Module7_Lab1_FMML20210660.ipynb

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  "metadata": {
    "colab": {
      "name": "Module7_Lab1_FMML20210611.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "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/SreenadhSingamaneni/IIITH-FMML20210660/blob/main/Module7_Lab1_FMML20210660.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 Arpan Dasgupta\n",
        "\n",
        "arpan.dasgupta@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": "b69783ec-ce0d-4868-e2e2-73045ae5e235"
      },
      "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[:5])"
      ],
      "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"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GHfSomXy91rb"
      },
      "source": [
        "#DEFINE ALL THE FUNCTIONS & VARIABLES WE NEED TO DO CLUSTERING\n",
        "#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": 0
        },
        "id": "gcTPXjLe-7nC",
        "outputId": "c8dbe00b-03dd-4c9a-f1c5-a37dd777f404"
      },
      "source": [
        "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 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": "211d22b6-cd4d-47b8-d509-513f3e70d34c"
      },
      "source": [
        "# Generating Synthetic Data\n",
        "\n",
        "k=5\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[:5])"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Shape = (500, 2)\n",
            "Sample:\n",
            "[[-7.32786741  4.23641465]\n",
            " [ 1.12565931  6.32088416]\n",
            " [-0.49239887 -5.28550826]\n",
            " [-7.12432134  6.16236021]\n",
            " [ 2.38696269  4.11331935]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "2_HmX5BaAfjq",
        "outputId": "7a84af25-6fea-4c81-cb38-7ea3e9d4d0fa"
      },
      "source": [
        "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 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 our KMeans algo can be run 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",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hP0Isa2gD7n3",
        "outputId": "25f30231-127c-4c92-b8c9-f74b70e3061e"
      },
      "source": [
        "from sklearn.cluster import KMeans\n",
        "\n",
        "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": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "KMeans(n_clusters=5)"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "xHll4yqNFCSn",
        "outputId": "c4d9bdd2-393a-4ed4-9dfd-e80a48d39cf5"
      },
      "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": 10,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "ITERATIONS TO CONVERGE = 2\n",
            "CLUSTER CENTROIDS = \n",
            "[[ 5.56873506 -9.60861515]\n",
            " [-6.06533341  5.2400571 ]\n",
            " [-6.78567723 -8.26282547]\n",
            " [ 2.78561142  4.93182424]\n",
            " [-0.06909909 -5.56399319]]\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": "89fa33df-1c2f-421a-932f-0bc9035091be"
      },
      "source": [
        "from sklearn.datasets import load_digits\n",
        "\n",
        "digits = load_digits()\n",
        "digits.data.shape"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(1797, 64)"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xUBgYLeN9Sa-",
        "outputId": "62f57992-fc0d-47a4-c572-b45a694c2155"
      },
      "source": [
        "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": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(10, 64)"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "lSVbUHUi9n18",
        "outputId": "261a5455-8111-4c50-d1b9-61c32b347650"
      },
      "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": 13,
      "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": 14,
      "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": "b8808504-2edc-4e7e-8ee2-8406c8c23803"
      },
      "source": [
        "from sklearn.metrics import accuracy_score\n",
        "accuracy_score(digits.target, labels)"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.7935447968836951"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "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": 0
        },
        "id": "1idrQbsg-OQZ",
        "outputId": "4adc55ec-4ba0-4e46-f41f-7d5a6611badf"
      },
