agglomerative_algorithm-2.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "agglomerative algorithm.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xy1YS_ld5UNN"
      },
      "source": [
        "**1.Importing important libraries and defining data on which algorithm is to be applied**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AR9OvpphvUZQ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a19e0bc9-6521-4ae7-c815-ac126f1eca46"
      },
      "source": [
        "import pandas as pd\n",
        "import tensorflow as tf\n",
        "import numpy as np\n",
        "#Our Dataset\n",
        "# data = np.array([0.40,0.53,0.22,0.38,0.35,0.32,0.26,0.19,0.08,0.41,0.45,0.30]).reshape(6,2)\n",
        "data=[[np.random.randint(1,50),np.random.randint(50,100)] for i in range(100)]\n",
        "print(data)\n",
        "from sklearn.metrics.pairwise import pairwise_distances\n",
        "import sys\n",
        "data=np.array(data)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[47, 80], [6, 72], [48, 68], [8, 79], [19, 84], [22, 97], [39, 64], [17, 94], [30, 79], [33, 72], [22, 94], [27, 53], [24, 81], [47, 50], [43, 88], [46, 77], [45, 78], [38, 91], [24, 70], [47, 73], [40, 58], [8, 85], [46, 65], [48, 76], [25, 82], [44, 88], [1, 65], [41, 96], [47, 63], [6, 89], [3, 88], [7, 90], [12, 71], [44, 89], [10, 97], [40, 73], [35, 58], [26, 95], [31, 61], [21, 96], [1, 53], [46, 55], [21, 86], [32, 97], [16, 71], [39, 97], [27, 59], [14, 58], [31, 73], [21, 64], [18, 68], [33, 66], [1, 62], [18, 67], [7, 63], [37, 75], [24, 54], [36, 76], [35, 85], [37, 70], [36, 84], [2, 64], [39, 94], [44, 84], [36, 97], [46, 89], [44, 67], [49, 93], [27, 95], [19, 69], [43, 95], [27, 95], [33, 69], [39, 59], [30, 81], [33, 82], [22, 76], [25, 86], [41, 83], [11, 70], [5, 90], [31, 92], [23, 73], [37, 71], [36, 90], [21, 87], [10, 82], [28, 74], [8, 92], [8, 68], [43, 92], [8, 72], [6, 95], [21, 77], [35, 80], [25, 90], [13, 93], [12, 63], [33, 86], [24, 60]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HxPGBBPsZzXO"
      },
      "source": [
        "**2.Visualizing Data**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sx_chhdayZpP",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 325
        },
        "outputId": "8d7030a0-a98b-4d31-d6a1-0ee0f67d2906"
      },
      "source": [
        "\n",
        "import matplotlib.pyplot as plt\n",
        "fig = plt.figure()\n",
        "fig.suptitle('Scatter Plot for clusters')\n",
        "ax = fig.add_subplot(1,1,1)\n",
        "ax.set_xlabel('X')\n",
        "ax.set_ylabel('Y')\n",
        "ax.scatter(data[:,0],data[:,1])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f0923d652b0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 19
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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0rr+u37Q1m+OVe99zqicROeWMm+JccrpG9dczzt848r1DPF659z0HfkuWxz6GJYXj1VRePoW6tMmpHkuWxz6Gpe/j1WRevu+6tM2B35LlsY9h6ft4NZmX77subfNCLGaWBS/Cs7NxC7E4xz9gOd9nnLqc2j6XuuSel2+SUz0Dlft9xinLqe1zqkvuefkmOfAPVO73Gacsp7bPqS655+Wb5FTPQOV+n3HKcmr7nOoCng+zUL7iHygvKt6fnNo+p7rYwjnwD5Tzmd246KotHLPmMg5d/WWOWXMZF121JYm2H1WuaaRQF+ueA/9AOZ/ZvnEDn0Cvbd/kgKz7UZl8H7/ZGMesuWzk7YHLlizm8tXH91CiSqrlsvSMu4+/1St+SWdIulbSNZLOk/R4SYdK2iDpJknnS9qrzTKYTSvVgc9Uy2XD0Vrgl7QM+D3gqIh4FrAIeAPwAeAjEXEY8CPgLW2VwWx3pDrwmUK5mhpjKEVq7dV2jn8PYLGkPYAnAHcAxwMX1D9fB5zachnMppLqwGff5cpp0lcXUmyv1gJ/RGwBPgR8nyrg/zNwJbAtIh6q33Y74FEkS1KqA599lyunSV9dSLG9WpvAJWkf4NXAocA24LPAyyb4/VXAKoDly5e3UUSzXUp1QlCf5fIYw2RSbK82Z+6eCNwSEVsBJF0IHAMskbRHfdV/EDDy752IWAushequnhbLmYRcHpRl3eizv/hhaJNJsb3azPF/Hzha0hMkCTgBuA5YD/xG/Z7TgC+0WIZBSDEHaOnqu7/0PcYwNCm2V5s5/g1Ug7jfBq6u97UWeBfwXyTdBOwHnNNWGYYixRygpavv/tL3GMPQpNherT6kLSLeDbx7zubvAS9oc79Dk2IO0NKVQn9JdewjVam1l5/OmYAUc4CWLveXfuUwHudn9SQgxRygpcv9pT99j680xYE/ASnmAC1d7i/96Xt8pSlO9SQitRygpc39pR8pjK80wYHfspNDDtbSNN/4ypD6nVM9lpVccrCWpnHjK8etXDqofufAb1nJJQdraRo3vrJ+09ZB9TuneiwrueRgLV2jxlfOOH/jyPem2u98xW9ZSeFZ9VaeofU7B37Lynz3uKe2GEaOSm3jaedW9NVeTvVYVmb+BJ97dwXA2Rde/UgedvbC6aneeTE0MwPrJbbxuH43X737bC8vtm5F8ALl7XMbT6aL9uplsXWzVHjQt31u48n02V5O9VgR/GCz9uUyuakrffZJX/FbEfxgs/blMrmpK332SQd+K4IfbNa+XCY3daXPPunBXTNr1aGrv8yoKCPgljWndF2coowb3HWO36xnuee/Pb6SHqd6zHpUwkPlPL6SHgd+sx6V8FA5j6+kZ2yqR9LfAv8pIm7trjhmZSnl3ncvHJOW+XL8fw18TdI64E8jYntHZTLrXF959qbz37mPF8Aw65hamccG/oj4rKT/C/xX4ApJnwAenvXzD3dQPrPW9fnMlDNPPvwx+4bp898lPCtniHVMscy7yvE/CNwPPA540pwvsyz0mWdvMv9dwnjBEOuYYpnny/G/DPgwcDHwvIj4aWelMutQ33n2pvLffdejC0OsY4plni/H/wfAayPi2q4Kk5NJc3qp5QBLkst95tPWY0h9b4jHKsUyj031RMSvOuhPZ9J7s0u4lztludxnPk09htb3hnisUiyz7+NvwaQ5vRRzgCXJ5T7zaeoxtL43xGOVYpn9yIYWTJrTSzEHWJpc7jOftB5D7HtDPFapldlX/C2YdOHloS3UbPlw3yuTA38LJs3pdZkD7GJx51IX3B6irvqe+0RanOppwaQLL0+zUPM0uphIkuJkFRuvi77nPpEeP4+/IF0s7uwFt20u94n+dL7YuqTDJW2c9fVjSW+XtK+kSyTdWP+7T1tlsMfqYiBviIOF1i73ifS0Fvgj4oaIODIijgR+Bfgp8HlgNXBpRDwduLR+bQ0al0/tYiAvt8FC56Z3X259IgddDe6eANwcEbcBrwbW1dvXAad2VIYizDchp4uBvBQnq0xraJObUnXcyqUTbbf2dRX43wCcV3+/f0TcUX9/J7B/R2UownwTcrqYSJLiZJVpDW1yU6rWb9o60XZrX+t39UjaC3gVcPbcn0VESBo5uixpFbAKYPny5a2WMSe7yqd2MZEktckq03Juuhlux/R0cTvny4FvR8Rd9eu7JB0QEXdIOgC4e9QvRcRaYC1Ud/V0UM4spPhAqN3R5wPEcmvLcdpu41LacUi6SPW8kUfTPFA95vm0+vvTgC90UIZiOMfenJzacpwu2riEdhyaVgO/pL2Bk4ALZ21eA5wk6UbgxPq1NcQ59ubk1JbjdNHGJbTj0LSa6omI+4H95my7l+ouH2uJc+zNyaUtx+mqjXNvx6HxIxsSMaTFMNowqv7ODbfPbdyvvs57P6QtAX3nsvs2rv7HrVzq3HDLnH/vT5/nvQN/AvrOZfdtXP3Xb9rq3HDLnH/vT5/nvVM9CUghl92n+erv3HD73Mb96PO8d+BPQOl51tLrb2nKeX6DUz0JKD3P6me5WGpyn9/gwJ+A0vOsfpaLpSb3+Q1O9SSi5Dxr6WMclp7c5zf4it965+e1W2py75MO/Na70sc4+ubFZnaWe590qsd619Vi87YzL4Q+Wu590outmxXMC6HnrfPF1s0sfR5YL1O2qZ7SH3pmthCePNecIcWcLK/4S3/omdlC5T6I2ZWhxZwsA3/pDz0zW6jSJw82ZWgxJ8tUj/OWZgtX8uTBpgwt5mQZ+OfLWw4pD2fT8THOw5CO49DGSrJM9YzLWx63cumg8nA2uaHlWm20oR3HoY2VZBn4x+Ut12/aOqg8nE1uaLlWG21ox3FoYyVZpnpgdN7yjPM3jnxvqnk4m9zQcq022hCP45DGSrIN/KOkkIfrO2/Z9/7blsIxtt2X23FM7bzLMtUzTt95uL7zln3vvwt9H2NrRk7HMcXzrqjA33ceru+8Zd/770Lfx9iakdNxTPG8KyrVA/3m4frOW/a9/64MKddq4+VyHFM877IN/Knl1KD/vGXf+zcrUYrnXZapnhRzatB/3rLv/ZuVKMXzLsvAn2JODfrPW/a9f7MSpXjeZbkQy6Grv8yoWgm4Zc0pjZXLzCxlRS3EkvtCyWZmuyPLwJ9iTs2sC1443RYiy7t6cl8o2WwUL5xuC5Vl4Id87gE2W6j5bmrwuWCztZrqkbRE0gWSNkm6XtKLJO0r6RJJN9b/7tNmGcxKkeJEIUtT2zn+jwJfiYiVwHOA64HVwKUR8XTg0vq1WZKGlDP3TQ22UK0FfklPBn4NOAcgIh6MiG3Aq4F19dvWAae2VQaz3ZHqRMBxfFODLVSbV/yHAluBv5Z0laSPSdob2D8i7qjfcyewf4tlMJtaqhMBx0lxopClqc3B3T2A5wG/GxEbJH2UOWmdiAhJI2eQSVoFrAJYvnx5i8U0G22IOXPf1GAL0Wbgvx24PSI21K8voAr8d0k6ICLukHQAcPeoX46ItcBaqGbutlhOs5GafrhWig8OTJnbqz2tpXoi4k5gs6SZBOMJwHXAxcBp9bbTgC+0VQaz3dFkznxo4wV9c3u1q+27en4X+JSk7wJHAn8CrAFOknQjcGL92iw5TebMhzZe0De3V7tancAVERuBnR4QRHX1b5a8pnLmQxwv6JPbq13Zzty1ZjjP2owUF+PYHW33i/nay31y92X5kDZrhvOszcnpHvsu+sW49jpu5VL3yQY48NtYzrM2J6d77LvoF+Paa/2mre6TDXCqx8ZynrVZudxj31W/GNVeZ5y/sZN9585X/DaWn/1io/TZL9wnm+HAb2PllJe25vTZL9wnm+FUj43lBW1slD77hftkM7JcbN3MzApbbN3MzMZz4DczK4wDv5lZYRz4zcwK48BvZlYY385pZtaAIT08zoHfzGw3zTy4buY5QjMPjwOSDP5O9ZiZ7aahPdDQgd/MbDcN7YGGTvWYzWNIeVvrz9AW2vEVv9kYXojGFmpoD49z4DcbY2h5W+vP0BbacarHbIyh5W2tX0NaaCfbwO/crO2upvO27pOWiixTPc7NWhOazNu6T1pKsgz8zs1aE5rM27pPWkqyTPU4N2tNaSpv6z5pKcnyit8LMltq3CctJVkG/qHdU2v5c5+0lGSZ6vGCzJYa90lLiRdbNzPLlBdbNzMzwIHfzKw4DvxmZoVx4DczK4wDv5lZYVq9nVPSrcB9wA7goYg4StK+wPnACuBW4HUR8aM2y2Fm1qfUHtDXxRX/cRFx5KxbilYDl0bE04FL69dmZllK8QF9faR6Xg2sq79fB5zaQxnMzDqR4gP62g78AXxN0pWSVtXb9o+IO+rv7wT2H/WLklZJukLSFVu3bm25mGZm7UjxAX1tB/5jI+J5wMuB35H0a7N/GNW04ZFThyNibUQcFRFHLV26tOVimpm1I8UH9LUa+CNiS/3v3cDngRcAd0k6AKD+9+42y2Bm1qcUH9DXWuCXtLekJ818D7wUuAa4GDitfttpwBfaKoOZWd9SXIi9zds59wc+L2lmP5+OiK9I+hbwGUlvAW4DXtdiGczMepfaQuytBf6I+B7wnBHb7wVOaGu/ZmY2P8/cNTMrjAO/mVlhHPjNzArjwG9mVphBLL0oaSvVHUDzeQpwTwfFSVHJdYey6++6l2sh9T8kInaaATuIwL8Qkq4YtbZkCUquO5Rdf9e9zLrD7tXfqR4zs8I48JuZFSanwL+27wL0qOS6Q9n1d93LNXX9s8nxm5nZwuR0xW9mZgsw+MAv6WWSbpB0k6Tsl3GU9HFJd0u6Zta2fSVdIunG+t99+ixjWyQdLGm9pOskXSvpbfX27Osv6fGSvinpO3Xd/6jefqikDXX/P1/SXn2XtU2SFkm6StKX6tdF1F/SrZKulrRR0hX1tqn7/aADv6RFwP+iWujlCOCNko7ot1StOxd42Zxtpaxj/BDwjog4AjiaanGfIyij/j8Djo+I5wBHAi+TdDTwAeAjEXEY8CPgLT2WsQtvA66f9bqk+je2fvmgAz/Vwi43RcT3IuJB4G+o1vTNVkT8PfDDOZuLWMc4Iu6IiG/X399HFQCWUUD9o/KT+uWe9VcAxwMX1NuzrPsMSQcBpwAfq1+Lguo/wtT9fuiBfxmwedbr2+ttpVnQOsY5kbQCeC6wgULqX6c5NlKtWncJcDOwLSIeqt+Se///M+As4OH69X6UU/+p1y8fpc2FWKwHERGSsr5VS9ITgc8Bb4+IH9eL/QB51z8idgBHSlpCtZTpyp6L1BlJrwTujogrJb2k7/L04NiI2CLpqcAlkjbN/uGk/X7oV/xbgINnvT6o3laaYtYxlrQnVdD/VERcWG8upv4AEbENWA+8CFgiaeYCLuf+fwzwKkm3UqV0jwc+SiH1b3r98qEH/m8BT69H9vcC3kC1pm9piljHuM7pngNcHxEfnvWj7OsvaWl9pY+kxcBJVGMc64HfqN+WZd0BIuLsiDgoIlZQneeXRcRvUkD921i/fPATuCS9gir3twj4eES8r+citUrSecBLqJ7MdxfwbuAi4DPAcup1jCNi7gDw4Ek6FvgH4GoezfP+PlWeP+v6S/plqgG8RVQXbJ+JiD+W9ItUV8D7AlcBb4qIn/VX0vbVqZ53RsQrS6h/XcfP1y9n1i9/n6T9mLLfDz7wm5nZZIae6jEzswk58JuZFcaB38ysMA78ZmaFceA3MyuMA7/ZhOqnhN4iad/69T716xX9lsxsYRz4zSYUEZuBvwTW1JvWAGsj4tbeCmU2Ad/HbzaF+tERVwIfB04HjoyI7f2Wymxh/JA2sylExHZJZwJfAV7qoG9D4lSP2fReDtwBPKvvgphNwoHfbAqSjqR6UNrRwBkzT0k0GwIHfrMJ1U8J/Uuq9QC+D3wQ+FC/pTJbOAd+s8mdDnw/Ii6pX/8F8ExJ/6rHMpktmO/qMTMrjK/4zcwK48BvZlYYB34zs8I48JuZFcaB38ysMA78ZmaFceA3MyuMA7+ZWWH+P6YWd8q8uhXkAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Tjko3pM55nr-"
      },
      "source": [
        "**3.Function that deals with distancing , clustering and plotting**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hhz5LiW5yoxi"
      },
      "source": [
        "def hierarchical_clustering(data,linkage,no_of_clusters):  \n",
        "    #first step is to calculate the initial distance matrix\n",
        "    #it consists distances from all the point to all the point\n",
        "    color = ['r','g','b','y','c','m','k','w']\n",
        "    initial_distances = pairwise_distances(data,metric='euclidean')\n",
        "    #making all the diagonal elements infinity \n",
        "    np.fill_diagonal(initial_distances,sys.maxsize)\n",
        "    clusters = find_clusters(initial_distances,linkage) \n",
        "    \n",
        "    #plotting the clusters\n",
        "    iteration_number = initial_distances.shape[0] - no_of_clusters\n",
        "    clusters_to_plot = clusters[iteration_number]\n",
        "    arr = np.unique(clusters_to_plot)\n",
        "    \n",
        "    indices_to_plot = []\n",
        "    fig = plt.figure()\n",
        "    fig.suptitle('Scatter Plot for clusters')\n",
        "    ax = fig.add_subplot(1,1,1)\n",
        "    ax.set_xlabel('X')\n",
        "    ax.set_ylabel('Y')\n",
        "    for x in np.nditer(arr):\n",
        "        indices_to_plot.append(np.where(clusters_to_plot==x))\n",
        "    p=0\n",
        "    \n",
        "    print(clusters_to_plot)\n",
        "    for i in range(0,len(indices_to_plot)):\n",
        "        for j in np.nditer(indices_to_plot[i]):\n",
        "               ax.scatter(data[j,0],data[j,1], c= color[p])\n",
        "        p = p + 1\n",
        "        \n",
        "    plt.show()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-DpiylFn575a"
      },
      "source": [
        "**4.This function finds minimum element and updates proximity matrix.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hcoa5Qmzy9s4"
      },
      "source": [
        "def find_clusters(input,linkage):\n",
        "    clusters = {}\n",
        "    row_index = -1\n",
        "    col_index = -1\n",
        "    array = []\n",
        "    \n",
        "\n",
        "    for n in range(input.shape[0]):\n",
        "        array.append(n)\n",
        "        \n",
        "    clusters[0] = array.copy()\n",
        "\n",
        "    #finding minimum value from the distance matrix\n",
        "    #note that this loop will always return minimum value from bottom triangle of matrix\n",
        "    for k in range(1, input.shape[0]):\n",
        "        min_val = sys.maxsize\n",
        "        \n",
        "        for i in range(0, input.shape[0]):\n",
        "            for j in range(0, input.shape[1]):\n",
        "                if(input[i][j]<=min_val):\n",
        "                    min_val = input[i][j]\n",
