWBw2K/ValFY6DxtotfrxTa3ymoVYDBUN+oY7kqlUkKr9YbBUAOLRfpFixkpUYgO9cGaT44h97wBz735H4wf0gl9urSVurQWI7c+ae3YH/LC/pCX5uwPrda7QSNQLhWKYmNjAdjWDNl/tr/28PBAVFSU2C4nJweCIDisK8rNzUV8fHyj6+BVCtdnsVhl8zvqGB2EheN6Y+0/f8H/8i5i9c5jOHGmHCPv7QAPdeuZTpNTnxD7Q27YH/IiZX+41ERqVFQU2rdvjz179jhsz8rKQt++faHRaAAAaWlp0Ov1yMnJEdvk5ubi+PHjSEtLa9GaSXpB/p6Y+VgSht51OxQA9v1YgL9+eBhF5RzxIyKiy2Q1UlRTU4P9+/cDAAoKClBZWSkGoN69eyM4OBhTp07FzJkzER0djZSUFGRlZeHo0aPYsGGDeJzk5GSkpqZi7ty5mD17Njw9PfHWW28hISEBgwYNkuTcSFoqpRIPpcUhPjIQa/91HOeKKrFo/fcYl9EJd3YMk7o8IiKSAVndvDE/Px/33nvvVfd98MEHSElJAWB7zEdmZibOnz+PmJgY/PnPf0b//v0d2ldUVGDJkiX4/PPPYTabkZqainnz5iE8PLxRNfLmjdfmKjdCK6+owzufHsPJfNvVigN6RODRAXfAww2vKnSVPmkt2B/ywv6QFzncvFFWocgVMBRdmyv9D8ZiteKTr3OxO+csAOD2tv545sGuCAt0r6tQXKlPWgP2h7ywP+RFDqHI/f5pTNQAKqUSD98Th+l/7A4/bw+cLazAovXf4dCvfGgwEVFrxVBErVq3uDZYOO5OdIgMQE2dBas/OYaPPj8JE//VSETU6jAUUasXrPXCrMeSkd4nGgDwxeF8LNlwGDnHClFcXg3OMBMRtQ6yuvqMSCpqlRJ//EMHxEcG4t1dx3GmsAKZu44DAPx9PBDXLgBxEVrEtgtAzG3+8NLwjw4Rkbvh/9mJ6uneIQSLxvfG54fycKpAj7OFFaioNuHIqQs4cuoCAEChAKJC/RAbEYC4dlrERQQgPMjb6QHERETkWhiKiK4QrPXCowPuAACYzFacK6rA6fMGnC7Q4/R5PcoMdThXXIlzxZX4z48FAAA/bw/EttOKISnmNi28PfnHi4jIlfD/2kTX4aFWIi4iAHERAcCdtsfIlFfUiQHp9HkDzvxegcoaE46eLsXR06UAAAWAiFBf23svTb2FB/tAydEkIiLZYigiuklB/p7o1TEMvS7dCdtsseJcUaUtJBXocbrAgFJDLfJLqpBfUoX9R84DAHy91IhtF+AwmuTjxT+CRERywf8jEzWSWqVEbDstYttpcV8v22jSxco6nC4wiEHpTGEFqmrN+FlXip91l0eT2oX4Ii5Ci7h2AYiNCMBtbTiaREQkFYYiomYQ6OeJngmh6JkQCsA2mpRXXAndpbVJpwr0uKCvRcGFKhRcqEL2T78DAHw81WLA6hARgNh2Wvh4eUh5KkRErQZDEVELUKuUiLlNi5jbtLi3ZyQAQF9lhK5Aj1Pn9dAVGJBbaEB1nRnHcstwLLdMfO9tbXwQFxEghqR2Ib4cTSIiagYMRUQSCfDVIDk+FMnxttEki9WK/OIqh7VJxRdr8HtpNX4vrcaBo7bRJG9PFWJvs90zKe5SUPLz5mgSEVFjMRQRyYRKqcTtbf1xe1t/DOhhG00yVBuhq7c2Kff3CtTUWfDLmXL8cqZcfG/bYB9xbVJcRAAiQnyhVHI0iYjoZjAUEcmY1keDpDtCkHRHCADbaFJBSdXl+yYV6FFUXoPCsmoUllXj4M+FAABPjW00qUNkAGIjg+Cpso1MBft7wVOjkvKUiIhki6GIyIWolEpEh/sjOtwf/ZMjAAAV1UbbAu7ztik33e8G1BktOHG2HCfOlgM443AMH081grSeCPb3QpC/J4L9PW3ftbbXQf6evPEkEbVK/D8fkYvz99Gge4cQdO9gG02yWgUUXLCtTTpbWAFDtQlFZdUoNdSizmhBdZ0Z1SVmFJRUXfOY3p4qMTTVD0z1AxSDExG5G/5fjcjNKJUKRIX5ISrMD2q1EkFBvigvr4LZbEVNnRllFXUoN9TavlfUobyiFmUG289lFXWoqTOjps6Cgjrb7QKuxUujuhyUtF5OI07Bl0ac+Ew4InIVDEVErYi3pxoRnmpEhPhes01NnflSWKpDWUWt7bvhcoAqr6hDVa0ZtUaLeGXctXh6qBCs9RRHnIL8vRCstY842cKTrxeDExHJA0MRETnw9lTD21ONdtcJTrXGy8HJFppqxZEm++uqWjPqTDcOThoPpS0siSNNlwNT8KWRJwYnImoJDEVEdNO8NGrc1kaN29pcOzjVmSy4eCkgldULUOX1tlXWmGA0WVFUVo2ismsHJw+1ElofD/h6e8Df2/5dA19vNfy8PeDn4wG/K7Z5eqgYpIjopjAUEVGz8PRQITzYB+HBPtdsYzRZUF5Zh3LD5ek625qny9N1hmoTTGYrSg11KDXUNfjz1Sol/LzV8PPW2L77aGwBqv42b8dt3p4MUkStGUMREUlG46FCeJAPwoOuHZxMZgvKK42orDahssaIyhoTKmvMl342o7Lavu3yl9kiwGyx4mKlERcrjQ2uR6VUwNfb41JQ8rgiRF2x/dLolI+Xmo9dIXITDEVEJGseahXCAr0RFujdoPaCIKDOZHEKSrZQdfmrqsaEinrfjSYrLFYBhiojDFUND1IKBeDrdXlq72rBydfLA/4+Hgjw08CqVKKuzgyVQsG7jhPJDEMREbkVhUIBL40aXho1QgIaFqQA24hUZY0ZFdVGp8DkFKKqTaiqNaGmzgJBgBi0im6yVo1aCS+NCp4aFbw06kvfVfDyuLzN69I2z0vbvOu18/RQwctTLbbXqJWc/iNqBIYiIiLYRqSC/G33Xmoos8WKqitHpK42OlV76edaM2rqzLBaBQCA0WyF0WwFqk1Ncg4KBS6FKLUtMF0Rnhy22UOXh8o5mHmo4OVpe59apWyS2ohcAUMREdEtUquUCPDzRIBfw4KUWq1EYKAPii9UoKrahFqjBXVGC2pNFtQazbafxS/bLQ3sr+vE77Z7RNWa6m0zWQAAggDU1FlQU2dp0nO8HKxUYojSXBqd8vSwfWk8VPD0UIqvPe1txC/bPs2l93BUi+SIoYiIqAUpFApo1CoofRTwv/b68ptiFQTUXQpHlwOUWQxMDkHLHsLq7Pscw5h9m9liG80yW6yorLGisqZpRrPsFIAYpDQel0e0NPVClX2fZ/0vjQqa+uHLHso0l8OXxkPFxe90SxiKiIhcnFKhEG+62VTMFqtjwKo3MmUbxbKizmiB0WQLUpe/rLZtxsvbjJe215ksMJmtAAABEPcDTRu4ANt6rSsDlkPoujTypfXzgtlkhlKhgEqlgFqlhEp56ful12qVEmqlbb/q0s/27Vd9j1IJ9aXtXEzvWhiKiIjIie0+T0r4eXs06XGtVqFeULoclupMFhiNjuGq7mrhynhF+DLV328VP8e+XqupR7hulkIBqOqFpPqhSSWGLef9YiC7yv76x7PvV6kU4hWNqkvblArbz/Zt4r6rbLu8T3l5W/33qxStYvSNoYiIiFqMUtn0o1p2VkGAqV7Icgxb1isClG3USqlWoaraCJPZCrPFCovFKt7nymIVLr+22r5fb7/FIsByaRG9nSDYRt3MFgBourVeUlAANwxYSqXycqBS1duvuHEoU6uUiIkIxB+SbpPsHBmKiIjILSgVCttUmUbVoPZqtRJBQb4oL6+C2Wy98RsawCoIsFqFS0Ho6qHKcpX9Fqtj2HLYb70ijNULYfWPa7XaQpnFaqvBcqkWW3gTYBXs+y63dXqP1TnY2QnAdfc3hf1HzqPz7YEI0Xo122dcD0MRERFRE1EqFFBemtpyZfZwZx/9uhyobAGufoi6XsASvwuXA+GVgc1aL2hFtwtAeJA3LJbmC17Xw1BEREREDi6Hu5b7zPojd7ZxqZbn2lGWiIiIqIkwFBERERGBoYiIiIgIAEMREREREQCGIiIiIiIADEVEREREANw8FJ0+fRrjxo1DUlIS+vXrh9dffx1Go1HqsoiIiEiG3PY+RXq9Hk888QTat2+PFStWoKioCK+++ipqa2uxYMECqcsjIiIimXHbULRp0yZUVVVh5cqVCAwMBABYLBYsWrQITz/9NMLDw6UtkIiIiGTFbafPsrOz0bdvXzEQAUB6ejqsVisOHjwoXWFEREQkS247UqTT6fDwww87bNNqtQgNDYVOp2vUsdVqt82SjaK69KwflYs/88edsE/khf0hL+wPeZFDf7htKDIYDNBqtU7bAwICoNfrb/m4SqUCQUG+jSnN7Wm13lKXQFdgn8gL+0Ne2B/yImV/uG0oai5WqwCDoVrqMmRJpVJCq/WGwVADi8UqdTkE9oncsD/khf0hL83ZH1qtd4NGoNw2FGm1WlRUVDht1+v1CAgIuOXjKpUK/qviBnx9PaUuga7APpEX9oe8sD/kpTn6Q6lUNKid24ai2NhYp7VDFRUVKCkpQWxs7C0fV6FQQKVq2C+3teL8vPywT+SF/SEv7A95kbI/3Pa/hLS0NHzzzTcwGAzitj179kCpVKJfv34SVkZERERypBAEQZC6iOag1+sxZMgQxMTE4OmnnxZv3vjAAw/w5o1ERETkxG1DEWB7zMcrr7yCH3/8Eb6+vhg+fDhmzJgBjUYjdWlEREQkM24dioiIiIgaym3XFBERERHdDIYiIiIiIjAUEREREQFgKCIiIiICwFBEREREBIChiIiIiAgAQxERERERAIYiIiIiIgAMRUREREQAGIqoCXz22Wd45plnkJaWhqSkJAwfPhzbtm0Db5YuD1VVVUhLS0NCQgJ+/vlnqctptXbu3IkHH3wQiYmJSElJwcSJE1FbWyt1Wa3Sl19+iT/+8Y9ITk5GamoqnnvuOeTl5UldVqtw9uxZLFiwAMOHD0fnzp0xdOjQq7bbunUrBg8ejMTERAwbNgz79u1rkfoYiqjR3nvvPXh7e2POnDlYs2YN0tLSMH/+fKxatUrq0gjA6tWrYbFYpC6jVVuzZg1eeeUVZGRkYN26dXj55ZcRGRnJfpHAt99+iylTpqBDhw5YtWoV5s6di19//RXjx49nSG0Bv/32G/bv34/bb78dcXFxV22ze/duzJ8/H+np6cjMzERSUhKmTJmCI0eONH+BAlEjlZaWOm2bN2+e0KNHD8FisUhQEdmdOnVKSEpKEj7++GMhPj5eOHr0qNQltTqnT58WOnfuLPznP/+RuhQSBGH+/PnCgAEDBKvVKm7LyckR4uPjhe+//17CylqH+n8nzJ49WxgyZIhTm0GDBgl//vOfHbY9+uijwsSJE5u9Po4UUaMFBwc7bevUqRMqKytRXV0tQUVkt3jxYowcORIxMTFSl9Jq7dixA5GRkbjnnnukLoUAmM1m+Pr6QqFQiNv8/f0BgFP+LUCpvH7syMvLw5kzZ5Cenu6wPSMjAzk5OTAajc1ZHqfPqHkcPnwY4eHh8PPzk7qUVmvPnj04efIk/vSnP0ldSqv2008/IT4+HqtXr0bfvn3RtWtXjBw5Ej/99JPUpbVKDz30EE6fPo2NGzeioqICeXl5ePPNN9G5c2f06NFD6vJaPZ1OBwBO/5CLi4uDyWRq9rVfDEXU5A4dOoSsrCyMHz9e6lJarZqaGrz66quYMWMGg6nESkpKcODAAXz66ad46aWXsGrVKigUCowfPx6lpaVSl9fq9OrVCytXrsTSpUvRq1cvDBw4EKWlpcjMzIRKpZK6vFZPr9cDALRarcN2+2v7/ubCUERNqrCwEDNmzEBKSgrGjh0rdTmt1po1a9CmTRs8/PDDUpfS6gmCgOrqarz99tu4//77cc8992DNmjUQBAEbNmyQurxW54cffsCsWbPwf//3f3j//ffx9ttvw2q14qmnnuJCa4Ja6gLIfRgMBkyaNAmBgYFYsWLFDeeOqXkUFBTgH//4B1atWoWKigoAENd2VVdXo6qqCr6+vlKW2KpotVoEBgaiY8eO4rbAwEB07twZp06dkrCy1mnx4sXo06cP5syZI25LSkrCH/7wB3z66ad49NFHJayOAgICAAAVFRUIDQ0VtxsMBof9zYWhiJpEbW0tnn76aVRUVGDz5s3iwkVqefn5+TCZTHjqqaec9o0dOxbdu3fHli1bJKisderQoQPOnTt31X11dXUtXA2dPn0a9957r8O2tm3bIigo6Jr9RC0nNjYWgG1tkf1n+2sPDw9ERUU16+czFFGjmc1mTJ8+HTqdDhs3bkR4eLjUJbVqnTp1wgcffOCw7cSJE1iyZAkWLVqExMREiSprnfr3748dO3bgxIkT6NSpEwCgvLwcv/zyC5588klpi2uF2rVrh+PHjztsKygoQHl5OSIiIiSqiuyioqLQvn177NmzBwMHDhS3Z2VloW/fvtBoNM36+QxF1GiLFi3Cvn37MGfOHFRWVjrcYKtz587N/h8xOdJqtUhJSbnqvi5duqBLly4tXFHrNnDgQCQmJmLatGmYMWMGPD09sXbtWmg0GowaNUrq8lqdkSNH4m9/+xsWL16MAQMG4OLFi+IavCsvA6emV1NTg/379wOwhdHKykrs2bMHANC7d28EBwdj6tSpmDlzJqKjo5GSkoKsrCwcPXq0RdbgKQTemIEaacCAASgoKLjqvi+//BKRkZEtXBFd6dtvv8XYsWOxbds2jhRJoKysDEuWLMG+fftgMpnQq1cvvPDCC+jQoYPUpbU6giBg06ZN+Pjjj5GXlwdfX18kJSVhxowZ17zDMjWd/Px8p+lLuw8++ED8B93WrVuRmZmJ8+fPIyYmBn/+85/Rv3//Zq+PoYiIiIgIvCSfiIiICABDEREREREAhiIiIiIiAAxFRERERAAYioiIiIgAMBQRERERAWAoIiIiIgLAUEREREQEgKGIiNzA0aNHMXLkSCQlJSEhIQEnTpy45WPl5+cjISEBO3bsaMIKicgVMBQRUYPs2LEDCQkJSExMRFFRkdP+MWPGYOjQoS1el8lkwvTp03Hx4kW88MILeP3119GuXbsWr6OhTp06hRUrViA/P1/qUojoCgxFRHRTjEYj1q5dK3UZonPnzqGgoAATJkzAo48+iuHDhyMgIEDqsq7p1KlTWLly5TWfF0hE0mEoIqKb0qlTJ2zZsuWqo0VSKCsrAwD4+/tLXIm0qqurpS6ByOUxFBHRTXn66adhtVqRmZl5w7ZmsxmrVq3CwIED0bVrVwwYMABvvvkmjEZjgz4rJycHo0aNQlJSEnr16oVnnnkGp0+fFvfPmTMHo0ePBgA899xzSEhIwJgxY657TIPBgL/97W8YMGAAunbtirS0NMyaNUsMV1czZsyYqx53zpw5GDBggMO23bt346GHHkJycjJ69OiBBx54AO+//z4A2xTkc889BwAYO3YsEhISkJCQgG+//VZ8//79+8VzTk5OxlNPPYXffvvN6XOTk5Nx7tw5TJo0CcnJyZg5cyYA4MyZM5g6dSr69euHxMREpKWlYcaMGaioqLju74WIALXUBRCRa4mMjMTw4cOxZcsWTJo0CeHh4ddsO2/ePOzcuRODBw/GuHHjcPToUbzzzjs4ffo0Vq1add3P+eabbzBp0iRERkZiypQpqK2txYYNG/DYY49hx44diIyMxKOPPorw8HD8/e9/x5gxY5CYmIiQkJBrHrOqqgqPP/44Tp8+jYcffhidO3dGeXk5vvrqKxQVFSE4OPiWfy8AcPDgQfz5z39G3759xZCi0+nwww8/4IknnsCdd96JMWPG4MMPP8TkyZMRGxsLAIiLiwMAfPLJJ5gzZw5SU1Mxc+ZM1NTU4OOPP8aoUaOwc+dOREZGip9lNpsxYcIE9OzZE7Nnz4aXlxeMRiMmTJgAo9GI0aNHIyQkBEVFRfjPf/4Dg8HQ6kfTiG5IICJqgO3btwvx8fHC0aNHhXPnzgmdO3cWXnnlFXH/6NGjhSFDhoivT5w4IcTHxwsvvviiw3FeffVVIT4+XsjJybnu5w0fPlzo27evUF5e7nDMjh07CrNmzRK3/fe//xXi4+OFzz777Ibn8Pbbbwvx8fHC3r17nfZZrVZBEAQhLy9PiI+PF7Zv3+5wbqNHj3Z6z+zZs4X+/fuLrxcvXiz06NFDMJvN16zhs88+E+Lj44X//ve/DtsrKyuFXr16CfPmzXPYXlJSIvTs2dNh++zZs4X4+HjhjTfecGh7/PjxBv8uiMgZp8+I6KZFRUVh2LBh2LJlC4qLi6/aZv/+/QCAcePGOWwfP368w/6rKS4uxokTJzBixAgEBgaK2zt27Ii77rrruu+9nr1796Jjx4647777nPYpFIpbOmZ9Wq0WNTU1OHjw4E2/95tvvoHBYMCQIUNQVlYmfimVSnTv3t1his3usccec3jt5+cHADhw4ABqampu7SSIWjGGIiK6Jc8++ywsFss1r0QrKCiAUqlEdHS0w/bQ0FBotdrrXn11/vx5AEBMTIzTvri4OJSXl9/SwuJz587hjjvuuOn3NdSoUaPQvn17TJo0CWlpaXjhhReQnZ3doPeeOXMGAPDEE0+gb9++Dl8HDhxAaWmpQ3u1Wo22bds6bIuKisK4ceOwdetW9OnTBxMmTMDGjRu5noiogbimiIhuSf3Roqeeeuqa7ZpiBEauLBaLw+s2bdrgk08+wYEDB5CdnY3s7Gzs2LEDDz74IF577bXrHksQBADA66+/jtDQUKf9KpXK4bVGo4FS6fzv2jlz5mDEiBH48ssvcfDgQSxevBjvvPMOtmzZ4hSiiMgRQxER3bJnnnkG//znP696JVpERASsVivOnj0rLiQGgAsXLsBgMCAiIuKax7XffDE3N9dpn06nQ1BQEHx8fG663ujoaKcruRoiICAAeXl5TtvtI1r1aTQaDBgwAAMGDIDVasXChQuxefNmPPvss7j99tuvGRKjoqIA2ILVXXfdddM11me/qu3ZZ5/FDz/8gMceewwff/wxZsyY0ajjErk7Tp8R0S2Ljo7GsGHDsHnzZpSUlDjsu+eeewBAvBzdbv369Q77ryYsLAydOnXCJ598AoPBIG4/efIkDh48eN33Xs+gQYPw66+/4vPPP3faZx+puZqoqCjodDqHy/Z//fVX/PDDDw7tysvLHV4rlUokJCQAgHgbAm9vbwBwmtK6++674efnh3feeQcmk8mphuvdMsCusrISZrPZYVt8fDyUSmWDb4NA1JpxpIiIGmXy5Mn49NNPkZub67Bep2PHjhgxYgQ2b94Mg8GAO++8Ez///DN27tyJgQMHok+fPtc97qxZszBp0iQ8+uijeOSRR8RL8v39/TFlypRbqnXChAn497//jeeeew4PP/wwunTpAr1ej6+++gqLFi1Cx44dr/q+Rx55BO+99x4mTJiARx55BKWlpdi0aRM6dOiAqqoqsd28efOg1+vRp08fhIeH4/z589iwYQM6deokjpZ16tQJKpUKmZmZqKiogEajQZ8+fdCmTRssXLgQs2bNwkMPPYSMjAwEBwfj/Pnz2L9/P3r06IEFCxZc9/z++9//4uWXX8b999+P9u3bw2Kx4NNPP4VKpcLgwYNv6XdG1JowFBFRo9x+++0YNmwYdu7c6bRv8eLFiIyMxM6dO/HFF18gJCQETz/9dINCzV133YV3330Xy5cvx/Lly6FWq3HnnXfiL3/5izjVdLN8fX2xceNGrFixAp9//jl27tyJNm3aoG/fvte931JcXBxee+01LF++HEuWLEGHDh3w+uuvY9euXfjuu+/EdvY1Vh999BEMBgNCQ0ORnp6OqVOniut/QkNDsWjRIrzzzjt48cUXYbFY8MEHH6BNmzZ44IEHEBYWhrVr12LdunUwGo0IDw9Hr1698NBDD93w/BISEpCamop9+/ahqKgI3t7eSEhIQGZmJpKSkm7pd0bUmiiE640ZExEREbUSXFNEREREBIYiIiIiIgAMRUREREQAGIqIiIiIADAUEREREQFgKCIiIiICwFBEREREBIChiIiIiAgAQxERERERAIYiIiIiIgAMRUREREQAGIqIiIiIAAD/Hx7NrzFNqd7eAAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "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": "707abeac-53c2-414a-d8ce-d59956d8891c"
      },
      "source": [
        "kmeans3 = KMeans(n_clusters=3)\n",
        "y_kmeans3 = kmeans3.fit_predict(x)\n",
        "print(y_kmeans3)\n",
        "\n",
        "kmeans3.cluster_centers_"
      ],
      "execution_count": 22,
      "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 2 2 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n",
