project 61 Hierarchical_Clustering1(numpy).ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 27,
      "metadata": {
        "id": "olEIvKziHJoe"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "from scipy.spatial.distance import pdist, squareform\n",
        "from scipy.cluster.hierarchy import linkage, dendrogram\n",
        "import matplotlib.pyplot as plt\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "single linkage methods on numpu"
      ],
      "metadata": {
        "id": "pnmCENniNEfX"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "data = np.array([\n",
        "    [1, 2],\n",
        "    [2, 3],\n",
        "    [3, 4],\n",
        "    [4, 5],\n",
        "    [5, 6],\n",
        "    [6, 7]\n",
        "])"
      ],
      "metadata": {
        "id": "aMWnmyy7IuJs"
      },
      "execution_count": 28,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "distance_matrix = squareform(pdist(data, metric='euclidean'))  #euclidean distance matrix\n",
        "distance_matrix"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wlB3cCqLI49K",
        "outputId": "ee1631eb-1209-4709-b3aa-d536ed6221bf"
      },
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.        , 1.41421356, 2.82842712, 4.24264069, 5.65685425,\n",
              "        7.07106781],\n",
              "       [1.41421356, 0.        , 1.41421356, 2.82842712, 4.24264069,\n",
              "        5.65685425],\n",
              "       [2.82842712, 1.41421356, 0.        , 1.41421356, 2.82842712,\n",
              "        4.24264069],\n",
              "       [4.24264069, 2.82842712, 1.41421356, 0.        , 1.41421356,\n",
              "        2.82842712],\n",
              "       [5.65685425, 4.24264069, 2.82842712, 1.41421356, 0.        ,\n",
              "        1.41421356],\n",
              "       [7.07106781, 5.65685425, 4.24264069, 2.82842712, 1.41421356,\n",
              "        0.        ]])"
            ]
          },
          "metadata": {},
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "linkage_matrix = np.array([\n",
        "    [0, 1, 0.5, 2],\n",
        "    [2, 3, 0.8, 3],\n",
        "    [4, 5, 1.0, 4],\n",
        "    [6, 7, 1.2, 5],\n",
        "    [8, 9, 1.5, 6],\n",
        "])"
      ],
      "metadata": {
        "id": "F0RZCGPLJTib"
      },
      "execution_count": 30,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "dendrogram(linkage_matrix, labels=[f'P{i + 1}' for i in range(len(data))])\n",
        "\n",
        "plt.title('Hierarchical Clustering Dendrogram')\n",