        "                    row_index = i\n",
        "                    col_index = j\n",
        "        \n",
        "        #once we find the minimum value, we need to update the distance matrix\n",
        "        #updating the matrix by calculating the new distances from the cluster to all points\n",
        "        \n",
        "        #for Single Linkage\n",
        "        if(linkage == \"single\" or linkage ==\"Single\"):\n",
        "            for i in range(0,input.shape[0]):\n",
        "                if(i != col_index):\n",
        "                    #we calculate the distance of every data point from newly formed cluster and update the matrix.\n",
        "                    temp = min(input[col_index][i],input[row_index][i])\n",
        "                    #we update the matrix symmetrically as our distance matrix should always be symmetric\n",
        "                    input[col_index][i] = temp\n",
        "                    input[i][col_index] = temp\n",
        "        #for Complete Linkage\n",
        "        elif(linkage==\"Complete\" or linkage == \"complete\"):\n",
        "             for i in range(0,input.shape[0]):\n",
        "                if(i != col_index and i!=row_index):\n",
        "                    temp = min(input[col_index][i],input[row_index][i])\n",
        "                    input[col_index][i] = temp\n",
        "                    input[i][col_index] = temp\n",
        "        #for Average Linkage\n",
        "        elif(linkage==\"Average\" or linkage == \"average\"):\n",
        "             for i in range(0,input.shape[0]):\n",
        "                if(i != col_index and i!=row_index):\n",
        "                    temp = (input[col_index][i]+input[row_index][i])/2\n",
        "                    input[col_index][i] = temp\n",
        "                    input[i][col_index] = temp\n",
        "        \n",
        "        elif(linkage==\"Centroid\" or linkage ==\"centroid\"):\n",
        "            for i in range(0,input.shape[0]):\n",
        "                if(i!=col_index and i!=row_index):\n",
        "                    dist_centroid = cal_dist_from_centroid(i,row_index,col_index)\n",
        "                    input[col_index][i] = dist_centroid\n",
        "                    input[i][col_index] = dist_centroid\n",
        "                   \n",
        "        #set the rows and columns for the cluster with higher index i.e. the row index to infinity\n",
        "        #Set input[row_index][for_all_i] = infinity\n",
        "        #set input[for_all_i][row_index] = infinity\n",
        "        for i in range (0,input.shape[0]):\n",
        "            input[row_index][i] = sys.maxsize\n",
        "            input[i][row_index] = sys.maxsize\n",
        "            \n",
        "        #Manipulating the dictionary to keep track of cluster formation in each step\n",
        "        #if k=0,then all datapoints are clusters\n",
        "       \n",
        "        minimum = min(row_index,col_index)\n",
        "        maximum = max(row_index,col_index)\n",
        "        for n in range(len(array)):\n",
        "            if(array[n]==maximum):\n",
        "                array[n] = minimum\n",
        "        clusters[k] = array.copy()\n",
        "           \n",
        "    return clusters"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qUeFE0UxaJp8"
      },
      "source": [
        "**5.different clusters shown as different colors**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LY4IHp1zzkOY",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 345
        },
        "outputId": "c49ce2ce-5d7d-409a-97a8-1b25300d665f"
      },
      "source": [
        "hierarchical_clustering(data,\"single\",6)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 11, 1, 13, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 40, 13, 1, 0, 1, 0, 1, 47, 0, 1, 1, 0, 1, 1, 1, 0, 11, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hlDwHRSgaND0"
      },
      "source": [
        "**6.DATA POINTS WITH SMALEEST EUCLIDEAN DISTANCE BETWEEN ARE TAKEN INTO SINGLE CLUSTERS**\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "19_jbITo5Lnu"
      },
      "source": [
        "* Data point (2,5) clustered together"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kzzFf6XV0JnT",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 325
        },
        "outputId": "ead34198-72da-41d4-e710-2f5f26511ef2"
      },
      "source": [
        "hierarchical_clustering(data,\"single\",5)\n",
        "#you can see that the color of data[2] and data[5] became same, thus they are in same cluster now"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0, 1, 1, 3, 3, 3, 6, 0, 8, 3, 0, 3, 3, 0, 1, 3, 0, 3, 3, 3, 0, 0, 3, 3, 0, 1, 3, 8, 3, 3, 3, 1, 3, 1, 3, 1, 3, 3, 3, 1, 1, 8, 3, 0, 3, 3, 6, 3, 3, 3]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAEjCAYAAADdZh27AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAeIElEQVR4nO3df5RkZX3n8fenB2htNPwcO/zqKifgKGIk0hpUkriOMagg7J4Iuu0Gf9G7HncjOSpL0ruL5KTPYuIqZpO46ahhVloEf0PW9cAZJRod0ZmICuIsOHQ3IPQMPwaVNsNAf/ePe6umpqeqp7vmVt1bdT+vc+pU36du3fvU7dv17ft87/M8igjMzMwABvKugJmZFYeDgpmZ1TkomJlZnYOCmZnVOSiYmVmdg4KZmdU5KFjpSXq/pGsy3N47Jc1L+oWkY7LabpP9vEXSP3Vq+1ZODgq2YpLOkvQtSY9JekTSNyW9+CC3ud8Xm6SrJf3ZwdV2v/1cLemJ9Iv6EUk3S3puG9uZkfSqZV4/FPgQ8OqIeEZEPHww9e4GSSHp5LzrYcXgoGArIulXgH8A/idwNHACcAWwO896NSPpkBYv/XlEPAM4EdgBXN2B3Q8DTwPuWO0bleipv8lljrX1qJ46AS1XzwGIiGsj4qmI+GVE3BQRP6itIOliSXdK+rmkH0l6UVp+maSfNJT/67T8ecD/Al6a/ge/S9I4MAZcmpbdmK57vKTPSdop6R5Jf9iw3/dL+qykayT9DHjLch8kIhaATwGnNXtd0usl3ZHW55a0nkj6JDAC3JjW7dIl73sOsC1d3CXpq2n5yyR9N73C+q6klzW85xZJk5K+CSwA65rU5yRJn08/+8OS/qrJOtX0P/5DGspukfSO9OeTJf1jWoeHJF2Xln89Xf376We6MC0/R9Jt6TH4lqRfb9jujKT/LOkHwOOSDkmX709/x9skbVjud2AFFhF++HHAB/ArwMPARuA1wFFLXn8DcD/wYkDAyUCl4bXjSf4JuRB4HDgufe0twD8t2dbVwJ81LA8AW4H/BhxG8sW5Hfi99PX3A3uA89N1n96k/vVtAs8gCQrfaHj/NenPz0nr97vAocClwN3AYenrM8CrljlOVSCAQ9Llo4FHgX8HHAK8KV0+Jn39FmAOeH76+qFLtrcG+D7wYeBwkquQs5Yeu6X7bdj2O9KfrwUm0uNT30b6WgAnNyz/BsmV1G+m+78o/dyDDcfgNuAk4OnAeuBe4PiGuvxa3uesH+09fKVgKxIRPwPOIvkC+Ttgp6QbJA2nq7yDpHnmu5G4OyJm0/d+JiJ+GhGLEXEdcBfwklXs/sXA2oj404h4IiK2p3V4Y8M6myPii+k+ftliO++VtIvkS/4ZNL+iuBD4PxFxc0TsAT5I8sX3sibrrsTrgLsi4pMR8WREXAv8GDi3YZ2rI+KO9PU9S97/EpKA+r6IeDwi/iUi2kku7wEqJF/cB9rGOPC3EXFrJFeFG0maCc9sWOcvI+Le9Fg/BQwCp0o6NCJmIuInbdTRCsBBwVYsIu6MiLdExIkkTS/HA1elL58ENP0ikPQHDU0Ru9L3HruKXVeA42vvT7fxJyTt9zX3rmA7H4yIIyPiVyPi9S2+uI4HZmsLEbGYbvuEVdS35fZSs0u2t1zdTwJmI+LJNvdfcynJFdx30qaxty2zbgV4z5LjfRLJZ9mvzhFxN3AJyRXXDkmfltS4rvUQBwVrS0T8mKRJptYufy/wa0vXk1Qh+a/+P5I0mRwJ3E7yBQXJlcd+m1+yfC9wT/qFXns8MyJeu8x72vVTki/FWv1F8oV4f5v72Wd7qZGG7R1om/cCIytI6D6ePg81lP1qfQcRD0bExRFxPPDvgb9Z5o6je4HJJcd7KL3KaVrniPhURJxF8lkD+MAB6msF5aBgKyLpuZLeI+nEdPkkkvbxb6erfIykeeaM9C6ak9OAcDjJl8TO9H1vZd8E7zxwoqTDlpQ1Jly/A/w8TWY+XdIaSafpIG+HbeF64HWSNii5vfQ9JE0n32pRtwP5MvAcSf82TcheCJxKcifXSnwHeAC4UtLhkp4m6eVLV4qInSSB5s3p8XkbDUFa0htqvzuSnEYAiy0+098B/0HSb6a/y8MlvU7SM5tVUNJ6Sa+UNAj8C/DLhm1bj3FQsJX6OUni8VZJj5MEg9tJvjSJiM8AkyQJ3J8DXwSOjogfAf8D2Ezy5fMC4JsN2/0qye2bD0p6KC37OEn79C5JX4yIp4BzgNOBe4CHSILQEVl/yIjYBryZ5Nbbh0ja/s+NiCfSVf478F/Sur13Bdt7OK37e0gS9ZcC50TEQ8u+ce/7n0rrcDJJQvo+krxHMxcD70v383z2BjJI8jK3SvoFcAPw7jQ3A0mzz8b0M10QEVvSbf0VSQC5m+Xv6BoEriQ5Xg8CzwL+eCWfz4pHEZ5kx8zMEr5SMDOzOgcFMzOrc1AwM7M6BwUzM6tzUDAzszoHBTMzq3NQMDOzOgcFMzOrc1AwM7M6BwUzM6tzUDAzszoHBTMzq3NQMDOzOgcFMzOrc1AwM7M6BwUzM6tzUDAzs7oDTQZeaMcee2xUq9W8q2Fm1lO2bt36UESsbfZaTweFarXKli1b8q6GmVlPkTTb6jU3H5mZWV3HgoKkT0jaIen2hrKjJd0s6a70+ai0XJL+UtLdkn4g6UWdqpeZmbXWySuFq4Gzl5RdBmyKiFOATekywGuAU9LHOPDRDtbLzMxa6FhQiIivA48sKT4P2Jj+vBE4v6H8f0fi28CRko7rVN3MzKy5bucUhiPigfTnB4Hh9OcTgHsb1rsvLduPpHFJWyRt2blzZ+dqamZWQrklmiMigGjjfVMRMRoRo2vXNr2jynrY9DRUqzAwkDxPTxdjW2Zl0e1bUuclHRcRD6TNQzvS8vuBkxrWOzEtsxKZnobxcVhYSJZnZ5NlgLGx/LZlVibdvlK4Abgo/fki4EsN5X+Q3oV0JvBYQzOTlcTExN4v8ZqFhaQ8z22ZlUnHrhQkXQu8AjhW0n3A5cCVwPWS3g7MAhekq38ZeC1wN7AAvLVT9bLimptbXXm3tmVWJh0LChHxphYvbWiybgDv6lRdrDeMjCTNPM3K89yWWZm4R7MVxuQkDA3tWzY0lJTnuS2zMnFQsMIYG4OpKahUQEqep6baSwxnuS2zMlHSctObRkdHwwPimZmtjqStETHa7DVfKZiZWZ2DgpmZ1TkomJlZnYOCmZnVOSiYmVmdg4KZWQ+Znp+nunkzA7fcQnXzZqbn5zPdfk/P0WxmVibT8/OMb9vGwuIiALO7dzO+bRsAY8PDy711xXylYGbWIya2b68HhJqFxUUmtm/PbB8OCmZmPWJu9+5VlbfDQcH24YlpzLpntfmBkcHBVZW3w0HB6moT08zOQsTeiWkcGMyyV8sPzO7eTbA3P7BcYJhct46hgX2/tocGBphcty6zejkoWJ0npjHrnnbyA2PDw0ytX09lcBABlcFBptavzyzJDL77yBp4Yhqz7mk3PzA2PJxpEFjKVwpW12oCGk9Mk3C+xbLUjfxAOxwUrM4T07TmfItlrRv5gXY4KFidJ6ZpzfkWy1o38gPt8CQ7ZiswMJBcISwlwZJcoVnheZIds4PkfItB58cdKgIHBbMVcL7F2ulX0IscFMxWwPkW68a4Q0XgfgpmKzQ25iBQZt0Yd6gIfKVgfasI/QqKUAfLRlH7FWTNQcH6UhH6FRShDpadovYryJpvSbW+VK0mX8JLVSowM1OeOli2pufnmdi+nbnduxkZHGRy3brc+xW0Y7lbUh0UrC8VoV9BEepg1oz7KVjpFKFfQRHqYLZaDgrWl4rQr6AIdTBbLQcF60tF6FdQhDqYrZZzCmZmJVO4nIKkd0u6XdIdki5Jy46WdLOku9Lno/Kom5lZmXU9KEg6DbgYeAnwQuAcSScDlwGbIuIUYFO6bGZmXZTHlcLzgFsjYiEingT+Efg3wHnAxnSdjcD5OdTNzKzU8ggKtwO/JekYSUPAa4GTgOGIeCBd50GgaY8QSeOStkjasnPnzu7U2MysJLoeFCLiTuADwE3AV4DbgKeWrBNA0wx4RExFxGhEjK5du7bT1TUzK5VcEs0R8fGIOCMifht4FPh/wLyk4wDS5x151M3MrMzyuvvoWenzCEk+4VPADcBF6SoXAV/Ko25mZmWW13wKn5N0DLAHeFdE7JJ0JXC9pLcDs8AFOdXNzKy0cgkKEfFbTcoeBjbkUB0zM0t5mAvrGE8wY9Z7PB2ndURtgpmFhWS5NsEMeOwfsyLzlYJ1xMTE3oBQs7CQlJtZcTkoWEfMza2u3MyKwUHBOsITzJj1JgcF6whPMGPWmxwUrCM8wYxZb/LdR9YxY2MOAma9xlcKPc59AcwsS75S6GHuC2BmWfOVQg9zXwAzy5qDQg9zXwAzy5qDQg9zXwAzy5qDQg9zXwAzy5qDQg9zXwAzy5rvPupx7gtgZlkq3ZWC7+u3rPmcsn5SqisF39dvWfM5Zf1GEZF3Hdo2OjoaW7ZsWfH61WryR7tUpQIzM5lVy0rE55T1IklbI2K02Wulaj7yff2WNZ9T1m9KFRR8X3/73G7eXNnOqekfTlO9qsrAFQNUr6oy/UOfCP2mVEHB9/W3p9ZuPjsLEXvbzR0YynVOTf9wmvEbx5l9bJYgmH1slvEbxx0Y+kypgoLv62+Px1hqrUzn1MSmCRb27HsiLOxZYGKTT4R+UqpEs7VnYCC5QlhKgsXF7tfH8jFwxQDB/ieCEIuX+0ToJU402z5Wmx8oW7u5NTdyRPNfeKty600OCiXTTn6gTO3m1trkhkmGDt33RBg6dIjJDT4R+omDQsm0kx8oU7u5tTb2gjGmzp2ickQFISpHVJg6d4qxF/hE6CfOKZSM8wNm5pxCH8iqn4DzA2a2HAeFHpBlPwHnB8xsOQ4KPSDLfgLOD5jZcpxT6AHOA5hZlgqXU5D0R5LukHS7pGslPU3SsyXdKuluSddJOiyPuhWR8wDt8XhNZqvX9aAg6QTgD4HRiDgNWAO8EfgA8OGIOBl4FHh7t+tWVM4DrJ7HazJrT145hUOAp0s6BBgCHgBeCXw2fX0jcH5OdSsc5wFWz+M1mbWn6zOvRcT9kj4IzAG/BG4CtgK7IuLJdLX7gBOavV/SODAOMFKi9hPPxbw6nufArD15NB8dBZwHPBs4HjgcOHul74+IqYgYjYjRtWvXdqiW1uuchzFrTx7NR68C7omInRGxB/g88HLgyLQ5CeBE4P4c6pYZJznz5TxMuXjyn+zkERTmgDMlDUkSsAH4EfA14PfTdS4CvpRD3TLhJGf+nIcpD0/+k61c+ilIugK4EHgS+B7wDpIcwqeBo9OyN0fE7uW2U9R+Cp7M3ax7qldVmX1s/z+4yhEVZi6Z6X6FesBy/RS6nmgGiIjLgcuXFG8HXpJDdTLnJKdZ98w91vwPq1W5Lc/DXHRAmZKczp2USxHb7j35T7YcFDqgLElO507Kpaht9578J1sOCh1QliSnO4iVy8SmCRb27PsLX9izwMSmfH/hnvwnWx4Qz9rmgfrKZeCKAYL9f+FCLF7uX3gvKdyAeNYfypQ7Mbfdl4WDgrWtLLkTS7jtvhwcFKxtZcmdWMJt9+XgnIKZWck4p9DA99WbmbWWS4/mvNTuq6/dRlm7rx7c5GFmBiW7UvB99WZmyytVUPCYRGZmyytVUPB99Wa2EkUc46lbWgYFSV+WVO1eVTrP99Wb2YEUdYynblnuSuHvgZskTUg6tFsV6iTfV29mB1LUMZ66peXdRxHxGUn/F/ivwBZJnwQWG17/UBfql7mxMQcBM2ut7PMzHCin8ATwODAIPHPJw8ys75R9jKeWVwqSzgY+BNwAvCgiFlqta2bWLyY3TDJ+4/g+TUhlGuNpuc5rE8AbIuKOblXGzCxvtbGcJjZNMPfYHCNHjDC5YbI0Yzx57CMzs5Lx2EdmZrYiDgpmZlbnoGBmZnUOCmZmVuegYGY9r8xjFWWtVPMpmFn/qY1VVOtXUBurCCjNbaRZ8pWCmfW0so9VlDUHBTPraWUfqyhrDgpm1tPKPlZR1koXFKanoVqFgYHkedr5KLOeNrlhkqFD950opUxjFWWtVEFhehrGx2F2FiKS5/FxBwazXjb2gjGmzp2ickQFISpHVJg6d8pJ5jaVauyjajUJBEtVKjAzk1m1zMwKrVBjH0laL+m2hsfPJF0i6WhJN0u6K30+Kut9z7XIO7UqNzMrm64HhYjYFhGnR8TpwBnAAvAF4DJgU0ScAmxKlzM10iLv1KrczKxs8s4pbAB+EhGzwHnAxrR8I3B+1jubnIShffNRDA0l5WZmln9QeCNwbfrzcEQ8kP78IDCc9c7GxmBqKskhSMnz1JTnbDYzq8kt0SzpMOCnwPMjYl7Srog4suH1RyNiv7yCpHFgHGBkZOSM2WaZYzMza6lQieYGrwH+OSLm0+V5SccBpM87mr0pIqYiYjQiRteuXbvqnbqfQnvm56fZvLnKLbcMsHlzlfl5H7hOyXtwt7z3b/nKc0C8N7G36QjgBuAi4Mr0+UtZ77DWT2EhHSal1k8B3IS0nPn5abZtG2dxMTlwu3fPsm1bcuCGh33gspT34G5579/yl0vzkaTDgTlgXUQ8lpYdA1wPjACzwAUR8chy23E/he7YvLnK7t37H7jBwQovfelM9yvUx6pXVZl9bP9jXTmiwswlM32/f+uO5ZqPcrlSiIjHgWOWlD1McjdSx7ifQnt2725+gFqVW/vyHtwt7/1b/vK++6ir3E+hPYODzQ9Qq3JrX96Du7W7/yzzEM5p5KtUQcH9FNqzbt0kAwP7HriBgSHWrfOBy1reg7u1s/9aHmL2sVmCqOch2vkyz3Jb1p5SBQX3U2jP8PAY69dPMThYAcTgYIX166ecZO6AvAd3a2f/WU5y4wlz8leqAfHMLHsDVwwQ7P89IsTi5Yu5bctaK2o/hb7m/hBWFlnmQfLOqZiDQkd43gYrkyzzIHnnVMxBoSMmJvZ2kKtZWEjKzfpNlnmQvHMq5pxCRwwMJFcIS0mw6GZRM8uZcwpd5v4Q2fPYS2bd4aDQAe4Pka3a2EvJUBtRH3vJgcEsew4KHeD+ENnavn2iPhhfzeLiAtu3O0ljlrU8R0nta2NjDgJZ8dhLZt3jKwUrPI+9ZNY9DgpWeB57yax7HBSs8Dz2kln3OKdgPWF4eMxBwKwLfKVgZmZ1DgpmZlbnoGBmZnUOCmZmVuegYGZmdQ4KZmZW56BgZmZ1DgpmZlbnoGBmZnUOCmZmvWR6GqrVZIrHajXzyd89zIWZWa+Ynobx8b2TwM/OJsuQ2Vj9vlIwM+sVExN7A0LNwkJSnhEHBTOzXjHXYmKpVuVtcFBo0OGmOjOzgzPSYmKpVuVtcFBI1ZrqZmchYm9TnQODmRXG5CQM7TvhFENDSXlGHBRSXWiqMzM7OGNjMDUFlQpIyfPUVKYTwisiMtvYincqHQl8DDgNCOBtwDbgOqAKzAAXRMSjy21ndHQ0tmzZkkmdBgaSK4T96wqLi5nswsysECRtjYjRZq/ldaXwEeArEfFc4IXAncBlwKaIOAXYlC53TRea6szMCq/rQUHSEcBvAx8HiIgnImIXcB6wMV1tI3B+N+vVhaY6M7PCy+NK4dnATuDvJX1P0sckHQ4MR8QD6ToPAsPdrFQXmurMzAqv6zkFSaPAt4GXR8Stkj4C/Az4TxFxZMN6j0bEUU3ePw6MA4yMjJwxOzvbpZqbmfWHouUU7gPui4hb0+XPAi8C5iUdB5A+72j25oiYiojRiBhdu3ZtVyqctV7sD1HkOhe5blYirU7EXjtBI6LrD+AbwPr05/cDf5E+LkvLLgP+/EDbOeOMM6LXXHNNxNBQRHKvU/IYGkrKi6rIdS5y3axEWp2I73xnIU9QYEu0+F7N65bU00luST0M2A68leSq5XpgBJgluSX1keW2k+Utqd1SrSYd45aqVGBmptu1WZki17nIdbMSaXUirlkDTz21f3nOJ+hyzUe5BIWs9GJQ6MX+EEWuc5HrZiXS6kRsJecTtGg5hVLrxf4QRa5zketWKr3Wbp61VifcmjWrW78AHBS6rBf7QxS5zkWuW2l44LDWJ+L4eO+doK2SDb3w6MVEc0SSY6pUIqTkuReSokWuc5HrVgqVyr6J1NqjUsm7Zt3V6kQs4AlK0RLNWenFnIJZ33Fip+c4p2BmnePETl9xUDCzg+PETl9xUDCzg+OBw/rKIXlXwMz6wNiYg0Cf8JWCmeWjW30byt6HYpV8pWBm3Vfr21CbA7fWtwGyveLo1n76iG9JNbPu69agVR4cqynfkmpmxTI3t7ryou+njzgo2Iq4WdYy1a2+De5DsWoOCnZAHtrGMtetvg3uQ7FqDgp2QBMTe/N0NQsLSblZW7rVt8F9KFbNiWY7IA9tY9ZfnGi2g+JmWbPycFCwAypTs6wT6lZ2Dgp2QGVplnVC3cw5BbM693OysnBOwWwF3M/JzEHBrK7dhHqp8hCl+rDl5KBglmonoV6qPESpPmx5Oadg1mB6OumUNzeXXCFMTi6fUC9VHqJUH7a/LZdTcFAwOwil6thXqg/b35xoNuuQUnXsK9WHLS8HBbODUKaOfeX6sOXloGB2EMrSsQ8o2YctL+cUzMxKxjkFMyuvIvetKGDdDsm7AmZmHVPrW1GbEKTWtwLyb/YqaN3cfGRm/avIfStyrJubj8ysnIo8oFVB65ZLUJA0I+mHkm6TtCUtO1rSzZLuSp+PyqNuZtZHity3oqB1y/NK4V9FxOkNlzCXAZsi4hRgU7psZta+IvetKGjditR8dB6wMf15I3B+jnUxs35Q5L4VBa1bLolmSfcAjwIB/G1ETEnaFRFHpq8LeLS2vOS948A4wMjIyBmzzRI1ZmbW0nKJ5rxuST0rIu6X9CzgZkk/bnwxIkJS02gVEVPAFCR3H3W+qmZm5ZFL81FE3J8+7wC+ALwEmJd0HED6vCOPupmZlVnXg4KkwyU9s/Yz8GrgduAG4KJ0tYuAL3W7bmZmZZdH89Ew8IUkbcAhwKci4iuSvgtcL+ntwCxwQQ51MzMrta4HhYjYDrywSfnDwIZu18fMzPbq6WEuJO0kuao4Fngo5+rkzcfAxwB8DMr++WFlx6ASEWubvdDTQaFG0pZWt1eVhY+BjwH4GJT988PBH4MidV4zM7OcOSiYmVldvwSFqbwrUAA+Bj4G4GNQ9s8PB3kM+iKnYGZm2eiXKwUzM8tAzwcFSWdL2ibpbkmlGG5b0ick7ZB0e0NZaeajkHSSpK9J+pGkOyS9Oy0v0zF4mqTvSPp+egyuSMufLenW9O/hOkmH5V3XTpO0RtL3JP1DulyqY5D1/DQ9HRQkrQH+GngNcCrwJkmn5lurrrgaOHtJWZnmo3gSeE9EnAqcCbwr/b2X6RjsBl4ZES8ETgfOlnQm8AHgwxFxMslIxG/PsY7d8m7gzoblMh6DzOan6emgQDKQ3t0RsT0ingA+TTIvQ1+LiK8DjywpLs18FBHxQET8c/rzz0m+EE6gXMcgIuIX6eKh6SOAVwKfTcv7+hgASDoReB3wsXRZlOwYtND230KvB4UTgHsblu9Ly8poOCIeSH9+kGSMqb4nqQr8BnArJTsGabPJbSQjCt8M/ATYFRFPpquU4e/hKuBSYDFdPobyHYMAbpK0NZ1vBg7ibyGv+RSsg5abj6KfSHoG8Dngkoj4WTrIIlCOYxARTwGnSzqSZAj65+Zcpa6SdA6wIyK2SnpF3vXJUdvz0zTT61cK9wMnNSyfmJaVUanmo5B0KElAmI6Iz6fFpToGNRGxC/ga8FLgSEm1f/b6/e/h5cDrJc2QNB2/EvgI5ToGmc9P0+tB4bvAKendBocBbySZl6GMSjMfRdpu/HHgzoj4UMNLZToGa9MrBCQ9HfhdktzK14DfT1fr62MQEX8cESdGRJXkb/+rETFGiY5BJ+an6fnOa5JeS9KuuAb4RERM5lyljpN0LfAKktEQ54HLgS8C1wMjpPNRRMTSZHRfkHQW8A3gh+xtS/4TkrxCWY7Br5MkENeQ/HN3fUT8qaR1JP81Hw18D3hzROzOr6bdkTYfvTcizinTMUg/6xfSxdr8NJOSjqHNv4WeDwpmZpadXm8+MjOzDDkomJlZnYOCmZnVOSiYmVmdg4KZmdU5KJhlJB299R5JR6fLR6XL1XxrZrZyDgpmGYmIe4GPAlemRVcCUxExk1ulzFbJ/RTMMpQOv7EV+ARwMXB6ROzJt1ZmK+cB8cwyFBF7JL0P+ArwagcE6zVuPjLL3muAB4DT8q6I2Wo5KJhlSNLpJIPTnQn8UW2kSrNe4aBglpF09NaPkszvMAf8BfDBfGtltjoOCmbZuRiYi4ib0+W/AZ4n6XdyrJPZqvjuIzMzq/OVgpmZ1TkomJlZnYOCmZnVOSiYmVmdg4KZmdU5KJiZWZ2DgpmZ1TkomJlZ3f8H6u7qP6lakLMAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qGMrZEexaXot"
      },
      "source": [
        "**AND THIS PROCESS GOES ON UNTIL THERE IS ONE SINGLE CLUSTER**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "g_A7qjT56ihd"
      },
      "source": [
        "* Data point (1,4) is new cluster after (2,5)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5PCWuwD21a1K",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 325
        },
        "outputId": "8dee7e36-67d1-4cc9-c802-f6315a074e28"
      },
      "source": [
        "hierarchical_clustering(data,\"single\",4)\n",
        "#you can see that the color of data[1] and data[4] also became same in color, thus they are in same cluster nowproximity.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0, 1, 1, 3, 3, 3, 3, 0, 8, 3, 0, 3, 3, 0, 1, 3, 0, 3, 3, 3, 0, 0, 3, 3, 0, 1, 3, 8, 3, 3, 3, 1, 3, 1, 3, 1, 3, 3, 3, 1, 1, 8, 3, 0, 3, 3, 3, 3, 3, 3]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAEjCAYAAADdZh27AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAdW0lEQVR4nO3df5RkZX3n8fenBxhpNPwcJ/zqbgmIIkYirSFKEpcxLioIuyeCbrvBX/Sux91IjsqS9O4iOemzmLiK2WzcdNQwqy2CP4Gs65EzSjSK6ExEBZEFh+kBhJnhx6DSZhiY7/5xn6qp6anq6a65de+tup/XOXWq69atW9+6fbu+fZ/vfZ5HEYGZmRnAUNkBmJlZdTgpmJlZk5OCmZk1OSmYmVmTk4KZmTU5KZiZWZOTgtWepPdJ+mSO23uHpC2SfiHpyLy22+Z93izpH3u1fasnJwVbMklnSvqWpMclPSrpm5Jesp/b3OuLTdLVkv5s/6Ld632ulvRk+qJ+VNJNkp7XxXY2SXrlIs8fCHwQeFVEPDMiHtmfuIsgKSSdWHYcVg1OCrYkkn4F+HvgfwBHAMcCVwA7yoyrHUkHdHjqzyPimcBxwFbg6h68/WrgGcAdy32hMn31N7nIvrY+1VcHoJXquQARcU1EPB0Rv4yIr0TEDxorSLpY0p2Sfi7pR5JenJZfJuknLcv/VVr+fOB/Ab+V/oPfLmkSmAAuTctuTOseI+lzkrZJulfSH7a87/skfVbSJyX9DHjzYh8kIuaBTwGntnte0usk3ZHiuTnFiaRPACPAjSm2Sxe87rnAXenhdklfTctfJum76Qzru5Je1vKamyVNS/omMA+c0Cae4yV9Pn32RyT9VZt1xtJ//Ae0LLtZ0tvTzydK+ocUw8OSrk3Lv55W/376TBem5edIui3tg29J+vWW7W6S9J8k/QB4QtIB6fED6Xd8l6Q1i/0OrMIiwjff9nkDfgV4BFgLvBo4fMHzrwceAF4CCDgRGG157hiyf0IuBJ4Ajk7PvRn4xwXbuhr4s5bHQ8AG4L8CB5F9cW4E/mV6/n3ATuD8tO7BbeJvbhN4JllS+EbL6z+Zfn5uiu/3gAOBS4F7gIPS85uAVy6yn8aAAA5Ij48AHgP+LXAA8Mb0+Mj0/M3AZuAF6fkDF2xvBfB94EPAIWRnIWcu3HcL37dl229PP18DTKX909xGei6AE1se/wbZmdRvpve/KH3ulS374DbgeOBg4GTgPuCYllh+rexj1rfubj5TsCWJiJ8BZ5J9gfwtsE3SDZJWp1XeTtY8893I3BMRc+m1n4mIn0bEroi4FrgbeOky3v4lwKqI+NOIeDIiNqYY3tCyzi0R8cX0Hr/ssJ33SNpO9iX/TNqfUVwI/J+IuCkidgIfIPvie1mbdZfitcDdEfGJiHgqIq4Bfgyc27LO1RFxR3p+54LXv5Qsob43Ip6IiH+OiG6KyzuBUbIv7n1tYxL4m4i4NbKzwrVkzYRntKzzlxFxX9rXTwMrgVMkHRgRmyLiJ13EaBXgpGBLFhF3RsSbI+I4sqaXY4Cr0tPHA22/CCT9QUtTxPb02qOW8dajwDGN16dt/AlZ+33DfUvYzgci4rCI+NWIeF2HL65jgLnGg4jYlbZ97DLi7bi9ZG7B9haL/XhgLiKe6vL9Gy4lO4P7Tmoae+si644C716wv48n+yx7xRwR9wCXkJ1xbZX0aUmt61ofcVKwrkTEj8maZBrt8vcBv7ZwPUmjZP/V/weyJpPDgNvJvqAgO/PYa/MLHt8H3Ju+0Bu3Z0XEaxZ5Tbd+Sval2IhfZF+ID3T5PntsLxlp2d6+tnkfMLKEgu4T6X64ZdmvNt8g4qGIuDgijgH+HfDXi1xxdB8wvWB/D6eznLYxR8SnIuJMss8awPv3Ea9VlJOCLYmk50l6t6Tj0uPjydrHv51W+ShZ88zp6SqaE1NCOITsS2Jbet1b2LPAuwU4TtJBC5a1Fly/A/w8FTMPlrRC0qnaz8thO7gOeK2kNcouL303WdPJtzrEti9fAp4r6d+kguyFwClkV3ItxXeAB4ErJR0i6RmSXr5wpYjYRpZo3pT2z1tpSdKSXt/43ZHVNALY1eEz/S3w7yX9ZvpdHiLptZKe1S5ASSdLOkvSSuCfgV+2bNv6jJOCLdXPyQqPt0p6giwZ3E72pUlEfAaYJivg/hz4InBERPwI+O/ALWRfPi8Evtmy3a+SXb75kKSH07KPkbVPb5f0xYh4GjgHOA24F3iYLAkdmveHjIi7gDeRXXr7MFnb/7kR8WRa5b8B/znF9p4lbO+RFPu7yQr1lwLnRMTDi75w9+ufTjGcSFaQvp+s7tHOxcB70/u8gN2JDLK6zK2SfgHcALwr1WYga/ZZmz7TBRGxPm3rr8gSyD0sfkXXSuBKsv31EPBs4I+X8vmsehThSXbMzCzjMwUzM2tyUjAzsyYnBTMza3JSMDOzJicFMzNrclIwM7MmJwUzM2tyUjAzsyYnBTMza3JSMDOzJicFMzNrclIwM7MmJwUzM2tyUjAzsyYnBTMza3JSMDOzJicFMzNr2tdk4JV21FFHxdjYWNlhmJn1lQ0bNjwcEavaPdfXSWFsbIz169eXHYaZWV+RNNfpOTcfmZlZU8+SgqSPS9oq6faWZUdIuknS3en+8LRckv5S0j2SfiDpxb2Ky8zMOuvlmcLVwNkLll0GrIuIk4B16THAq4GT0m0S+EgP4zIzsw56lhQi4uvAowsWnwesTT+vBc5vWf6/I/Nt4DBJR/cqNjMza6/omsLqiHgw/fwQsDr9fCxwX8t696dle5E0KWm9pPXbtm3rXaRmZjVUWqE5IgKILl43ExHjETG+alXbK6qsj83OwtgYDA1l97Oz1diWWV0UfUnqFklHR8SDqXloa1r+AHB8y3rHpWVWI7OzMDkJ8/PZ47m57DHAxER52zKrk6LPFG4ALko/XwRc37L8D9JVSGcAj7c0M1lNTE3t/hJvmJ/Plpe5LbM66dmZgqRrgFcAR0m6H7gcuBK4TtLbgDnggrT6l4DXAPcA88BbehWXVdfmzctbXtS2zOqkZ0khIt7Y4ak1bdYN4J29isX6w8hI1szTbnmZ2zKrE/dotsqYnobh4T2XDQ9ny8vcllmdOClYZUxMwMwMjI6ClN3PzHRXGM5zW2Z1oqzlpj+Nj4+HB8QzM1seSRsiYrzdcz5TMDOzJicFMzNrclIwM7MmJwUzM2tyUjAzsyYnBTOzPrJlyyy33DLGzTcPccstY2zZku9Ij309R7OZWZ1s2TLLXXdNsmtXNrDXjh1z3HVXNtLj6tX5dMLxmYKZWZ/YuHGqmRAadu2aZ+PG/EZ6dFIwM+sTO3a0H9Gx0/JuOCnYHjwxjVlxllsfWLmy/YiOnZZ3w0nBmhoT08zNQcTuiWmcGMzy16gP7NgxB0SzPrBYYjjhhGmGhvYc6XFoaJgTTshvpEcnBWvyxDRmxemmPrB69QQnnzzDypWjgFi5cpSTT57JrcgMvvrIWnhiGrPidFsfWL16ItcksJDPFKyp0wQ0npgm43qL5amI+kA3nBSsyRPTdOZ6i+WtiPpAN5wUrMkT03TmeovlrYj6QDc8yY7ZEgwNZWcIC0mwa1fx8ZjtD0+yY7afXG8x6P24Q1XgpGC2BK63WDf9CvqRk4LZErjeYkWMO1QF7qdgtkQTE04CdVbEuENV4DMFG1hV6FdQhRgsH1XtV5A3JwUbSFXoV1CFGCw/Ve1XkDdfkmoDaWws+xJeaHQUNm2qTwyWry1bZtm4cYodOzazcuUIJ5wwXXq/gm4sdkmqk4INpCr0K6hCDGbtuJ+C1U4V+hVUIQaz5XJSsIFUhX4FVYjBbLmcFGwgVaFfQRViMFsu1xTMzGqmcjUFSe+SdLukOyRdkpYdIekmSXen+8PLiM3MrM4KTwqSTgUuBl4KvAg4R9KJwGXAuog4CViXHpuZWYHKOFN4PnBrRMxHxFPAPwD/GjgPWJvWWQucX0JsZma1VkZSuB34bUlHShoGXgMcD6yOiAfTOg8Bq9u9WNKkpPWS1m/btq2YiM3MaqLwpBARdwLvB74CfBm4DXh6wToBtK2AR8RMRIxHxPiqVat6Ha6ZWa2UUmiOiI9FxOkR8TvAY8D/A7ZIOhog3W8tIzYzszor6+qjZ6f7EbJ6wqeAG4CL0ioXAdeXEZuZWZ2VNZ/C5yQdCewE3hkR2yVdCVwn6W3AHHBBSbGZmdVWKUkhIn67zbJHgDUlhGNmZomHubCe8QQzZv3H03FaTzQmmJlPU9o2JpgBj/1jVmU+U7CemJranRAa5uez5WZWXU4K1hObO8xl3mm5mVWDk4L1hCeYMetPTgrWE55gxqw/OSlYT3iCGbP+5KuPrGcmJpwEzPqNzxT6nPsCmFmefKbQx9wXwMzy5jOFPua+AGaWNyeFPua+AGaWNyeFPua+AGaWNyeFPua+AGaWNyeFPua+AGaWN1991OfcF8DM8lS7MwVf12958zFlg6RWZwq+rt/y5mPKBo0iouwYujY+Ph7r169f8vpjY9kf7UKjo7BpU25hWY34mLJ+JGlDRIy3e65WzUe+rt/y5mPKBk2tkoKv6++e283bq9sxNfvDWcauGmPoiiHGrhpj9oc+EAZNrZKCr+vvTqPdfG4OIna3mzsx1OuYmv3hLJM3TjL3+BxBMPf4HJM3TjoxDJhaJQVf198dj7HUWZ2Oqal1U8zv3PNAmN85z9Q6HwiDpFaFZuvO0FB2hrCQBLt2FR+PlWPoiiGCvQ8EIXZd7gOhn7jQbHtYbn2gbu3m1t7Ioe1/4Z2WW39yUqiZbuoDdWo3t86m10wzfOCeB8LwgcNMr/GBMEicFGqmm/pAndrNrbOJF04wc+4Mo4eOIsTooaPMnDvDxAt9IAwS1xRqxvUBM3NNYQDk1U/A9QEzW4yTQh/Is5+A6wNmthgnhT6QZz8B1wfMbDGuKfQB1wHMLE+VqylI+iNJd0i6XdI1kp4h6TmSbpV0j6RrJR1URmxV5DpAdzxek9nyFZ4UJB0L/CEwHhGnAiuANwDvBz4UEScCjwFvKzq2qnIdYPk8XpNZd8qqKRwAHCzpAGAYeBA4C/hsen4tcH5JsVWO6wDL5/GazLpT+MxrEfGApA8Am4FfAl8BNgDbI+KptNr9wLHtXi9pEpgEGKlR+4nnYl4ez3Ng1p0ymo8OB84DngMcAxwCnL3U10fETESMR8T4qlWrehSl9TvXYcy6U0bz0SuBeyNiW0TsBD4PvBw4LDUnARwHPFBCbLlxkbNcrsPUiyf/yU8ZSWEzcIakYUkC1gA/Ar4G/H5a5yLg+hJiy4WLnOVzHaY+PPlPvkrppyDpCuBC4Cnge8DbyWoInwaOSMveFBE7FttOVfspeDJ3s+KMXTXG3ON7/8GNHjrKpks2FR9QH1isn0LhhWaAiLgcuHzB4o3AS0sIJ3cucpoVZ/Pj7f+wOi23xXmYix6oU5HTtZN6qWLbvSf/yZeTQg/Upcjp2km9VLXt3pP/5MtJoQfqUuR0B7F6mVo3xfzOPX/h8zvnmVpX7i/ck//kywPiWdc8UF+9DF0xRLD3L1yIXZf7F95PKjcgng2GOtVOzG33deGkYF2rS+3EMm67rwcnBetaXWonlnHbfT24pmBmVjOuKbTwdfVmZp2V0qO5LI3r6huXUTauqwc3eZiZQc3OFHxdvZnZ4mqVFDwmkZnZ4mqVFHxdvZktRRXHeCpKx6Qg6UuSxooLpfd8Xb2Z7UtVx3gqymJnCn8HfEXSlKQDiwqol3xdvZntS1XHeCpKx6uPIuIzkv4v8F+A9ZI+Aexqef6DBcSXu4kJJwEz66zu8zPsq6bwJPAEsBJ41oKbmdnAqfsYTx3PFCSdDXwQuAF4cUTMd1rXzGxQTK+ZZvLGyT2akOo0xtNindemgNdHxB1FBWNmVrbGWE5T66bY/PhmRg4dYXrNdG3GePLYR2ZmNeOxj8zMbEmcFMzMrMlJwczMmpwUzMysyUnBzPpenccqylut5lMws8HTGKuo0a+gMVYRUJvLSPPkMwUz62t1H6sob04KZtbX6j5WUd6cFMysr9V9rKK81S4pzM7C2BgMDWX3s65HmfW16TXTDB+450QpdRqrKG+1SgqzszA5CXNzEJHdT046MZj1s4kXTjBz7gyjh44ixOiho8ycO+Mic5dqNfbR2FiWCBYaHYVNm3ILy8ys0io19pGkkyXd1nL7maRLJB0h6SZJd6f7w/N+780d6k6dlpuZ1U3hSSEi7oqI0yLiNOB0YB74AnAZsC4iTgLWpce5GulQd+q03MysbsquKawBfhIRc8B5wNq0fC1wft5vNj0Nw3vWoxgezpabmVn5SeENwDXp59UR8WD6+SFgdd5vNjEBMzNZDUHK7mdmPGezmVlDaYVmSQcBPwVeEBFbJG2PiMNann8sIvaqK0iaBCYBRkZGTp9rVzk2M7OOKlVobvFq4J8iYkt6vEXS0QDpfmu7F0XETESMR8T4qlWrlv2m7qfQHe+34pQ9uFvZ72/lKnNAvDeyu+kI4AbgIuDKdH993m/Y6Kcwn4ZJafRTADchLcb7rThlD+5W9vtb+UppPpJ0CLAZOCEiHk/LjgSuA0aAOeCCiHh0se24n0IxvN+KM3bVGHOP772zRw8dZdMlmwb+/a0YizUflXKmEBFPAEcuWPYI2dVIPeN+Ct3xfitO2YO7lf3+Vr6yrz4qlPspdMf7rThlD+7W7fvnWYdwTaNctUoK7qfQHe+34pQ9uFs379+oQ8w9PkcQzTpEN1/meW7LulOrpOB+Ct3xfitO2YO7dfP+eU5y4wlzylerAfHMLH9DVwwR7P09IsSuy3eVti3rrKr9FAaar+u3usizDlJ2TcWcFHrC8zZYneRZBym7pmJOCj0xNbW7o1fD/Hy23GzQ5FkHKbumYq4p9MTQUHaGsJAEu9wsamYlc02hYL6uP3+u0ZgVw0mhB3xdf75cozErjpNCD/i6/ny5RmNWHNcUrPJcozHLl2sK1tdcozErjpOCVZ5rNGbFcVKwynONxqw4Zc68ZrZkExNOAmZF8JmCmZk1OSmYmVmTk4KZmTU5KZiZWZOTgpmZNTkpmJlZk5OCmZk1OSmYmVmTk4KZmTU5KZiZ9ZMezzjlYS7MzPpFY8apxgQjjRmnILdxYHymYGbWLwqYccpJwcysX2zevLzlXXBSaOHJ4c2s0gqYccpJIfHk8GZWeQXMOOWkkHhyeDOrvAJmnFK0mxG9xyQdBnwUOBUI4K3AXcC1wBiwCbggIh5bbDvj4+Oxfv36XGLy5PBmVheSNkTEeLvnyjpT+DDw5Yh4HvAi4E7gMmBdRJwErEuPC+PJ4c3MSkgKkg4Ffgf4GEBEPBkR24HzgLVptbXA+UXG5cnhzczKOVN4DrAN+DtJ35P0UUmHAKsj4sG0zkPA6iKD8uTwZmYl1BQkjQPfBl4eEbdK+jDwM+A/RsRhLes9FhGHt3n9JDAJMDIycvrc3FxBkZuZDYaq1RTuB+6PiFvT488CLwa2SDoaIN1vbffiiJiJiPGIGF+1alUhAeetH/tDVDnmKsdmNdLpQOy3AzQiCr8B3wBOTj+/D/iLdLssLbsM+PN9bef000+PfvPJT0YMD0dk1zplt+HhbHlVVTnmKsdmNdLpQHzHOyp5gALro8P3almXpJ5GdknqQcBG4C1kZy3XASPAHNklqY8utp08L0ktythY1jFuodFR2LSp6GiWpsoxVzk2q5FOB+KKFfD003svL/kAXaz5qJSkkJd+TAr92B+iyjFXOTarkU4HYiclH6BVqynUWj/2h6hyzFWOrVb6rd08b50OuBUrlrd+BTgpFKwf+0NUOeYqx1YbHjis84E4Odl/B2inYkM/3Pqx0ByR1ZhGRyOk7L4fiqJVjrnKsdXC6OiehdTGbXS07MiK1elArOABStUKzXnpx5qC2cBxYafvuKZgZr3jws5AcVIws/3jws5AcVIws/3jgcMGygFlB2BmA2BiwklgQPhMwczKUVTfhrr3oVgmnymYWfEafRsac+A2+jZAvmccRb3PAPElqWZWvKIGrfLgWG35klQzq5bNm5e3vOrvM0CcFGxJ3CxruSqqb4P7UCybk4Ltk4e2sdwV1bfBfSiWzUnB9mlqanedrmF+Pltu1pWi+ja4D8WyudBs++ShbcwGiwvNtl/cLGtWH04Ktk91apZ1Qd3qzknB9qkuzbIuqJu5pmDW5H5OVheuKZgtgfs5mTkpmDV1W1CvVR2iVh+2npwUzJJuCuq1qkPU6sPWl2sKZi1mZ7NOeZs3Z2cI09OLF9RrVYeo1YcdbIvVFJwUzPZDrTr21erDDjYXms16pFYd+2r1YevLScFsP9SpY1+9Pmx9OSmY7Ye6dOwDavZh68s1BTOzmnFNwczqq8p9KyoY2wFlB2Bm1jONvhWNCUEafSug/Gavisbm5iMzG1xV7ltRYmxuPjKzeqrygFYVja2UpCBpk6QfSrpN0vq07AhJN0m6O90fXkZsZjZAqty3oqKxlXmm8C8i4rSWU5jLgHURcRKwLj02M+telftWVDS2KjUfnQesTT+vBc4vMRYzGwRV7ltR0dhKKTRLuhd4DAjgbyJiRtL2iDgsPS/gscbjBa+dBCYBRkZGTp9rV6gxM7OOFis0l3VJ6pkR8YCkZwM3Sfpx65MREZLaZquImAFmILv6qPehmpnVRynNRxHxQLrfCnwBeCmwRdLRAOl+axmxmZnVWeFJQdIhkp7V+Bl4FXA7cANwUVrtIuD6omMzM6u7MpqPVgNfyMoGHAB8KiK+LOm7wHWS3gbMAReUEJuZWa0VnhQiYiPwojbLHwHWFB2PmZnt1tfDXEjaRnZWcRTwcMnhlM37wPsAvA/q/vlhaftgNCJWtXuir5NCg6T1nS6vqgvvA+8D8D6o++eH/d8HVeq8ZmZmJXNSMDOzpkFJCjNlB1AB3gfeB+B9UPfPD/u5DwaipmBmZvkYlDMFMzPLQd8nBUlnS7pL0j2SajHctqSPS9oq6faWZbWZj0LS8ZK+JulHku6Q9K60vE774BmSviPp+2kfXJGWP0fSrenv4VpJB5Uda69JWiHpe5L+Pj2u1T7Ie36avk4KklYA/xN4NXAK8EZJp5QbVSGuBs5esKxO81E8Bbw7Ik4BzgDemX7vddoHO4CzIuJFwGnA2ZLOAN4PfCgiTiQbifhtJcZYlHcBd7Y8ruM+yG1+mr5OCmQD6d0TERsj4kng02TzMgy0iPg68OiCxbWZjyIiHoyIf0o//5zsC+FY6rUPIiJ+kR4emG4BnAV8Ni0f6H0AIOk44LXAR9NjUbN90EHXfwv9nhSOBe5reXx/WlZHqyPiwfTzQ2RjTA08SWPAbwC3UrN9kJpNbiMbUfgm4CfA9oh4Kq1Sh7+Hq4BLgV3p8ZHUbx8E8BVJG9J8M7AffwtlzadgPbTYfBSDRNIzgc8Bl0TEz9Igi0A99kFEPA2cJukwsiHon1dySIWSdA6wNSI2SHpF2fGUqOv5adrp9zOFB4DjWx4fl5bVUa3mo5B0IFlCmI2Iz6fFtdoHDRGxHfga8FvAYZIa/+wN+t/Dy4HXSdpE1nR8FvBh6rUPcp+fpt+TwneBk9LVBgcBbyCbl6GOajMfRWo3/hhwZ0R8sOWpOu2DVekMAUkHA79HVlv5GvD7abWB3gcR8ccRcVxEjJH97X81Iiao0T7oxfw0fd95TdJryNoVVwAfj4jpkkPqOUnXAK8gGw1xC3A58EXgOmCENB9FRCwsRg8ESWcC3wB+yO625D8hqyvUZR/8OlkBcQXZP3fXRcSfSjqB7L/mI4DvAW+KiB3lRVqM1Hz0nog4p077IH3WL6SHjflppiUdSZd/C32fFMzMLD/93nxkZmY5clIwM7MmJwUzM2tyUjAzsyYnBTMza3JSMMtJGr31XklHpMeHp8dj5UZmtnROCmY5iYj7gI8AV6ZFVwIzEbGptKDMlsn9FMxylIbf2AB8HLgYOC0idpYbldnSeUA8sxxFxE5J7wW+DLzKCcH6jZuPzPL3auBB4NSyAzFbLicFsxxJOo1scLozgD9qjFRp1i+cFMxykkZv/QjZ/A6bgb8APlBuVGbL46Rglp+Lgc0RcVN6/NfA8yX9bokxmS2Lrz4yM7MmnymYmVmTk4KZmTU5KZiZWZOTgpmZNTkpmJlZk5OCmZk1OSmYmVmTk4KZmTX9f+6e1CtuOBg8AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4fLRO7gZ6qY1"
      },
      "source": [
        "* data points (1,4) and (2,5) are now one single cluster"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MFsUCXSVwp7Q",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 325
        },
        "outputId": "551a1a05-dc8a-46c1-f672-90876a0a2587"
      },
      "source": [
        "hierarchical_clustering(data,\"single\",3)\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0, 1, 1, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 8, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 8, 0, 0, 0, 0, 0, 0, 0, 0]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "K7V3Qwej6y1j"
      },
      "source": [
        "* It goes on and adds data point (3) with [ [1,4] , [2,5] ]"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_8aSQBxgPZcI",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 325
        },
        "outputId": "fb9edf46-9171-465c-8b6e-f250de32f5d3"
      },
      "source": [
        "hierarchical_clustering(data,\"single\",2)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "l2UhvRMJ6-bc"
      },
      "source": [
        "* Finally one single cluster is there : [ [2,5] , [1,4] , [3] , [0] ]"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Jwc4jF3dzGXF",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 325
        },
        "outputId": "b5ffbbde-ffcd-4132-8ad3-c825fd95f64f"
      },
      "source": [
        "hierarchical_clustering(data,\"single\",1)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "34xsx79g7yVQ"
      },
      "source": [
        "**7.Final representation using dendrogram**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Jk8Rs8cT74oV",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 429
        },
        "outputId": "bb797f40-6dae-489c-c8aa-58fcd1438543"
      },
      "source": [
        "from scipy.cluster.hierarchy import dendrogram, linkage\n",
        "from matplotlib import pyplot as plt\n",
        "\n",
        "linked = linkage(data, 'single')\n",
        "\n",
        "labelList = range(0, 50)\n",
        "\n",
        "plt.figure(figsize=(10, 7))\n",
        "dendrogram(linked,\n",
        "            orientation='top',\n",
        "            labels=labelList,\n",
        "            distance_sort='ascending',\n",