            " 2 2 2 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 0 0 0 0 2 0 0 0 0\n",
            " 0 0 2 2 0 0 0 0 2 0 2 0 2 0 0 2 2 0 0 0 0 0 2 0 0 0 0 2 0 0 0 2 0 0 0 2 0\n",
            " 0 2]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.10/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": [
              "array([[6.85      , 3.07368421, 5.74210526, 2.07105263],\n",
              "       [5.006     , 3.428     , 1.462     , 0.246     ],\n",
              "       [5.9016129 , 2.7483871 , 4.39354839, 1.43387097]])"
            ]
          },
          "metadata": {},
          "execution_count": 22
        }
      ]
    },
    {
      "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": 454
        },
        "id": "GOPhGuicFBkV",
        "outputId": "607625e4-c166-4050-fd70-ff429c7fe352"
      },
      "source": [
        "plt.scatter(x[:,0], x[:,1], c=y_kmeans3, cmap='rainbow')"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7b7a6c5c82e0>"
            ]
          },
          "metadata": {},
          "execution_count": 23
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "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": [
        "#1. Is feature scaling essential for KMeans as it is for most ML algos?#\n",
        "Feature scaling is indeed important for KMeans clustering, just like it is for many other machine learning algorithms. KMeans clustering algorithm works by partitioning the input data into 'k' clusters based on the mean of the data points. The distance metric used in KMeans, typically Euclidean distance, is sensitive to the scale of features.\n",
        "\n",
        "If the features have different scales, it can lead to biased cluster assignments because features with larger scales will dominate the clustering process. Therefore, it's recommended to scale the features so that each feature contributes equally to the distance computations.\n",
        "\n",
        "Popular methods for feature scaling include:\n",
        "\n",
        "Standardization (Z-score normalization): This scales the features so that they have a mean of 0 and a standard deviation of 1. It's suitable when the data is normally distributed or when the algorithm (like KMeans) assumes zero-centered data.\n",
        "\n",
        "Min-Max Scaling: This scales the features to a fixed range, often between 0 and 1. It's useful when the algorithm doesn't assume zero-centered data or when the features have a bounded range.\n",
        "\n",
        "Normalization: This scales each feature to a range between 0 and 1 based on the minimum and maximum values of that feature. It's particularly useful when the features have different units or scales.\n",