        "plt.xlabel('Data Points')\n",
        "plt.ylabel('Distance')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 476
        },
        "id": "2NwWXbinJAgB",
        "outputId": "2db95789-11fb-45e4-d59d-bcb370bca0a4"
      },
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "EXPERIMENTING WITH DIFFERENT TYPES OF METHODS USED FOR LINKAGE MATRISES"
      ],
      "metadata": {
        "id": "8pjxKz89LQlF"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "linkage_matrix = linkage(distance_matrix, method='single')\n",
        "\n",
        "dendrogram(linkage_matrix, labels=[f'P{i + 1}' for i in range(len(data))])\n",
        "\n",
        "plt.title('Hierarchical Clustering Dendrogram')\n",
        "plt.xlabel('Data Points')\n",
        "plt.ylabel('Distance')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 511
        },
        "id": "RBhqxPBeLDWx",
        "outputId": "91600423-cd29-40f1-8d04-6028451e49d8"
      },
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-32-85a336fc138f>:1: ClusterWarning: scipy.cluster: The symmetric non-negative hollow observation matrix looks suspiciously like an uncondensed distance matrix\n",
            "  linkage_matrix = linkage(distance_matrix, method='single')\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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DDh48qOXLl6tChQq5ftaNh4eH+vbtq3fffVcmk0l16tTRF198kW0+yG+//ab7779f/fr1U0BAgMqUKaPVq1crKSlJ//73vy39mjdvrnnz5mny5Mny9/eXp6enOnXqZJNr4E6EhoaqVatWGjlypI4ePar69etr3bp1ls9Kye2O062+//57Xbt2TZmZmfrrr7/0ww8/aN26dfLw8NDq1aut5h9NnTpVmzZt0r333qtBgwYpICBA58+f165du/Ttt98W+HNaHBwcNHnyZP3nP/9Rp06d9Oijj+rEiRNasmRJrnNucjrGtGnTNHDgQHXo0EH9+/e3vBXcz89PL730kqXvG2+8oV69eqlt27YaOHCgLly4oPfee0+BgYH5vlZtfb3DGAg3MARXV1dt3rxZb7zxhlasWKEPPvhA7u7uuueeezRhwoRc3+lxs/DwcCUmJmr+/PnasGGDAgICtGzZMq1YsSLbB9DlJigoSD/++KNef/11zZs3T9euXVPNmjXVr1+/OzzDv7m5uen777/XuHHjtHr1ai1dulSenp66//77Vb16dZudx638/f21Z88ezZw5U6tXr9aaNWuUlZUlf39/PfPMM3rhhRfy3P/dd99VRkaGoqKi5OTkpH79+umtt96ymnzt6+ur/v37KyYmRh9++KHKlCmj+vXr67PPPrOaRD127FidPHlSb775pi5duqQOHTqoU6dONrkG7kTp0qX15Zdf6sUXX9TSpUtVqlQp9e7dW+PGjVPbtm3z/cnH77zzjqS/Q0L58uXVoEEDTZgwQYMGDco2qdnLy0s///yzJk6cqFWrVmnu3LmqVKmSGjZsWOhPjR48eLAyMzP11ltv6eWXX1ajRo20bt06vf766/k+Rnh4uFxdXTV16lS98sorKlu2rHr37q1p06ZZPuNG+r9HnuPHj9d///tf1a1bV9HR0Vq6dKkOHjyY79ey9fWOks9kZrYUANw1a9asUe/evbV161a1bdvW3uWUCE2aNFGVKlW0ceNGe5eCEoo5NwBgI1evXrVaz8zM1Lvvvit3d3c1a9bMTlUVXxkZGdnmQsXGxmrv3r1WX6sBFBSPpQDARp5//nldvXpVwcHBSktL06pVq7Rt2za98cYbRfqW6ZIiISFBISEheuKJJ1StWjUdPnxYUVFR8vb2zvahiUBB8FgKAGxk+fLlmj59uo4ePapr167J399fzz77rIYNG2bv0oql5ORkDR48WD/88IPOnj2rsmXL6