      "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": 16,
      "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": [
        "#Import 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"
      ],
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "wJWkYsYtA9Bi",
        "outputId": "bdab6812-56bb-43fb-fe89-9b40a5ef0264"
      },
      "source": [
        "#import the dataset\n",
        "iris = datasets.load_iris()\n",
        "# print(iris.data[:10])\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": 18,
      "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-de2b69a7-41a5-488b-b1b5-b52db84885cc\">\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-de2b69a7-41a5-488b-b1b5-b52db84885cc')\"\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-de2b69a7-41a5-488b-b1b5-b52db84885cc 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-de2b69a7-41a5-488b-b1b5-b52db84885cc');\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": 18
        }
      ]
    },
    {
      "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": "81b2e06c-a24e-4218-9de8-6d1cd3792e54"
      },
      "source": [
        "kmeans5 = KMeans(n_clusters=5)\n",
        "y_kmeans5 = kmeans5.fit_predict(x)\n",
        "print(y_kmeans5)\n",
        "\n",
        "kmeans5.cluster_centers_"
      ],
      "execution_count": 19,
      "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 3 3 3 2 3 3 3 2 3 2 2 3 2 3 2 3 3 2 3 2 3 2 3 3\n",
            " 3 3 3 3 3 2 2 2 2 3 2 3 3 3 2 2 2 3 2 2 2 2 2 3 2 2 0 3 4 0 0 4 2 4 0 4 0\n",
            " 0 0 3 0 0 0 4 4 3 0 3 4 3 0 4 3 3 0 4 4 4 0 3 3 4 0 0 3 0 0 0 3 0 0 0 3 0\n",
            " 0 3]\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[6.52916667, 3.05833333, 5.50833333, 2.1625    ],\n",
              "       [5.006     , 3.428     , 1.462     , 0.246     ],\n",
              "       [5.508     , 2.6       , 3.908     , 1.204     ],\n",
              "       [6.20769231, 2.85384615, 4.74615385, 1.56410256],\n",
              "       [7.475     , 3.125     , 6.3       , 2.05      ]])"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "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": 0
        },
        "id": "8VSBRjiLEQ7V",
        "outputId": "c8ed53e2-043f-400c-f4d8-43741703e817"
      },
      "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",
        "import matplotlib.pyplot as plt\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": 20,
      "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": "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": "b58d3852-b0d7-4931-ef44-3edc5d03c44b"
      },
      "source": [
        "kmeans3 = KMeans(n_clusters=3)\n",
        "y_kmeans3 = kmeans3.fit_predict(x)\n",
        "print(y_kmeans3)\n",
        "\n",
        "kmeans3.cluster_centers_"
      ],
      "execution_count": 21,
      "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": "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": 21
        }
      ]
    },
    {
      "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": 0
        },
        "id": "GOPhGuicFBkV",
        "outputId": "8fe0d032-72aa-4372-bf23-228a894841ec"
      },
      "source": [
        "plt.scatter(x[:,0], x[:,1], c=y_kmeans3, cmap='rainbow')"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7fcdf0b54850>"
            ]
          },
          "metadata": {},
          "execution_count": 22
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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/3JYOzUac7d4GAF4PvZ+eTli4OhaHNhdEg0bTH3j9Nn9HgHcRWDHB4v/Kf9W2JhMd5Lug1tNKlqy3gKKt3Tt+pNSZbdhZ8sGnhM1esxUHRYuR3eveYBY48bRG00c4NjRvyW4SaFirw9SRoHuvC4rs7CMIR6iOfC5HStjxYarMRGCmkhQ5PgTkTDYWcAqjQaPpa4QEX0n29wKVhc/MeDShg3wXHBcdne4Lx/WfT4hX4TvMLI8HMy5RgYEkLaOAAgPJhEQVAuH60w9aqGQqyZzoqIJo0Gj6GiFg9jXJjvzq+zEDirnX6rKPR4IO8l0wOlXOaa0T8TkmppIYSnBMvIoPtE0q2D5MDD7WNJtKK4xUAkMJyu0Q85tmd4zg58ZGMTM2oiP9r+lI5kRGMSM+vGA6NJq+5rjrksy6yg30ZlDhCSnmXpdkxhd6NhXvYEe7aw7B1MQwJieGEpEJ/I4nZ471I6HUDnJJ09yOQtVB5U17XyA4OTqO46NjCFR5iNen3NG/RjOIEBJO/laS429MEqsTBIeovCstaXKjg3weSESv1Bc9OLh3plFGeC28iVbilBUHOLVtAiVOsON9B4d3gjtY79uDgWBWdCTTE9VpbbTJBGv8NTQZMapTxUxODD3s4iK5sHHY5Ktjm7eBSsKMNSoos4OH/kONph3TD0Wj9Dx8ocjrG37NNdewc+dOpJQEg0G+/e1vM3Xq1LRt7r33Xv74xz8yZIhbU3Tu3LncfvvthVd8FLLVU89zJas7/t/ijbOt/G0uaprJCKsMB4dHy5bSZiTcrGQKFhVtZKN/DwuajwWg1mzhHyXvYbfnit/mq2dZcCcXN87p8uLSHVLYPFG6nCYjhiUdNrOPt8u2cXbLZMYnqwqyD41G0z3yCvJ33XUXRUVuoquXXnqJW2+9lb///e8Z2y1YsICbb765sAo1vFS8zv1lv8OsPZC/WLyOKxpOYWVg94EA32m7Gk8LNWYzw6xiFhatJ9UpHbElHByZZGloGx8oUC3YNYEaGs1YhyXUwb2gvFK0gTH1FXqKSaPpA/L61u0P8ABtbW2IQpcT1+TEwiElbDLyjAmISfeB1Hpfbc6/XxXYTUykOkr6dcYRii3efQXT+r6vLqvnX+GuB9BoNL1P3hOyt912G4sXL0Ypxa9//eus2zzzzDO8/vrrVFVV8bWvfY05c+Z0S0xFRX65z3uKqqr80vL2Jk5XK2uFqzmIj3qiWd8v8QcY6s+d48ZnmAU77hA5pn0kDCkroor+17/76Y+ffTYGik4YOFoHu06hlOrWE44nnniCZ555hgcffDDt9bq6OkpLS/F4PCxevJgbb7yRZ599lrKysrzbrq9vw3H65oFLVVURdXWtfbLvQ/GHsrfckXjn0byCCivEJ5uOY7ungWdKVmWO9hVc3nAiYcfP0yXvscvTlLaC13AkJ0THMCdWGL/9Zu8+Xi5ah9W5SpWCYsfPZxpOyDvtcW/Tnz/7zgwUnTBwtA50nVKKQw6Ouz1JumDBApYsWUJjY3rt0KqqKjwedwXmqaeeSnV1NRs3buxu85osLGiehUd1WjClwKsMPto0E3D9/JPjQ933O/2cHBlHuN0VdHbLFErtIB7HwOMYGEoyJlXO7E754o+UcckKpsWrMZTA4xh4MQk6Xi5sntFvA7xGM9g55HRNJBKhpaWF6mrXjrdw4UJKSkooLU3Pfrhnzx6GDh0KwNq1a9m1axfjxo3rAclHH2HHzxfq57HRV0dzcYzyliATk0PStjmrbTLHR0fzXmA3phLMjo4k0Gn6JKi8XNp4HLVmC61GnCqrqODWRoHg1MgEZsVGUONpYVhxMeEGH1IHeI2mzzhkkI/FYlx33XXEYjGklJSUlHD//fcjhOCqq67i2muvZebMmfz4xz9m9erVSCnxeDzcfffdVFUNDttcgxFhr9lKyPExIlV6WEFrg28PuzxNVFghZsSHIw/DaZLCxm5/EOvgZLThUQZDrDASiSEOSpXQji0c1/VymFk0LRyWBXfQJuNMSFQxOlWesU2R46co4aeKIurov7fCoqUZ78svQtiHOP5UVFnmsRyK2D7Bjn8ZSA+MPtvCe9Cds3Jg12KD1p2CqlkOldN1bnRN79LtOfmepL/NyTsoXipay1ZfA0K5I1W/MpnfNDvvxVFxkjxasZSkOJAP20BwScNxlDn5jaRbZJw/l73tOlfa7ZMeZfCZ+hMIto/WV/trWBzehFQAAiUU5zVP6wjCEZngyZIVRGUKhQIBI5KlnNcyLW9r4w5PI8+UrEy7dhTbfj7deHzWi1Z/nu/0/uNJir9yNcowkEKgUilaf3wviYsvzbuN1Q97eP1bPqQJCDegn/+bGKPPcj/ryB7BE/MDRPdIVPsU2ojTLc7/bRzjMHLL9ef+PJiBonWg6+yROfmjidX+3WzzNWALB0s6pKRNm0zwYvHavNt4pmSVG+AFHT82iqdKV+TdxlMlKw4EeNw2UsLmqdL3ALe4yeLwJmzhkGrXaQmHf5asISEsAF4uWk+LEXffkw6WcNjpbWJFYGfeOp4tWUX7NaTjp8WIsyj8ft5t9AfE3r0UX3MVIhZDtrVBaysiHqfoG19D7tyRVxuNGyWvf9uHnRCkIoJUm8CKCp7/fIBEi7vNS9f4adkmSUXc96yYYOcik+W/1NlDNb2HDvJdsDqwO71YB6AE7DPbOvLMHIq9nrasHveoTJHEOuTfOzi0dl7o1KmNRtO1TW7w7ck6/SIUbPXWkxAWNZ7mjNz4tnBYE6jJ6zh2mo047XcAB+vY6NubVxv9Bd8/nkRlm3JzHHxPZi7yy8b6v5g4WT4+IWHr8yaJFqh500DZ6fux44I1jxRmhbFGkw86yHeBJbJPHQlERvA/HApVXcoSTrbpdxRuIO9qP/lqSMjc5ddUjn7qr4h4HGFnOR7bRsRjebVhxQQqSxPKASsusBMi84K4fzfZa8BoND2CDvJdMCFeicxSGirgeChy8kuPF7Z9mQ9AlZsPPpBr8VAnJBKvMrK2sb9oyLhkRUbee3DvOkYnywgqL8V25jMEqUTeRcnHJHM8lFQwLJmj2kM/JXnueWBkySbq9ZL80Pl5tTH+QgszkPm6ctwHsMEqRfGYzAuo9CjGf+TQd3AaTaHQQb4L5sZGU2T7Owp2SCUwleTslil5+77Pb5nm/tLJ4w5wduuUvHWc2zI1axvntbddnSphfKLS1ancaRpTSY6LjDrgk2+d0uGPBzAdScjxckJkbF4aTCQnRcYe8OG36zAQnNOS/7H0B+xjJhG76kuoQBAlBAiBCgaJfeZyrJmz82qj+mSbCR+xMINuhwipMAOK47+RoGiE20Fn3xfHE1YYfvf/ZlARGqY44SZdBEPTe2h3TTu5nl5b2Lzvq2OXp4lix8/UeDXhPEfx+2mTCd4IbWKv2UapHeDUtvGUOaFutdEsoywOb6bFF6M0HuDUyMQ0h49CscvTxCZfHYaSTEoMZYiVvgw6KpKs8dfQbMSotko4Jj6k2/nxa8xm3gxtISqTjEqWcXJkHN4cTtz+7lwwly7B/9fHCPg9NJ1/EamT57klivJEKdi5yGDTUyaGDyZ/MsWQY9NH79E9gjWPemjaLBl+ss0xH0/hOczlCf29PzszULQOdJ35uGt0kG9nIHzYKWx8VR6SdSnMLMFZtRcYlwhC3bwQ9QQDoU+h53WmdrcS39BEcO4QjOLD/1yOVGfjBkFkj2D4KY5r++xB9GdfWI4kyOuiIQMAheLfoc2sCtRgIHAqFbOjIzkhOqZj2miP2cJLxeuIyCSgKLNCnNcylWIny8Sxplew25K8cc4q1mw+CUkxAod5Fyxh2sMn9aqOxvcFj384SKKx/S5FwvHfSHDiN3VZvaMBPSc/AHgnsJ3VgRps4ZDE9cCvCOxkpX83ADGR5OmSlbQYcddNIxT1Zht/L11RMAePpvu8ed57rN18AjZ+UoRJUszi505h63+926s6/nJ2qD3At/84grd/5GPTM4UvZanpf+gg389RKFYEd2ZYNi3pphcAWO/fg5PFz58SNtu96YnkNL2D1Rhj9caTsUifgE8R4u3fDu01HZv+YWDFIJuf883v9P2Unqbn0UG+n6MgLSVCZ+LtRUPcEXzmswxHKCIy0ZPyNDlI7cpdJKUtT9tqIWjckOsrLojV68RxRwM6yPdzJIISO/u8eoXlOnSGp0rwOJkfpQCGWgOjIMJgwzepHI/IUsgFh+GVvZcGYtz5uRaxKapm66m8owEd5AcAp7VNcBc7dfKnm0oyLzIBgHGJSoocP0anhVuGIxmRLKVKB/k+QXoNzrhsBR4iHa8JbDxEOfHuwqZ47oqKaQ6VM2zSV9MpkPDB/8lvda9mYKPdNQOA0alyPto0k6Wh7bR4Y5QmA5wQHdvhgzeQfKzpWJYFdvC+vw6pBFPj1cyMDe9j5Uc3E/73BAJjVvD2T4M0R4YwfNgWjr+7hJIP9W6dhYtfivHqjT42/MWDY0HZJIdzfhGnRJd7OCrQPvl2Brpftj8yULRqnYVnoGgd6DqPep98oxHl36HN1Hia8SmTWdGRzIwP71YpujqzlX+HtlBnthJwvMyNjmJyYmhHG0ksnilZRa3HzS9bbPs5v3kaFU5hi5Jv89azJLiVNhIUl/o5OTKOkan86+cebXj+vZjQd27HWLcWZ9QoIjd/i+SFH+lrWRlEltaw5Oq9bN01A4+MMeu01cx4ZC5G0M1LpBSsecTDsvu8JBphyPEB5t2eoGJqYefT696TvPHfPuqWGwSqHI67PsnkT1odC4DtBLz9Yy9rH/VgJwRjz7c45VsJgkMPDMo69znjxuK94f91u8+3vmiw5Ps+WrZJSic6nHxbglEfyJ0cT3NoBu1IvlXGeazsHVL7c7nj5muZGh/GaZGJGdtnu1LWGxEeL1uGhZPWxnHR0cyNjQbgN+VvkJDWAYdaezbeyxpO6nb6g1xs8taxsHh9mo3SVDKtKEh/pK9GSZ43Xqfk059AxA7MOatAgNa77yFx6Wcytu8rnYlNjfxpXpCYKkW1j7dMokyoXsbZK2YB8Ob3vLz3oBcr2n6CCYUnCJe8HKF0fGG+K/VrJH+7MIgVhf0nshl08/DMvdZ1cD39yQC73zSw4+77wlQEKhWfeSOCN9z9Ps/G+0+bLPyqHyt2YBBmBhTn//ZAIZZCczSM5Aftg9