        "            show_leaf_counts=True)\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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ddbyTEyCL9UB9c5JHVdUjktw8yRdX1Ytaa48fLdRaO57keJIcPny4LfB6sPvcAbfz1vFOTuDAm7sHqrX20621O7bWzk/y2CSvGw9PAAD7kYE0AQA6LWUgzdbaySQnlzEvAIBVpwcKAKCTAAUA0EmAAgDoJEABAHRaykXkizh+6fGcuGz64HibVz8rSXLkgqdOLXP0Hkdz7D5GJwbYVUbrn8927bZF+620PQ9QJy47kc2rN7Nxu8kjOm88Y3pwSpLNqwcbmAAFsMu2RpKfNiL/diP1JzeEhIMUALZrty3ab6XteYBKko3bbeTkE0/O9b9HLjiy1LoA0MFo/fNZtN22HNT2WwGugQIA6CRAAQB0EqAAADoJUAAAnQQoAIBOAhQAQCcBCgCgkwAFANBJgAIA6LQSI5EDABN43uDK0gMFAKtq67l502xsbP/MvM3N2R5eTBc9UACwyjxvcCXpgQIA6KQHal0t47y4c+Kw/007VpzpGOHYANvSA7WuFj0v7pw4HAzTjhXTjhGODTATPVDrbJHz4s6Jw8HRc6xwbICZ6IECAOikBwqWofc6E9eYcNDYR9hn9EDBMvRcZ+IaEw4i+wj7jB4oWJZZrzNxjQkHlX2EfUQPFABAJwEKAKCTAAUA0EmAAgDoJEABAHQSoAAAOglQAACdBCgAgE4CFABAJwEKAKCTAAUA0EmAAgDotFYPEz5+6fGcuOzGT+jevHrwdO8jFxy5Sfmj9ziaY/c5thtVW23Hj9/0yeZbT0Wf9NDOo0eTY9qNA8Q+wn4waTtOpm/LtuOFrFUP1InLTvxTYNqycbuNbNxu4yZlN6/evEnYOrBOnLhhB9qysTH4Gre5OXkHhP3MPsJ+MGk7TiZvy7bjha1VD1QyCEwnn3hy23KTeqQOtI2N5OTJ7ctN+rQNB4F9hP3Adrxr5u6BqqqvrKqLq+pdVfXOqnrKMisGALCqFumBuj7J01trb62qWyW5tKouaq29a0l1AwBYSXP3QLXWrmqtvXX4898nuSLJHZZVMQCAVbWUa6Cq6vwk907y5mXMDwA4ANb4DtiF78KrqnOSvCzJU1trn5jw92NVdaqqTp0+fXrRlwMA9os1vgN2oR6oqvqCDMLTi1trF04q01o7nuR4khw+fLgt8noAwD6zpncOLnIXXiV5bpIrWmu/srwqAQCstkVO4X1zku9P8qCq2hx+PWJJ9QIAWFlzn8Jrrb0hSS2xLgAAa2GtHuUCALAKBCgAgE4CFABAJwEKAKCTAAUA0EmAAgDoJEABAHQSoAAAOglQAACdBCgAgE4CFABAJwEKAKCTAAUA0EmAAgDoJEABAHQSoAAAOglQAACdBCgAgE4CFABAJwEKAKDTob2uALBEx48nJ07ceNrm5uD7kSM3LX/0aHLs2I5XC2C/0QMF+8mJEzcEpi0bG4OvcZubNw1bAMxEDxTsNxsbycmT25eb1CMFwEz0QAEAdBKgAAA6CVAAAJ0EKACATgIUAEAnAQoAoJMABQDQSYACAOgkQAEAdBKgAAA6CVAAAJ0EKACATgIUAEAnAQoAoJMABQDQSYACAOgkQAEAdBKgAAA6CVAAAJ0EKACATgsFqKp6WFW9p6r+sqqesaxKAQCssrkDVFWdleQ3kzw8yV2TPK6q7rqsigEArKpFeqDum+QvW2vva61dl+T3kjx6OdUCAFhdiwSoOyT54MjvVw6nAQDsa4d2+gWq6liSY8NfP1lV75lY7kk1+zx3qGxqzcquSj1Woeyq1GMVyq5KPVah7KrUY93Krko9VqHsqtRjFcquSj12t+xXTyu+SID62yRfOfL7HYfTbqS1djzJ8QVeBwBgpSxyCu8tSb62qu5UVWcneWySVyynWgAAq2vuHqjW2vVV9SNJXp3krCTPa629c2k1AwBYUdVa2+s6AACsFSORAwB0EqAAADoJUAAAnXZ8HKhxVfUFSR6W5COttTdW1eOTfEmSF7fWPrbb9Vm2qrpbks+11t49Mu0bWmtv3sNq7aiq+vrW2lv2uh7LUFX3SfKNSc5N8rEkf95aO7W3tZquqh6V5E9aa59e8nxv31q7qqoqgycM/Isk70/y0tba9ct8LWZTVfdI8k0ZbJvXJHl1a+2qva1Vn6r64dbab+51PdZFVd09yd2T/NV+OcbupOHx+4NJPpLkkUk+01p7zY693m5fRF5Vf5DBEAjnJrlPkv+b5MNJjrbWHjpW9seSvLK19r4FXm+mN/cz7dizrpSq+uUkt03y2SS3TvIDrbXTVfW61tqDtnn9uXaUSctXVeduhdGqeuTWfDN487vJCp81NFTVpB7LSvKq1tq3TSg/8wG/Z8PveXMfPrPxO8eXL8kfTij7q0m+MMmfJPl4ki9O8pAk17fWnjKlzjOHrUV37qr6jtba/xmb9qEkf5NB+/5Bkle01v6uY54/31r7TxOmv6619qCq+rUkn0nyuiQbSQ631v7VWNmusDXrh6jeD1u9YXKRDzuzBIHt9unO7fiZSW6R5O1JHpjkH5J8LskbW2svmLcOwzK97TbTfl1Vf5pk63izNULh3ZJc3lq7/wyvM7GNq+oLM9h/3ptBe/1ABtvoC1pr/zCh/Jcl+b4M9rsLk/z7DPbt32qtvX+sbA3nPbp8f3SGtpt5G+pot1e11h5WVU9N8uAkf5Tkm5Nc2Vr76bGy926tva2qbpHkB5P882Gb/PaUfaRrm+94b1i4Y2TKe9nM22ZVPTeD7ewfk9wmg3EpP5HkNq21Y2NlK8kjMtiHXtNa+/xw+qNbay+fpb7J3gSoi1trDxz+fHlr7e7j00fKvi+DA8btkrwqyYWttcumzHfmN/eeHbtzpVyy9f9Vdc8k/yPJTyT5xUkBqnNH6Vm+rTe/X8hgw3/5cL53bK09aazszKGhqj6dQfio3Lj97tla+/KxsjMf8HvaeGz5Znlzf2GSdyR57djy3au19vixspeMr/9p0+cIWz3b0deM///wfy9orX3rWNmLW2sPrKo7JXlMku8YvsbLW2u/NVb2A0k+kOTz2X67/5PW2kO2vo+/3ljZmdfHsPxMH6J6PmwNy88cJns+7HQeL3r26Z7t+LWttQeP/H5Ra+3bxtdPbx3maLee/fppSe6VwXZ7cjjtj1trD58w3542/sMkb81g+JwHJvnDDPalh7bWvnfCvF+T5IIMtqMfTPKfMwhT/6W1dmSs7HOSvHO4fA9KcqskH03yj621Z46V7dmGetpta7t4fZIHjry5v6G19i1Tyj4/yZtywzb0xNbaI+at77B8z3tDT8dIz3tZz7b5+tbaA4Y/X9Zau8fw50nHrBdlEDSvHy7Tv2mtvWdaW0zVWtvVrySvTPKzSX4hyeuTPD3Jk4aNN1724uH3Wyb57iQvSnIqg0AyXvbTGWw8Fw+/b/38kQlln5bBDnVkZNofT6nv60d+vmy8bmNl/yzJ2SO/f2kGB69rpsz7dVuvkeRmI9PfsODyvW687sPfT04oe8mUut1kepJLk3zJhOkXTZj22kllMvg0MXcbj85jfF5T1smfTpnHTaYn+ZUkv5Pke5J8+/D7s5M8a5F2m2M7+kSS5yX53bGvKyeUnfT/t01ybML0xyR58XB/O9TOvN1/f5LnDF/3RUn+bZJfT/JLi6yP8ekZvEFOLD9rufHpSe6UwXHlZAbj1P3QmdZTknsOyx7e2nfGyvYcL3r26Z7t+CVJfirJw5M8M8mvnaHszHWYo91m3q+H089O8u8yeNj8o87Qbj1tPLpdvGVa3Uamj+5779qmnce3wdeOLucC21DP8fDqJC/I4PmytxiZfmrSfDMIH6/OsENkfJnnqe94+e2mp2NfTd97Wc+2+WcjP3/HyM8nJ5Q9OfLzVyR5zXD7nNgW0752/RqoJN+bQVffXyX5+SRPSHLzJP962j+0Qffdy5K8rKoOZfDJYNwVSR7TxroLq+qiCfP71RqMnv7kqvrBJCfOUN/RNvqZ0VlPKPu0DBL4tcPX+bthF+RNPhUN3bWqXpDkzhkk/c8Mp998QtkrknxXa+3joxMnLV+Sr6uqS4bzP7e19rFh6r/VhLKnqup3klyUwRv3F2fwqfWtE8o+cqSOo27yiTLJtVX1Uxn0/hxJ8q7h9LMmlO1p4yR5/vCT4geHnyRen8EBYVI3+yuq6pUZ7Hhby/eATBg1v7X241V17yT3S/K1GXzqOt5ae9uE+fa0W+8yXp7kp1prp0cnVtXvTyj7zPEJrbVrMuHxSa21C5NcWFUPT/LCqnpTki+YVNnW2gur6rVJHppBIDuU5DmttbdPKD5tfUw7nfmpqvrZJF+U5CNV9fQMP+VPKXfOSLm/m1BuvO7vT/LLSX65qm6bwemxcWdV1dmttetaa++oqu/KICjebcL8eo4XPfv086vqf2a2dnt8ku9Kco8Mehq2TuV+35Q6vHDGOvyTGdttfL++Yjh90n6d1tp1SZ49XM7vz6AHZlK5njY+e+TnHxr5eWIdknxguH2eleSyqvr1DLa3D08oe1lVPTs3LN/Fw+mT3ivHt6HHJHlhJmxDuXG7PSBnPh5+w/D7f8yghyRVdc7w93G/kOR/ZXB67WRVvSGDU8EXzlDfqdv8UM8xrmdf7XkvSzLztnmsqs5qrX2uDS91GG5TvzKh7M2q6lattb9vrX2oBpe6HM+g92xmKz2QZlXdK4MNaNtztlV1uyQfHe6wW9N+OINzwZ87w2scymDHvkuSl7WbnoO9ewYHodFrVz6fJG3sepQ5lu/8DLpSb5bkbRmck91a3leNlf2KDFL4e0fq8ZkMEvpnJ8z77sP5XDH8/ZYZnGr78wll753BTntuBqHh1q21/7rgsh1K8tQMuq3flUGbfSqD3perxsreNcl7RtdTVf1okr+e1sbD9th6c/94kjdm0Ps36VqT+ye5awYHmU9kELS+ZnwbmmMZt8LWVru9KYOenUl1uFuSd48t49lJntFa+/mxsocy2B6XfjNCjVwDUVUPzOD6mL9Ywny31sdtMmiLL2+t/bcpZW+RGz5EvTeDD1GVwSfst4yUu2WSH8mgXd+ewZvlx5L83vgHpWH5hyU5ndmuV7xvBtvXtSPTDiX5mfH1Mfzb1vVrH03yY0m+t7X2jRPKffXIr1e11q4bvvn9+JT53j+D02tnZXBK53OttV8cL9djrA4faq19dngs/Kvx48qw/LePt1FNv/7orAyC3J2SvCeDIPdDGVxesZQL2keOyb/YWjtvwt+/PINeg89u7R81uAbnfq21P51QvpJ8awanCN+QwXZaST7RWvuzCeW/JYPTbC9vrb1jOO2bWmtvHCs3aRv6kSSnW2u/P1Z2q92+JsN2a619vqru31q7ZMammWh4rP/WDALLxzM4vt15wnvkfTP4wDT6HnJ9BmcVJgbW4f88aPh/1ydpbexU5rDc1j79l8OvJwz/5/mttU+Mlb19Br1N141Nn3QN1ENba6+e8HoL3bg0fO+9w7Aeo8fY+016j5w6nxUPUDt1nULPOdiu63M6l++5wx+v227ePfUYttttMtjgZ2230Z6QuyZ553i7zbFss9Z3dN1l+H9TLzbtXH8zt0Xn8vVeUN9b57luRtimzjs1365taNa26N33qup5wx9n2eamDeHy6kWOAXMcW5IZ9v8ePcfC3vJT1vXMF4bPWOetekyrQ++1PD3Hw3mOnVv1TaZs973Hi1l11rd3f+p5f5q0/hZuix1ut4WPhXtxCq/H17cbX5T9v6vqJ6aUvTAzXrCY5JO54WLo5IYDwj0nlP1n7cYXpn338OeLJ5Tt1TPvnrI71W49eurbW4et9Tdq2vrraYsePXUYLT/LNrdTdd6p+S6y/rZuSJjUFr373p07yo+uj9E3wUWPATs13x6966On/E4dL3rm27sd95Tf6fecUWc6Xsyqp76929tOHcN79pGesj2WcyxsHRdM7fZX+i/KnvWCxZ6LoWe+MG2e5Zt13r1ld6LddmrZeuvQu/562qJj+WauwwrVeUfmu1Prb45tqGcf2ZFjwAodW7r26c71t/TjRc98e7fjnvJzzHvp7zmdbda1bD3b2xzld+L9d8/b7YzzWaQSO/2V5L4ZdBeOTjsryWO3+b9DGdxp9Mwpf7/9aOON/t+EaXdLctaEDeVRS1i+mWEzHKcAAAB5SURBVOfdWXZH2m2nlq23Dp3rb662mGH5Zq7DCtV5R+a7U+uvdxvq3Ed25BiwKseWnvUxb/llHi965tu7HfeU36ljZ+/xoqOtepZtx/annWqLVWi3M32t9DVQAACryLPwAAA6CVAAAJ0EKACATgIUAEAnAQoAoNP/B+6on+I72vB5AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 720x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DTMNkzvzztWt"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}