v7779fUqVNVp04de5eHEoxwAwAADIU5NwAAwFAINwAAwFD+cROKs7Ky9Oeff6pcuXL5/lAtAABgX2azWZcuXVK1atVUqlTe92b+ceHmzz//LNSX/wEAAPs7deqU5UNLc/OPCzflypWT9PfguLu727kaAACQHykpKfL19bX8Hs/LPy7c3HgU5e7uTrgBAKCEyc+UEiYUAwAAQyHcAAAAQyHcAAAAQyHcAAAAQyHcAAAAQyHcAAAAQyHcAAAAQ7FruJk3b54aN25s+cyZ4OBgff3117n2j46OlslkslqcnZ2LsGIAAFDc2fVD/KpXr66pU6eqbt26MpvNWrp0qXr16qXdu3erYcOGOe7j7u6uI0eOWNb5figAAHAzu4abnj17Wq1PmTJF8+bN048//phruDGZTPL29i6K8gAAQAlUbObcZGZm6pNPPtHly5cVHByca7/U1FTVrFlTvr6+6tWrlw4ePJjncdPS0pSSkmK1AAAA47J7uNm/f7/c3Nzk5OSkIUOGaPXq1QoICMixb7169bR48WKtXbtWy5YtU1ZWltq0aaM//vgj1+NHRkbKw8PDsvCN4AAAGJvJbDab7VlAenq64uPjlZycrM8//1wLFy7U5s2bcw04N8vIyFCDBg3Uv39/TZo0Kcc+aWlpSktLs6zf+FbR5ORkvjgTAIASIiUlRR4eHvn6/W33bwV3dHSUv7+/JKl58+basWOHZs+erfnz5992XwcHBzVt2lRHjx7NtY+Tk5OcnJxsVm9RMZvNupqRae8ybutK+nV7l3BbLg6lmXhuAyXlmryaXvxrlCRnh1LF/rp0dbT7r4g8lZRrUir+YykZ6/+VxW60s7KyrO605CUzM1P79+/Xgw8+eJerKlpms1mPRG3XLycv2LsUAMA/RIuaFbRiSLAhAo5dw01ERIS6deumGjVq6NKlS1q+fLliY2O1YcMGSVJYWJh8fHwUGRkpSZo4caJat24tf39/Xbx4UW+99ZZOnjypZ555xp6nYXNXMzIJNgCAIrXz5AVdzcgsEXeZbseuZ3DmzBmFhYXp9OnT8vDwUOPGjbVhwwY98MADkqT4+HiVKvV/c54vXLigQYMGKTExURUqVFDz5s21bdu2fM3PKal2jgmRq2Npe5eRq+L8WOpqepbavblJkrRzzP2G+IG1lyvp19Vicowk6fvR98nF0e7vRchVcX8sdTU9S51nbZEkfT+6o1yK8c93cf6ZKUnXpFTcxzJTLSZ/a+8ybMquo71o0aI8t8fGxlqtz5w5UzNnzryLFRU/ro6li/UPRXGu7ebg5epYpljXWpJUcnNkLO/AzddlJTcnxtIGuCZxq+IddQEAAAqIcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAyFcAMAAAzFruFm3rx5aty4sdzd3eXu7q7g4GB9/fXXee6zYsUK1a9fX87OzmrUqJG++uqrIqoWAACUBHYNN9WrV9fUqVP1yy+/aOfOnerUqZN69eqlgwcP5th/27Zt6t+/v55++mnt3r1boaGhCg0N1YEDB4q4cgAAUFzZNdz07NlTDz74oOrWrat77rlHU6ZMkZubm3788ccc+8+ePVtdu3bVyy+/rAYNGmjSpElq1qyZ3nvvvSKuHAAAFFfFZs5NZmamPvnkE12+fFnBwcE59tm+fbtCQkKs2rp06aLt27fnety0tDSlpKRYLQAAwLjsHm72798vNzc3OTk5aciQIVq9erUCAgJy7JuYmCgvLy+rNi8vLyUmJuZ6/MjISHl4eFgWX19fm9YPAACKF7uHm3r16mnPnj366aef9Oyzz2rAgAH69ddfbXb8iIgIJScnW5ZTp07Z7NgAAKD4KWPvAhwdHeXv7y9Jat68uXbs2KHZs2dr/vz52fp6e3srKSnJqi0pKUne3t65Ht/JyUlOTk62LRoAABRbdr9zc6usrCylpaXluC04OFgxMTFWbRs3bsx1jg4AAPjnseudm4iICHXr1k01atTQpUuXtHz5csXGxmrDhg2SpLCwMPn4+CgyMlKS9OKLL6pDhw6aPn26unfvrk8++UQ7d+7UggUL7HkaAACgGLFruDlz5ozCwsJ0+vRpeXh4qHHjxtqwYYMeeOABSVJ8fLxKlfq/m0tt2rTR8uXLNWbMGL366quqW7eu1qxZo8DAQHudAgAAKGbsGm4WLVqU5/bY2NhsbX379lXfvn3vUkUAAKCkK3ZzbgAAAO4E4QYAABgK4QYAABgK4QYAABgK4QYAABgK4QYAABgK4QYAABgK4QYAABgK4QYAABgK4QYAABgK4QYAABgK4QYAABgK4QYAABgK4QYAABgK4QYAABgK4QYAABgK4QYAABgK4QYAABgK4QYAABgK4QYAABgK4QYAABgK4QYAABgK4QYAABgK4QYAABgK4QYAABgK4QYAABgK4QYAABgK4QYAABgK4QYAABgK4QYAABgK4QYAABgK4QYAABgK4QYAABgK4QYAABgK4QYAABgK4QYAABgK4QYAABgK4QYAABgK4QYAABiKXcNNZGSkWrZsqXLlysnT01OhoaE6cuRInvtER