flwR1YnQI8uN7yNYEaYiK/lX5LQ1vTAvz+Nt4JbsfC4X3v3vQAD26FIOCN0KaCHAfAv8ObM33ywuHf4c0F28dgInTnt9OCDYCIxQh957/coXE/Yf2tG0iqYEeAB7AIsqlmLi2v7iDZCit+1SnAAyiBFYd37imcx/2tu70ZXnorKnjnHh9WHPatlNQsORDgAZQlSLYI1v/FveMoRJ//+w5fWoAHN6XzG3doP/+RMGiDfK3ZmlEkA8BQkiYjm7Utk71mloIfuC9FZIIduRYaCdhrFmZ04KBozeF1bzK0OyIbxrrslbtkQwMiktu/3tvUrgpnLJYCkKRo+tc+mrfIrGUClS3Y827hvrp1yw2yflmAyG7BvtUya942KyrY87a7avZI+9yxoXVHdg1NmwZtmOoVBm3vldlBstWysIXKuz5rSZYc7ACOgIDydPjUM1Dk9LZ3F9leVzYbQUdXGMqGM2Jk1tdVIIAKdi/7Z09SPiqCQWYFEYVBeGYR4eEKO1tWYqEonVi4OfnicdnbcmwIDFEUj8lSEQww/IqyY9y/PdI+lwb4y7OP+DvP+2u6z6AN8nOiIzMKVBuOZFSyNO+58uOjYzKKcZiOZEp8KF5lMiM+HLl/fmY/7b/Pa5twJPLTmBsZnalDSU6IjCnYPgYT0W/eigqkj5CdYJDoV64D2X9O+anfGYVxUAlIgwRVwS2Uf3wigUq3wMj+fPT7Mf1w3HWFy0l/wg1JzMBB+wgopnwqhTfs5s4Pj3SQZvqJLj0w9bPu1Gch+vy4ryfb8/On6zjhJr1q+0gw7rjjjjv6WsR+YrFkwaZMg8rL0FQRtZ4WUsJGIjgmMYQPtk7OCP4AoZCPaDT9i1Ps+Cm1AtR4WrCFg4FkWryaeZHxSAQCwYR4JZt8+zrmzA0k57RMZqRVOOfLUKsIoSR1ZisI8DomJ0XGMj3Rv33w2SlJsI4AACAASURBVPq0N7CnTMWprMTz9ltg26hAkOhXv07s+puy5ovvK53eEUWMHr6eva+0EbeLkVhMrH6bc14ahlHi3kWOPdciulfQsF4ihCA03OHs++KMOLWAI/nRipKJDrVvGdgJMHww/XNJ5v13Emm4XTbxIovGDZKW7RIkVE53uPDhGCXj3C/swX0ugkEiXfR5NoYe515I9i43UAq8RXDSrQlmfK7nKmn11WffXXLpFEIQDHZ9Rz9o3TX7USiSwsZUMmtw309XT9nzaSNOEkuqgjlqsuGgKK4K0FoX65YNtK/oc+eC4yBaW1ChMJi53cJ9rhM357wIejBLs08R2kkoDRXRkmztTl2TbqEUJFvADJL1WQCAFXOncby5DB3tfV45tpq6xsN7ZuTYkGwFX7FbGL0n6Q+ffT5on3wXCAS+HHPa+ZAQFmv8Nez0NlJiB5gZG0GZnfmwzI+XXFl9oyLJ6sBuaj0tlFshZsZGUNzpuYCDw9Lgdtb5a1DA5PhQToqORR50QZEIAnhoyzKPq8mClKiS0r5W0SV2Ejb8zWTTU1X4SmHG51JUn5xpFzS84C+F1rrD20/D9//JqgcksVQxE2duZszDF2AOTe8bIcDXRbnef93oY/1fPCjLncK54OFYZrDf3+ddXFQPhTTcY9UUhkEf5I+EqEjyl7J3SQgLWzrsUk2s9+/plj+9Rcb4a9kyLGFjC8VuTzNr/DVc1DyLoVYxAH8ue4dmI9bxcGt5cCfv++r4bOMJGYFeM3iwk/D3+UEa1krXJikUW541OeGbCeZ8pXAFPTae/Sf+tfKzpPADBtvfbaN81vvMX64wq/ObVnx4TpDIrv3nomDXawYPHRPmys1teHVdmn6NjiBd8E5wO3GZwpbuEF0J15/+StEGFPlNK70R3kxSWB2pgB2hsKTDv4o2AvC+d29agAdAQJuRYK1vT0GPR9O/2Ph380CAB9cDHxO89UMf8YbC7MPaUMMrKy8jRQjaS0amCNOgjmHr557Lq40tLxjtAX5/4REAgbLh5S/n51TT9B06yHfBVl89ThYfZlJatMr8pkx2epqyWpAbjSgpbDb49+b8241+HeQHM1ueNdMXOrUjPbD7zcLcZNfftwSDzAd2KUJsXDUprzZW/DLXgz3BjkW6ulR/Rwf5LvDmmMtXKDwqv5M713YCd4491z4AfCrH0y/NoMBfrhAy+x2hr7gwBgTPsAAqS9F3cAi051s6FP6yXFoUHj1V0+/RQb4LZkWHYx5UjEMoGJYqJqDyW4g0PVad0YZUggmJKgwkJ0RG5/zbE9u0D34wM+0/UhgZZiyFJ6ioPqUwuVrKbjybAPUc7ArwEGPGZfmt/P7AXbnvWo/7hvaw93d0kO+CKYlhTIkPxVACr2NgOpJyK8Q5LVPzbmNObBRjkhUYSrptKMmwVDFntLlJ0kqcICdHxrmLqDr9HB8dXfBMlpr+xdA5DvP+O4HhV3iLFJ6wIjhM8dG/xJAFmgURXpP5/7uBYnbipQUfzZjEOH3yo1R+L78MkYEqOP6mBAefpMPn2cy6suc87JrCMOh98vnSlV82IhPUmW2EHB+VVuiwPOotMkaDGaXY9lNuZy7zTmKxOlCDwmFabAT+HMangeLrhYGjta91JlqgZomBtwiqT7RzesOPRKdKWtR/7wVSNVEqvnYi3pm57yBzkWyDN7/rI9ECJ96U6LLoSF/3ab4MdJ2D3idvYbPVV09UpqhOFWctdVdvtLHL20zA8TA2UYEn6/xk14QcH6Hk4S9ycnDY4qunxtNMuRVibjSAedBNlCUcfMpEobCkDY55UBuKHd5GNrMPr8dgRKq0bxZExWL4/vkssm4vqZNOwZp1bLebkLU1BH/0Q0RDA/FPfprU+Remb6AU5jtL8Sx7B3vYcJLnXQDebubpcRwCv/oFniVvYE2dRvS6G8Gf7gQRe/fie/4ZCHmR887EqT5oBXEySfDeH2OufI/UcScQ+/LXjsj/nQtfMYw9N/f0TFsNvHJ9gMQ+GPthD8dfn2mvNFavwvvGazgVlSTO/zAE09dyRBpMVkU+RtwSTN6VYtzM9P0pBXvekexdZhAaphh7noVxUJd7w3DGD49seia6V7DleRPlwNjzLMLV6YM6x4Yd/zJo2iQpn+ww8vTcF72exIrBln+axOoE1SfZVM3KXASzb7Vk9xsGgQrF2PMtPL1X1bFb5DWSv+aaa9i5cydSSoLBIN/+9reZOjV9ysK2bb773e/y2muvIYTg6quv5pJLLumWmO6M5OuNCE+WrsBBYQsHiWBUsowPtUxDIlAoXi5azxbfPhQKqdxEBBc1z8x6MeipK3qUJI9WvJWWKlgAn2icQ5Xt6ljnq2VR0fsdCdWUgHlt45kRd4NOTCT5e+kKojKJIxXSgSInwIKm2Ue00Ku7GGvXULrgQkglEakUSIPkmWfT8tAjYGRePLP1qe+3D1F08/Vpr9mTptC46E03x0kySfHll+Jd8m83JYHHA4EgTU8/jz0+sw5AVvbsoeLE2YhYpzlnw6DxxVexZ7h52n1/fpSim65HGe5KBGU7tN35feKf/yIAcsN6ys+cB6lOAdXno+HNd3FGjMpPRwFY/iuTN769/+IkAIX0wRc2tPvTHYeir1yN79mnwXFQpgdMg+a/Pd1xAV71Ww+Lbk4fpJRNcrh0URQpXb/+s5cHqFli4NjualczoPjY09HDzlmf7bNf92eTV2/yIwxAgXJg3p0JZn7e7ePYPsHjHw0Q3SOxk66O4jEOC56K4is+LBmHpbN+reTJBQHslMBOuaflqDMtznsojjRc3S99xc+WZ92LlTRBmDD/b9GsF4Oe0gkFzCd/11138dRTT/HEE0/whS98gVtvvTVjm6effprt27fzwgsv8Nhjj3Hvvfeyc+fOPA+heygU/yxeTUJYpKTtes+Fww5vI2v9NQBs9O1li9fNKWMLRUraJKXFc8Wr8/a4F4J/lK50A/x+i3F7PrN/lKwEoE0mWFT0PrZwsKT7YwuHN8KbaZHusvBF4fdpNeKkpI2NQ0o6NBnRguasPyRKUXzFZxCNDci2NkQigYhF8b7yMv5HH8mvjXicolu+0bkrEICxYR3BH34XgMCDv8Tz5huIaBSRSLj72ldH0VVX5C219NMfR8SiafvAtim5ZD4AsmY3RTddj0jEkdEoRKOIRJzw7bcit25x27hkPqRS6W0kEpRcPD9vHUeKbXNQgHf/dRLw5MdcW4vv8b/gfe4fiFjM7a9IG7K5meLLPwWOgxWHRbf44KBeb9wgeeuH7lD9vQc91LxpYEUFTkKQahPE9gleuKpw1pm2GsGrN/mxEwIr6q4HsBOCN2730bzVPbZFN/to3SZJtQmcpCAVETS+L3nj9t7LJ68UPH9FgHij2w