        "\n",
        "Applying feature scaling helps KMeans to converge faster and improves the quality of clustering by ensuring that all features contribute equally to the distance computations. Therefore, while feature scaling might not be strictly necessary for KMeans to run, it's highly recommended for better performance and more meaningful clustering results.\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "j0s-1g8u9xXv"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#2. How can we prevent initialization variation in KMeans?#\n",
        "Initialization variation refers to the sensitivity of KMeans clustering to the initial placement of cluster centroids. Different initializations can lead to different final clustering results, which may not always be optimal. However, there are strategies to mitigate this issue:\n",
        "\n",
        "Multiple Initializations: Instead of relying on a single initialization, perform KMeans clustering with multiple random initializations. This is often referred to as the KMeans++ initialization algorithm, which is the default initialization method in many implementations. The algorithm initializes centroids in a way that minimizes the variance of cluster distances.\n",
        "\n",
        "KMeans++ Initialization: Utilize the KMeans++ algorithm to initialize cluster centroids. KMeans++ selects initial centroids in a probabilistic manner that encourages them to be well spread out across the data points, reducing the chance of converging to suboptimal solutions.\n",
        "\n",
        "Smart Initialization Techniques: Develop or utilize smarter initialization techniques that are less sensitive to random initializations. For instance, some techniques use hierarchical clustering or density-based clustering to initialize centroids more intelligently.\n",
        "\n",
        "Post-Processing: After running KMeans with multiple initializations, choose the clustering result that yields the lowest inertia or distortion (sum of squared distances of samples to their closest cluster center). Alternatively, you can use clustering metrics such as silhouette score or Davies–Bouldin index to evaluate the quality of the clusters and select the best result.\n",
        "\n",
        "Deterministic Initialization: If reproducibility is crucial, you can set a fixed seed for random number generation to ensure deterministic behavior across multiple runs. This way, you can always reproduce the same clustering result given the same data and parameters.\n",
        "\n",