9OwtW64xWTtY+6breNj5tsec7sOIZURJBsFjx7eQDVMzH+iMgryBcVHRj5trW1IbIkz3j22We55JJLkFJSXl7OOeecw/PPP184pZ1oMmJEjGRG+lNLOKz11wKw1l+LJTN7PCks9pmRHtGVjXozkpmmVUBcWiSx2OLdB1kuOgrFpva7kGx+fUe47/cWxqb3MWprMw8lFsX/+9/l1Yb/D7/LWkBCQMeFwv+HR5AHF59QCnPDemRtTV77MVevytblyPp6aGnB++zTWVPnYtv4nnoCLAtZsztrG8am9/PSUAjW/XH/3VGmkrpl7nv+PzzsXqgO3qKlGXP1Stb8wZPt9AJER9Ba+wdPRrEOlHshiNQWZkpwy7Nm1j5XNmx6yoNyYMtzJo6VvpGTFLz/RO9ZiZs2ifZjzixesub3ro41f/BkXd+QbHFz7/c38r7Xv+2221i8eDFKKX79619nvF9TU8Pw4QfmNKurq6mtre2WmEPdduxHQc75aOkRVFUV5UwHIKSkpCxAFdmnbHoNAWVVIYJ42X8b3hklFIGwh6pwUc47DyVV72ne4wWZvc89ODl1pL3exdlmqP1tZB8KCSmpKPFDPsebYwZSAFVlAfAZ2S82ShH2G4S72Ieg984Tf5fxQnTZX1JKysJe/GbuFalCSaqqinI+2RFSUFYSpqQqX8XpdO6ngI+sFxulBAG/j6oqX84MtMoRPdrnndtWe3InRZMY7bElO0IKSsIhqg6zvw7F4fZB3kH+e9/7HgBPPPEEd999Nw8++OBh7bAr8p+TV3jKDVJG+sMjQ0nGR6qoi7Uy3l9Bbag5YzQvHTDrJXWkz2/11Jx8SZmfZiOePjBQ7iKpSH2CShmGcjJGOVJJqhqL2Ge3MbK4jJ3exrSVs0LBmEQ5da295AyoGkV5UTFGJP0uSPkDRD5+KbEsfZfRpws+ReU3v5kRVBQQm/9xInWtBBdcTOC+nyAT6Q/4rOrhNPpLIY/PqGz8BIzNmw7uclS4iHrbgzz1LMpF5jBBmR4aTz8HuzFGeVk5srEhow17+Agae8mNMfYS4PowmUNgRdkkh7q6KP6PXUJo2XJkLH0073g81I86htELWuGb2dsYPz9FXV2CCQu8LLvPi51I3yZU7ZDwR6g7jKRoB3/2VacKEKEMHdJUDDk9yr56h5GnB9i5yEA5B7YRpmLMhyzq6nomKV/GOVoFnqIQqchB9Rv8igkfT1BXl2L8xzzULsssVSg9Duaow+uvbuvcv8+eqPG6YMEClixZQmNjeum76upqdu/e3fH/mpoahg0b1t3m80Ig+FDLVExHYrRHPo9jUGmFmBFz7yamxIcxxCrC074QyVACU0nObZnqFvroJS5onu7ubf+1q/3f81qmAVDiBDg+MhpDSffBq3ILgsyOjqCi3Wp5Rtsx+JWnY1GV6UiCjpdTI4UrTHJIpKTlgd/hhEIonzs6dEIhrOkziLU/rDwkpaVEr//mwUsCcCorifz39wGIfuU67ImTcELusTv+AE64iNb7H8o7L3nzI38Gw0jvciFo+c3v3TbHjSfyjZtR/gDKMNzMiYEA0S9/FXuq+7m0PPxHECK9DSlp+cNj+R1rATC8MOtLSQ70lKtESPjoX92gHv/05Vhzj+voL+XzoQJBWh74HZgm/lI47vrObbg/gUrFvP92L6RzvpKkdKKDJ+Tuw/C7nv1z748VLK1xyTi3MLjhVwhDgVSYAcWxX05SMdUdiH3gR3H8FaqjcIgnpAhWKU77bu8tuBISznsgjhlSGL4DOiqmO8xof0A89dMphsy1D/SXzz2WDz0QR/ZDv+Ih3TWRSISWlhaqq6sBWLhwIbfffjuLFi1Km5t//PHHeeaZZ3jwwQdpampiwYIFPProo4walb8Tobs++ahIssG/l6hMMDxVyuhkeVoAVyi2exvZ5Wki4HiYlBhCKEe+9570yyaxeDO0hT2eVkrtAKdExmfkna83IrzvqwMU45NVVFnpV+cUNu/79xIvsgi0eJiYqMI8DDvokSLq6vD/9TFkbQ2peaeRPOdDWZ01kLtPzXeWErz7+8jGRhIXfYzYNV9Lrx5kWXiffxbPW2/ijBxF/OJPosoruie0pYXQd2/H8+472BOPIXLHd3GGVadtYqxdg++JvxEKeGg8+wKsmbPT26iro+jOb2OsWY01azZt/3UnlOWXfbSQ7Pq35NVv+kk1Ggw7OcWZ98bTMz86Dt5XXsLz2qs4VUNIXHwpztD0AVbtO5Kld/uIN7oFQGZfk0rrcseCLc+b1L4lCY9UTL44hf8IDjXXZ1+/VvL+EyZKwYSPWlTNTL/TTkVg4xMeGtZJKqfbTJxvYfZg6oRcOqN1gg1/NYnUCkbMsxl9jp22QE05sP0Vg12vGQSqFJMutgj1YJnCIxnJHzLI79u3j2uuuYZYLIaUkpKSEm6++WamT5/OVVddxbXXXsvMmTOxbZs777yTxYsXA3DVVVdx6aWXdutAemIxlI1DgxnB73i6rO060BdF9Ee60iq3b0M2N2FNmQaeLA/WIhHMTRtxhg7LCFgFQymMjRsoLw1QVzUq652CaKjH2LEde8xYVGmWtLyO4xax9nqxJ0zM2kZ0r6CtRlA2wcGT7ftoWRhr16CKinDG5l5h1OVnn0hgrl+LU16BM7L3LJ656MnzVDnQsE4ivYrSCeqI7jYGyvepR4N8b1LoIL/WV8visGszdIRiSCrMeS3TsuadGegfdn8km1ZZW0Px5z6DuXY1yjRBGrT9zz0kPnZxxzaB+35C6H9+gDJNRDJJ8owzaf3VQ6hw4R6+mStXUPz5y5D76hBCYJeU0vLrh7GOP9HdwLII3/R1/H99DOX1IpIpYpd9jsj37uq46/Asfo2i//wCItKGcBzs6uG0PPwn7MlTAEhF4eWv+tn2oon0gpOCOV9LcsKNyY7A5H3uGYqu+zJYFsKysY45hpaH/5Q1UOf67H1//D3hb90MCEQqRWrOXFp+8wdUZWXB+qu79NR5umuxwYv/6ScVESgHQtWKCx6OUT758LyLA+X7pIN8FnZ7mnmmZGXaIiSpBFVWmI83zcnYfqB/2P2RDK1KUfbBUzA2rEfYBx6aq0CApqf/iTXrWLxPP0nx1/4T0ckWqHw+kud8iJbfPloYYW1tVBw7FdnSnPayEw7T8O5qVGkZwe/8F4Ff/yrNzqkCQSI3fJPYtd9A7qml/KRj03UKgSqvoH75WvD5eOkrfjY9ZaY90DQDig/8T5zJn7Qw1q+j7EMfQHTeh2Fgjx5D45vLMu4Ksn32njffoOTSj6W3YXqwjp1D07MvHVk/HQE9cZ5G9ggePSmUbl8UCn+54nPLI1mSvR2agfJ96tUHrwOFFYGdWAfZyxyh2GdGaJaHV3tSc2QYq1Yit21LC/AAJBL4H7wfgOC996QFTgCRSOB98QVEU/rD/sPF948nwc6SWMu28f39b6AUgd/8OtOvH4sS/NXP3TYe+6O7Wqnz+0pBIo73xX+SipAR4MH1W797r3snGfjdryGZnutd2DZy7x7MpW/ldSyBX9wLB+u0UpirViI39+JiuV5g3WMe1MHZH5S7IGnri/3wiWc/YdAG+YhMZF18YShBVPb/6uyDEVm3J+tDWuE4GLt2tm+To4iKaSAaClMuSdbVIRKZjg0RiyH37nGLUUezL5gTTU1uG7t3Z2/DspB795Bsyz1RHNvnvid37si84AEI6erIg2yLtgCUx4PsCS9fHxLZLTIumuA+NI7t7f+F7fuKQRvkRyXLOuyVnbGF6rAmanoXa/ZcRDIzMDp+P8mzzwUgedoHXFvjQSivD2d0YfLrp046BZUl4ZkKhUidPA8MA3ty9nTS1rFz3TZO/0CHbTENIUidPI9glcJbkmXBlVSMmOcG9uRZ5+AEMrNaiVQS67jj8zqW5Jlno3yZ8xQilcKePj2vNgYKI08/YFvsjBBkLX6ucRm0QX5WbCQ+x4PsFOhNJTkxMqbLakyankNVVBC95lpUpwyJyudDVQ0hfvkVAERvugUVLnITbdHu6g4EafveXQXLAGmdcCKpeaehOgVYJxDAmj2H1OkfAKDthz9CBYKo9oesSkpUMEjbd38IQPK8C7AnTUb5A53aCJI470LsadMREs64K4EZOOBxF6bCDMFJt7oXuvgnP4NTXZ0WpJ1gkNjnv5iZETMHsf/8Ck5padpFSwWDRG6+taAPqvsDY8+zKJvkYPgPBHoz4GbMrJjWD5PG9BOMO+64446+FrGfWCyZc2lzd/FgMCk+BIVbk7XCCnFqZAJTEtnteKGQj2i0/0/jDBSdkF1r6rQzsCZNQe6pRYXCxD9zOa0/+2WHPVGVlJL4xCVugrFoFOvYubT9z09Inndhtl0cHkKQmP9xnMoK5N69GMOrafvS11znTPuFxBk1msS55yEbG8FxSH3wLFp//kBHFkukJH7xpahQCLmvDnvkKGI33Ez0lm91PDAtn+Qw/FSL2D6BlDDuAotzfxGnZFz7Se71kvjkp8HjQdbXY42fQPS224l96atZrZhZP/tgkPglnwbHQbY0Y02bTuQ7PyDxqc8Wrr8Og544T4WESRen8IQUsX2CopGK429IcNItycO2UQ6U71MunUIIgsGu03APWndNdxnoT9n7IwNFq9ZZeAaK1oGu86h212j6Kckkwe/eQcWk0VSOrKTk4osw1q9L28T/0ANUjBlK5ZBiKoeVUnTFZ8HpdDseiRC+5QYqxo+gclQVxf/xKeSO7QWXGrr1JiqHl7s6RlQQ/M7tae/Lmt0Uf+FyKkcPoWJcNeEbrkW0diqOrRT+3z1E+ewpVA6voPTMeXheezWtje3/kvxmSohfDAnziyFh/nJugHhTpw0ch8DPfkzFtAng9VJ64dmY775d8GP1vPkGpeeeQeWICspnTsL/wC9zJnrrzygFq37n4eHZIe4fHuaxM4PsfK3wK8P3rZT8/aIA948I85spIZb+yIvTTysh6pF8OwP9it4fyaa16Mr/wPfiPxFx1/anhECFwzS+9hbO8BH4/u+PFH31SxmJwVInnUzz0y+AUpRcdD6e5e92uFuUlKiychrefBdVUloQneEbrsX/+99l6IhedwPR226HSITyk+e4i6naHTLK68WaMo2mF18FIQjcew+hH92VVrxEBQI0PfYE1smnUL9O8tgZ+58LiI69+CsUX1jruntCt32TwB8eSW8jGKTx+Vewp+Rfa7grzOXvUjr/gjSvvRMIEvvSV4j+v28fVpt9dZ6+e6+Ht3+UnjzMDCg++lgs68PZw9HZvFnwf2eHSEXS9zHxYynO+knP5NnRI3nNgEBu34bvxec7Ajy43nKRSLgjRyB0+7cy/k4AniVvQmMD5vJ38axckWZfFI4D0Qj+x/5YMK3+Rx/Jmk8++Iufue8/8TdEa2uaBVIkkxibNuL592JIpQje86P06lS4Ns3QD78DwGu3+jq1fGAv8XrBlhcMRHMTgUd+l9EG8TjBn/zoyA+yneDd34d4epZHGYsSvP/nGR78/oydgnfuycwOacUES37YzfKRXbDs516sg2K5FRNs/JuHaD+0cuogr+k1zI3rs1oXRTKJZ8UyAGRjY84coZ4VyzHWr0Nl2ULGYhjLlxVGaDKZPj3UmfZygOZ7y5FZvPTCtjHWrkHW70NYmbVYAcz1awFoXCfJXr0Edi82MLZtRXkz8/oIx8F8b0UeB5If5prV7kKug1BSYNTsKth+epp4vcg5ZdKwvnChrm6FgbIyPzfDB82b+19I7X+KNIMWa/xERDLTIaA8HqzpM93fi4tzFmdMTZ+Zs86rEwhgt7dxxHi9udMat7tvrKnT0qyg+1GmiX3MJJzyiqx+f3D7AaBkvEOOsk0MO9HGHjU6e38JgTVtWh4Hkh/2MZOyqhC2gz20Oss7/RN/uXLrx2ahdHzhLJblUx03XfJB2AkoHtf/rJw6yGt6DWfceHexky89G6jyeold/WUA2m67PePvFGDNPhaqqrBOOBF74jHpvnAhwOsj/unC2QYTH7s4I/ApIHbFle77F1+a5qMH92LlDB9J6rQzwOsl9qWv4hx0IVCBgGuzBE7/fqJTywf24i1WTPiwjSorJ37Jp3ACB+Xa9fuJXnfjkR9kO5GbboWD9qECQWKfvxKyLfjqpxheOPZLyY589PsxA4oTbymcTXLO15IZeXIMv2LchT2bbvhwGbQ++e4y0P2y/ZFsWhMXfhTZUI+5dg3YNtbc42h96JGOzI32sXNQpolnyb87pkySp55O85PPu9kfhSCx4OPInTsx398ASpGad5qbuXHEyILpTH5kvlvXdp07tYKUxC/7HJG773H/7/WR+MhFmOvXuc4e0yRx4Udp+c0jEHQDY+rU08EwMd9bDvE49thxtN1zH6mzznH3O1RRPtVm+8smTvvuSyc6XPJCtCMlcfLsDyFiMczVKxGpFNaUabTe/xDW8Scc1rFmwxkxktTsOZjL30U0NKCKi4l+5Vr3oethGtD76jwdfqqNNBR17xnYcSgeqzjznjijz8q+IvZwdAYqFCNOtah7zyBaJzCDMOOKJGf8IJGWc76QaJ98ARgorpWBohMOoVUpN4jnmNIA3LnxLHP4aW0olV5wpNA689HhOG4w7Cog2naXx2olQZpdHIpSVFWEqGvILNpdUA6hM1/6w3nq2Bwy6B6pTsd2F2kVqoJWLrS7RpMXxqqVFF1zFaXnnUnojtuQtTV9osPz6isUX34ppR/5EIGf/xTRluNLliuwWhYl559F5dASKoeVUn7sVGhPcJY3joPvr49R8vGPwAc/iO/Pj4KV46ldVwEeOu4wstHR5xeek7XPU1FY8SsPTy4I8Oxlfra9nCMqCVGQ4HtIemMfvURPjaoP3kdPB/gjRY/k2+kPI498OFyd3pdfoPgLl0MigXAclNeLCoZofPFVnDFjCy+U7FoD995D6H/v6kgnrPwB7BEjaHxxEYS7HpHsp2JUFSKR6OQsd9m3ZjPkWSij6Iufw/vSP5HtOpxgkNSpp9Pyh/8r2Lf2UH1uxeGv5wVp3iqx221/ZlAx+0tJTsoyhzxQzlEYOFoHuk49kte4KEX4G9ciYjHXU45rWxQtzYR+8J1ekyGaGgnd/f20fPEiHsPYvYvAHx/Jqw3fg79MC/BwwIRYeslFebVhLnsH34sHAjyAjEbxLH7d9bgXgjz6fMNfPbRsOxDgAayoYPnPvf3Sb60ZmOggfxQg9u5FNtRnvu44eBf9q9d0mO++g/JmSYsbi+H953N5tRH87a+zvi4A86D0CLnwLH4dUlkeYsWieF5flFcbhyKfPt/6gpFe5agd6YHapYNn2kTTt+ggfxSgQqGceUicsizFqXtKR3m5+6Tq4NeFwBkyNK82nKoh2duGrBeQnDqy5ZP3+XEqKvJq45D7yKPPg0NUVr81uJ5vjaYQ6CB/NBAOkzj/wozVpk4w6Ka17SWs2XNwhlWnecsB8PuJffE/82qj+aHfA9mXEEWvvymvNhIfuShTAyCkIDH/E3m1cUjy6PMZV6QwDl7QKhS+EkX1SboIhqYw6CB/lND2k5+TOuVUlN+PU1yMmO5+7QAAGXlJREFU8vmI/8fniV/2ud4TIQTNj/0de+IxOMEgTlExTjBI2/fuxjouT993ZSXRr34daB+9t/+k5hxH7Lpv5NWEKi6h+c9/x6kaghMOQ1ERTnk5zX/4P1SeD27z4VB9XjnD4QM/juMJKTxFCjOoKBmruOhvUYT+ZmoKhHbXtDPQn7Lni9y2FWPnDqwp01AFmprIRU6tSrn5XZqbSM2eA1nSAxwSyyJ0202Ixiba7vwBDMteDKZLbBtzxTLKSgLUjZlcsMpTB3OoPrdisHeFgTesqJju5DT3DJRzFAaO1oGuMx93ja6Dd5ThjBnbY5ZJAJTCXPIm3jdeg7EjEWdd0FH1qQMhsKdNJ+eEhOPgefUVPMvewa4eTuKjCzLslbJuL874iRCPYzTUYx9OkDcMrLnHQ1URZPkC2QnY/JxJ8yZJ2WSHsedZmdMreXCoPjcDMFzXKB1QKAW1Swx2vWEQqFBMmJ/C3/0s172CDvKawmFZFF/xGTyvv+amE/b7KRc30Pznv2OddHJ+bcRilH7ioxhrVyOiUVQgSPj2W2l68nnsqW5SLu8Tj1N87Zfcb5ptE/rfu4n9x+eJtNdfLQSRWsHfzg+SaBakouAJQaBS8YnnogQq+s3Nr6YPcCx47go/u143seJg+uCNO3x85M+xfvksRc/8aQqG7y9/xvv6ImQ00p7jPYqMRCj5wmXucvk8CNx/H+aq95CRCEIpt62mJoqvvgIA0dxE8bVfQsTjrl/eshD/v707j4+qvPc4/jlnJrMlYQmGEAiCRagLSxSvFJdLCRDSGoRKRUGs9oK0KFxQKWCvt9qg3lKXF6igxKLeWqFpi4XGha0gi1jRK8pSpYjsIRFCErJMlpnz3D8GIpMZyCQkcyYzv/c/yZxzOPnOE/LLzMlznl+1G+cfXifuH9ta7Lls+oWdyiLN1xhCadRVaFQc1fjgv0ObwSOi194/W30FvkoDQ8Pj9v0/Wf0fjmCTx0wnRV60GMeyN/xudKpXVYV1V2jrnzvylqE1aGChAZZDB9ELjmHbsB4V7Nq52419xZ+akTqQMuDQeivK639x3PBofP2OvPmNdV8uiwt6f4OnSuPkrsgrqZGXSEQfjYtfKiCUKyThWEREbkQV56MRkf8/pMiLFlM94e6A9dPB15PU029AaOe4YwLK0WC9eU3D27MnRtdu1GYM92u5V8/ppPq2cc3K3ZCmQ4/hnoAblfQ4xXduidBuzSJsrphQF7BmPfjWHUruJ01DRBSrGTeeupuHYLjONNOIj8eIT+D0q2+GvBywe+p0PP0GYMTHo3Td97F9B07nvg7g+3zhSyiHE+VwoKxWlNOJ+yc/xfO9wS32XIY8XUN8F0VcggLN9zExzeDGnNZp1Czaju+O85B2s8dX6HXf/Q1x8YqsV90ReX+DzJM/o63Pl40YSmHd/hG2D7cS36MbJzN+gGrfxLllhkHclk3EffrJt1MoG3Qo0guPY89fCW43tSOy6mfeNMf5xtRbCwdWWyn9SifpzBRK3cRL8hH/vT9HW8na3JxKQeF2CwUfWnAkKS4fXYe9fSsEPEPmyUcDrxfrZ5+CYeC5ZmDzbsyprcW641OwxeEZcM1FN9NoFk3De/XV1HnqoHeP4AVeKSz/3PPtzVANW8zpOp7+A8BqxUhNDdqCzuiSivu+qa30JHwsNrj81ou/PGP9YAtxOz+nZsRIjMt7t0CyplMKiv+pU1Om0XmAl7i209UvImkapA7yRuSUyYYarSQlJSXMnj2bw4cPY7PZ6NGjBzk5OSQlJfkdN3fuXLZt20bHM4svZWVlMXVq6/4QRgvr9o9of+8EqHYDGtjiOP273/t6hYbItn4NiT+f7JsaYihUYiKn/5CHp3966wUPwrFkMQlP/hpliwOPh46X9aJs+V8wuvgaQuuHD9F+/Fj0Y0fBYkXzeKh44jdU332v7wRK4XoqB9fLi1B2G1ptHXXp13D698sDb6qKcHrBMTp+fzBaaSkA8Y/9Ek+/AZSu2xTWX8CnD2u8Pd5JxTEd3eKb533TE9Vcdbf8fSEWNHq5prS0lL179zJo0CAA5s+fT1lZGU899ZTfcXPnzqVv375MnDix2WFi8XKNdrqMpPQr0Ssq/LYrl4viT3YHrKUSLKd+7ChJNwxEc7v9thvt21O8818BTZpbS9ymjbS7Z7zfOu3KYsFzVV9K/74FlKLj4GuxHDxQv8Y6+Jpbl67Ix3Pd9dj/kkfCrBn+54izUfvvQzi9fEWr5G6t733SgO+iHz/uN+FC4WsCXr74lSafrzk5lYJlg+M5fVBDGd8msTp9a+R0ua51/lAY7Zdrwq1Vm4Z06NChvsADpKenU1BQ0IyYIhh7/iq/gneWMhT2lX8J6RyOvGXBbzbyerGvDW2d9pbgXLLIrzgDaF4v1q/+heWrfVg/34FeVBj4fKurcS7N9Z3jpRcCz1FXi23LZrQg67NHrKKigAIPvhl29lVvhS3Gic91qor8CzyApxp2LW2kraGICk268GsYBsuXLycjIyPo/tdee428vDy6d+/Oww8/TK9evZoUprHfSK0tOTkx/F+0rsrXKLoBvaaaxOoKEoNkCshZWRb8HF4v7eqqfGuzhENZSdDNWlwcSaoajOqgf2vQlMJRWowjORHKSoOfw2rhEqu31Z5Li3/vjx847y7N42n212vqvyszCP7HYqXhKY0jObkZi/GEyJSfp2aI9pxNKvLz5s3D5XIFvSTz4IMPkpycjK7rrFy5ksmTJ7N+/XosTWgMHIuXa6zp19MhzobWoIm04XRx+trvUdcgU7CctkE3kfjqq+iVlX7blVKUDLgeb5iel2voCFw7d6LV+E8zNDweirv1QqurpVOD1n3gu1xTMTST6hPlJAzJwLH8D4Hj4XJRHN8p6EJiF6tVvvcpPbhE1wPetSjAm9adkmZ8vebkdPQCT00CDe/SsToV3YbWcOJEXZNzhKKtXwaJNGHp8Tp//nwOHTrEggUL0IP80SglJaV++5gxY6iqqqKwsDDU08csT/q11GRm+d1EZLhc1N10M3WDbwzpHLXDMvGkXxtwjurb78Tbu0+LZz4f930/x+icgnH2ZiZNQzmdVP76SXC5UO07UDn7v1BOV/0NrL5G3mlU3/UTAKpmzUW171DfbEPpOsrppPzpBdCEFwym03UqZ/+yfr17zn7UNMoX5YYthr09XD+7Bqvz2yQWhyKhm8GVd7VOgReRJaRX8s899xy7d+8mNzcXW5C2aQBFRUWkpPhauG3ZsgVd1+sfiwsrX/Iq9pUrcLz5ezAMqu+8i5qx40K/Td9ioSzvrzj+tBz7n/4IDjvuu++lNnt06wZvQLXvQMmGrThe+x32tauJuzSNsnunUPe9G+qPcU+bgaf/AJyvvIReXExN9mjcP/lp/TRJI7UrpzZ/hDN3Mbatm/H26Il76jTflNA2xv3QbLy9Lid+3uPoJ0/g+e4VVDy7EG/f/mHNcc20OpL7G+x8JQ53scZ3sj30/UmdTKOMEY3Ortm3bx/Z2dn07NkTx5lXaGlpaSxatIjRo0eTm5tLSkoK9957L8XFxWiaRkJCArNnzyY9vWnT92Lxco2fs2/tLzC9LiJyhqK6muRunThRXNn4sSZrK2PaVnJC28na1nO2yM1QvXv3Zu/evUH3rVq1qv7z119/vbFTifPQiopI/MVMbOvWAIra72dQ8cxCjG5pZkdrMvv/vkrio3OhxreSZId+/SldtTqg6YcQIjwicKWFGFNXR8dbhmNbvwbN60HzerG9v4EOPxgGDZbcjXRxa1eT+IuZaDXV9X/ms+7aScd/v97UXELEMinyJrOtXY12qthvNonm9aKVl2N/e9UF/mXkSXh0TsA2DbAcPYpl52fhDySEkCJvNsv+rwLuVAXQKyuwfLXPhETNpxcVnnc5besnH4c1ixDCR4q8ybxXXIFyBC47YMQnXNTKimYwunU/b2+PuhtuCmsWIYSPFHmT1Q7LxOjaFRX37dRUZbWiOnWi5gfZJiZruvL5zwZsU4C31+UYV1wZ/kBCCCnyprNYKH17LdU/Hofhike5XNSMvo2S9zbAee5JiFSem4dweslrGO3a1d/4U3vzEEo2/cPsaELELFlPPgKojklULFxMxcLFZke5aLU/Gkvxj8YCvrm9p9vAHGQhollMv5JXKL62nWRl+89YzCY+ch2gWovMW70tu3aSOOluuPJKEn8+CcuXX5gdKSjtxAniH/8vOt74bzB0KLZ1q82OZCrr9o9od9c4Ot5wHQkPTkM/dNDsSCLGxHT7v+2ug3zuOopH891palEaTsPGuJKB2FXkvMmJ27aV9uPHQnU1mlK+/qkOB6VvvY3n2uvMjldPO3mSjt8fjF5agnZmVUzlclE56xHc02aYnO78WuuuR9vbq2j3wBRwu9Hwra2vXC5K17yPtxkdotrK3ZnQdrK29ZwtukBZtHFrdXzmOlJf4AG8msKt1fFPx3ETkwVKmPMwmtuNdub3sWYYaFVVJDw61+Rk/pxLFvkVeACtqor43z6JVhH5P0gtyjC+/b6d2aR5vWiVlbj+J8fUaCK2xGyRP2Etx6ICn75XNzhiO2VCovPwerH868ugu6yf7whzmAuzvb/Br8CfpeJsWPbsCX8gE+knvkE/fTpgu2YY2LZ9YEIiEatitsi7DBtGkFndmoIEr92EROeh6yhX8OUCjQ5BmmSbyEjtGnSevFZXh5GcHPY8ZjISEuE8dw0Yl8TWWAhzxWyR7+SNp53hQGvwc2hBp191N3NCBaNpuCdNwWjQp1U5Xbh/9oBJoYJz3z89oJ+sssbh6dsP4ztN6xLW5sXHUz36Ngy7w2+z4XJR9Z8PmhRKxKKYLfIaGtll/Uj2JGJROjYs2AwL3y/vQ7InstqBVc19lJqx41B2O7Rrh7I7cN91N+5pM82O5qfuezdQ/ptnMRISfa9kHQ7q/u16yt7IMzuaKSqeXkBt5kiU3Y6RmIhyOKl6YCY1P77D7GgihsT07JqzyvVqXJ1scML3Sj5SaSWnuKSimJPtklHtI+tSjZ+aGiz/2ktS70s54YjgnGe09gwL7ZtvsBQW4PnO5Re15HJbmQkCbSdrW8/ZIuvJx4JEw0EyiZwgsr/ZqmMS9OmBivT/lHY73n79fU23Izir7e1VOF96ESwa9nsmUTO26a+wrf/3MbZ334a4OGpuux1vn+8GHKM6d8bTuXNLRBaiyaTIi5jU7sejsW3eWP848R//wLH0FcreXR/yOeIfmYVz2Ru+df8tFlyLn6fiv3Oovu/nrRFZiGaJ3GsTQrQS65ZN2DZvRINv57ADcZ9sx/ZOfmjn+GQ7juV/qL9/QfN40KqrScj5FXqRNLAXkUOKvIg5rldeOu8+56u5IZ3D/reVQfsAKIuObW1sL+UgIosUeRFzzl3WOXBfXIjniAvecF3TQj6HEOEgRV7EnKoZD51/3/TQ5rDXjB0HQX5ZaF6D2pE/aHY2