        "By employing these strategies, you can reduce the variability caused by initialization in KMeans clustering and increase the likelihood of finding a better clustering solution. However, it's essential to keep in mind that KMeans is sensitive to the initial centroids, and in some cases, it may still converge to suboptimal solutions, especially in high-dimensional or noisy datasets."
      ],
      "metadata": {
        "id": "IFs0sbR2-LdI"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#3. What is the training and testing complexity of KMeans?#\n",
        "The training and testing complexity of KMeans clustering can be described as follows:\n",
        "\n",
        "1.Training Complexity:\n",
        "\n",
        "The training complexity of KMeans is typically O(I * K * N * d), where:\n",
        "I is the number of iterations (convergence typically occurs within a fixed number of iterations or when centroids stop changing significantly).\n",
        "K is the number of clusters.\n",
        "N is the number of data points.\n",
        "d is the number of dimensions (features) in the dataset.\n",
        "Each iteration involves assigning each data point to the nearest centroid (O(N * K * d)), followed by updating the centroids based on the mean of the points assigned to each cluster (O(K * d)).\n",
        "While the worst-case time complexity of KMeans is polynomial, the algorithm often converges much faster in practice, especially with smart initialization techniques like KMeans++.\n",
        "\n",
        "2.Testing Complexity:\n",
        "\n",
        "The testing complexity of KMeans refers to the process of assigning new data points to existing clusters once the centroids are trained.\n",
        "For each new data point, the complexity is O(K * d), where K is the number of clusters and d is the number of dimensions.\n",
        "This complexity arises from computing the distance between the new data point and each centroid (O(K * d)) and then assigning the point to the nearest cluster.\n",
        "Overall, while KMeans can be computationally efficient, especially for moderate-sized datasets, its performance can degrade with large datasets or high-dimensional data due to its quadratic dependence on both the number of data points and the number of dimensions. Additionally, the number of clusters (K) also influences the computational complexity. Therefore, it's important to consider the computational cost when applying KMeans to large-scale or high-dimensional datasets."
      ],
      "metadata": {
        "id": "msLbfl6J-Zqq"
      }
    },
    {
      "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": 23,
      "outputs": []
    }
  ]
}