IVqaFHkRc7z906meeA+Kb+9JVUDNj36M58abQzvHVVdTOeeXKLsDw+nEcLlQDienF+f6ZkEJESFkdo2ISRXPvUDV5KnEL1qAw2ah5Kc/w9s/vUnncD8wg5oxY7GtWwM2GzVZP0QldWqlxEI0jxR5EbOMq66ifFEujuREvM2cz290S6P63kktnEyIliOXa4QQIopJkRdCiCgmRV4IIaKYFHkhhIhiUuSFECKKSZEXQogoJkVeCCGimBT5tsTrhVOnfB+FECIEjRb5kpIS7rvvPkaOHMmoUaOYNm0ap06dCjjO7XYzc+ZMRowYQVZWFhs3bgxyNtEsSuF8/jk69bkUUlPpdMVlOF552exUQog2oNEir2kakydPZs2aNeTn59O9e3eeeeaZgOOWLl1KQkIC69at4+WXX+bRRx+lsrKyVULHGufLi4h/9rfo5eVQW4teVkrCE49jX/aG2dGEEBGu0SLfoUMHBg0aVP84PT2dgoKCgOPee+897rjD1z6tZ8+e9O3bl82bN7dg1NjlWvgsmrvKb5vmriL+md+YlEgI0VY0ae0awzBYvnw5GRkZAfsKCgro1q1b/ePU1FQKC5vWIaexhrStLTk50dSvH5TXC6eKg+6yFBVGZuZzRHq+syRny2srWaM9Z5OK/Lx583C5XEycOLFZX6wxxcUVGIZq/MBWEMld25O6X4rlyOGA7Z7Le1MSoZkhssf0XJKz5bWVrG09p65rjb44Dnl2zfz58zl06BALFixAD9IRp2vXrhw7dqz+8fHjx+nSpUuopxcXUPHrJ1FOp9825XRS8dgTJiUSQrQVIRX55557jt27d7No0SJstuCt07KyssjLywPg4MGD7Nq1i5tvDq0Bg7iw2uzRnH71Der6DYB27ai7ZiBlb+RRlzHc7GhCiAjX6OWaffv2sWTJEnr27Mmdd94JQFpaGosWLWL06NHk5uaSkpLCpEmTmDt3LiNGjEDXdXJyckhIMPcaezSpHZZJ7bBMkpMTKW0Dby+FEJGh0SLfu3dv9u7dG3TfqlWr6j93uVw8//zzLZdMCCHERZM7XoUQIopJkRdCiCgmRV4IIaJYRDXy1nUtpr9+qNpKTmg7WSVny2srWdtyzlCya0opc+4+EkII0erkco0QQkQxKfJCCBHFpMgLIUQUkyIvhBBRTIq8EEJEMSnyQggRxaTICyFEFJMiL4QQUUyKvBBCRLGIWtYgXF588UVeeOEF8vPz6dOnj9++uXPnsm3bNjp27Aj4mqFMnTo17BkzMjKw2WzY7XYAZs2aFdCExe1288gjj7Bnzx4sFgtz5sxh6NChEZczEsa0pqaGp556ig8//BC73U56ejrz5s3zO8br9fLEE0+wZcsWNE1jypQp3H777RGX84UXXmDZsmV07twZgGuvvZbHHnssrDmPHj3KAw88UP+4vLyciooKtm/f7nec2WMaas5IGNONGzeycOFClFIopZg2bRqZmZl+xzRnPGOuyO/Zs4fPPvvMr+l4Q1OmTGm1PrZN8fzzzwf8EjrX0qVLSUhIYN26dRw8eJC77rqLtWvXEh8fH8aUjecE88f06aefxm63s2bNGjRN4+TJkwHH5Ofnc/jwYdauXUtpaSljxoxh8ODBpKWlRVROgDFjxjBnzpyw5WooLS3Nr5/Ek08+idfrDTjO7DENNSeYO6ZKKWbPns2bb75Jnz59+PLLLxk/fjzDhw/3a7fanPGMqcs1tbW15OTk8Pjjj5sdpUW899573HHHHQD07NmTvn37snnzZpNTRZ7KykpWrlzJjBkz0DTfgk6XXHJJwHHvvvsut99+O7quk5SUxPDhw1m9enXE5Yw0tbW15OfnM3bs2IB9Zo/puS6UMxLouk55ua/rW3l5OZ07dw7op92c8YypV/ILFy7k1ltvbfRVxGuvvUZeXh7du3fn4YcfplevXmFK6G/WrFkopRg4cCAPPfQQ7dq189tfUFDg944kNTWVwsLCcMdsNCeYO6ZHjhyhQ4cOvPjii3z00UfEx8czY8YMrrvuOr/jjh8/TteuXesfh3s8Q80J8M4777B161aSk5OZPn0611xzTdhyNrRhwwZSUlK4+uqrA/aZPabnulBOMHdMNU1jwYIF3H///bhcLiorK8nNzQ04rjnjGTOv5Hfs2MHu3buZMGHCBY978MEHWbduHfn5+WRmZjJ58uTzvr1rTW+++SZ/+9vfWLFiBUopcnJywp4hFKHkNHtMvV4vR44c4aqrruKtt95i1qxZTJ8+nYqKirBlCEWoOe+8807+/ve/k5+fz6RJk7j//vspKSkxKTWsWLEiYl8dn+tCOc0eU4/Hw5IlS1i8eDEbN27kpZdeYubMmVRWVl70uWOmyH/88cfs37+fYcOGkZGRQWFhIZMmTWLr1q1+x6WkpNS/RRozZgxVVVWmvPJITU0FwGazMWHCBD799NOAY7p27cqxY8fqHx8/fpwuXbqELSOEltPsMU1NTcVqtZKdnQ3AgAED6NixIwcOHAg4rqCgoP5xuMcz1JzJycnExcUBcOONN5Kamsq+ffvClvNcRUVFfPzxx4waNSrofrPH9KzGcpo9pl988QXffPMNAwcOBGDgwIE4nU7279/vd1xzxjNmivyUKVPYunUrGzZsYMOGDXTp0oWlS5dy0003+R1XVFRU//mWLVvQdZ2UlJSwZq2qqqq/NqeU4t133+XKK68MOC4rK4u8vDwADh48yK5duwJmtkRCTrPHNCkpiUGDBvHBBx8AcODAAYqLi+nRo4ffcVlZWfz5z3/GMAxOnTrF+vXrGTlyZMTlPHc8v/jiC44dO8Zll10Wtpzn+utf/8qQIUPqZ041ZPaYntVYTrPHtEuXLhQWFvL1118DsH//foqLi7n00kv9jmvWeKoYNXToULV3716llFK33nqrKiwsVEopdc8996js7Gw1atQoNX78eLVjx46wZzt8+LAaPXq0ys7OVj/84Q/V9OnTVVFRUUDWyspKNX36dDV8+HCVmZmp1q1bF5E5I2VMJ06cqLKzs9WYMWPU+++/r5RSavLkyWrnzp1KKaU8Ho/61a9+pYYNG6aGDRum/vjHP0ZkztmzZ6tbbrlFjRo1St122231x5ghMzNTbdq0yW9bpI2pUo3njIQxXbVqVf3PyahRo+p/ni92PKUzlBBCRLGYuVwjhBCxSIq8EEJEMSnyQggRxaTICyFEFJMiL4QQUUyKvBBCRDEp8kIIEcWkyAshRBT7f0o9TFi501GeAAAAAElFTkSuQmCC\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? Explain.\n",
        "\n",
        "feature scaling ensures that all the features get same weight in the clustering analysis\n",
        "\n",
        "2. What are ways to prevent initialization variation in KMeans?\n",
        "\n",
        "Simple furthest point heuristic (Maxmin) reduces the number of erroneous clusters from 15% to 6%, on average, with our clustering benchmark. Repeating the algorithm 100 times reduces it further down to 1%. This accuracy is more than enough for most pattern recognition applications. However, when the data has well separated clusters, the performance of k-means depends completely on the goodness of the initialization.\n",
        "\n",
        "3. What is the training and testing complexity of KMeans?\n",
        "\n",
        "For Lloyd's algorithm the training complexity is K * I * N * M K-number of clusters I- number of iterations N- sample size M- number of variables"
      ]
    },
    {
      "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"
      ]
    }
  ]
}