0fLZDJZLc7OzkVUMQAAKO7sGm42b96soUOH6scff9TGjRuVkZGhzp076/Lly3nu5+7urtOnT1uWkydPFlHFAACguCtjzxdfv3691Xp0dLQ8PT31yy+/qH379rnuZzKZ5O3tfbfLAwAAJVCxmnOTnJwsSapYsWKe/VJTU1WzZk35+vqqV69eOnjwYFGUBwAASoBiE26ysrI0fPhwtW3bVoGBgbn2q1evnhYvXqy1a9dq2bJlysrKUps2bfTHH3/k2D8tLU0pKSlWCwAAMC67Ppa62dChQ3XgwAFt3bo1z37BwcEKDg62rLdp00YNGjTQ/PnzNWnSpGz9IyMjNWHCBJvXCwAAiqdicedm2LBh+uKLL7Rp0yZVr169QPs6ODioadOmOnr0aI7bIyIilJycbFlOnTpli5IBAEAxZdc7N2azWc8//7xWr16t2NhY1apVq8DHyMzM1P79+/Xggw/muN3JyUlOTk53WioAACgh7Bpuhg4dquXLl2vt2rUqV66cEhMTJUkeHh5ycXGRJIWFhcnHx0eRkZGSpIkTJ6p169by9/fXxYsX9dZbb+nkyZN65pln7HYeAACg+LBruJk3b54kqWPHjlbtS5YsUXh4uCQpPj5epUr939OzCxcuaNCgQUpMTFSFChXUvHlzbdu2TQEBAUVVNgAAKMbs/ljqdmJjY63WZ86cqZkzZ96ligAAQElXLCYUAwAA2ArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGModh5tr167Zog4AAACbKFS4ycrK0qRJk+Tj4yM3NzcdP35ckvT6669r0aJFNi0QAACgIAoVbiZPnqzo6Gi9+eabcnR0tLQHBgZq4cKFNisOAACgoAoVbj744AMtWLBAjz/+uEqXLm1pDwoK0uHDh21WHAAAQEEVKtwkJCTI398/W3tWVpYyMjLyfZzIyEi1bNlS5cqVk6enp0JDQ3XkyJHb7rdixQrVr19fzs7OatSokb766qsC1Q8AAIyrUOEmICBA33//fbb2zz//XE2bNs33cTZv3qyhQ4fqxx9/1MaNG5WRkaHOnTvr8uXLue6zbds29e/fX08//bR2796t0NBQhYaG6sCBA4U5FQAAYDBlCrPT2LFjNWDAACUkJCgrK0urVq3SkSNH9MEHH+iLL77I93HWr19vtR4dHS1PT0/98ssvat++fY77zJ49W127dtXLL78sSZo0aZI2btyo9957T1FRUYU5HQAAYCCFunPTq1cv/e9//9O3336rsmXLauzYsTp06JD+97//6YEHHih0McnJyZKkihUr5tpn+/btCgkJsWrr0qWLtm/fnmP/tLQ0paSkWC0AAMC4CnXnRpLatWunjRs32qyQrKwsDR8+XG3btlVgYGCu/RITE+Xl5WXV5uXlpcTExBz7R0ZGasKECTarEwAAFG+FunOzY8cO/fTTT9naf/rpJ+3cubNQhQwdOlQHDhzQJ598Uqj9cxMREaHk5GTLcurUKZseHwAAFC+FCjdDhw7NMSQkJCRo6NChBT7esGHD9MUXX2jTpk2qXr16nn29vb2VlJRk1ZaUlCRvb+8c+zs5Ocnd3d1qAQAAxlWocPPrr7+qWbNm2dqbNm2qX3/9Nd/HMZvNGjZsmFavXq3vvvtOtWrVuu0+wcHBiomJsWrbuHGjgoOD8/26AADAuAoVbpycnLLdPZGk06dPq0yZ/E/jGTp0qJYtW6bly5erXLlySkxMVGJioq5evWrpExYWpoiICMv6iy++qPXr12v69Ok6fPiwxo8fr507d2rYsGGFORUAAGAwhQo3nTt3tsxlueHixYt69dVXC/RuqXnz5ik5OVkdO3ZU1apVLcunn35q6RMfH6/Tp09b1tu0aaPly5drwYIFCgoK0ueff641a9bkOQkZAAD8cxTq3VJvv/222rdvr5o1a1o+tG/Pnj3y8vLShx9+mO/jmM3m2/aJjY3N1ta3b1/17ds3368DAAD+OQoVbnx8fLRv3z599NFH2rt3r1xcXDRw4ED1799fDg4Otq4RAAAg3wr9OTdly5bV4MGDbVkLAADAHSt0uPn999+1adMmnTlzRllZWVbbxo4de8eFAQAAFEahws3777+vZ599VpUrV5a3t7dMJpNlm8lkItwAAAC7KVS4mTx5sqZMmaJXXnnF1vUAAADckUK9FfzChQu8WwkAABRLhQo3ffv21TfffGPrWgAAAO5YoR5L+fv76/XXX9ePP/6oRo0aZXv79wsvvGCT4gAAAAqqUOFmwYIFcnNz0+bNm7V582arbSaTiXADAADsplDh5sSJE7auAwAAwCYKNecGAACguCr0h/j98ccfWrduneLj45Wenm61bcaMGXdcGAAAQGEUKtzExMTooYceUu3atXX48GEFBgYqLi5OZrNZzZo1s3WNAAAA+Vaox1IREREaNWqU9u/fL2dnZ61cuVKnTp1Shw4d+PwbAABgV4UKN4cOHVJYWJgkqUyZMrp69arc3Nw0ceJETZs2zaYFAgAAFEShwk3ZsmUt82yqVq2qY8eOWbadO3fONpUBAAAUQqHm3LRu3Vpbt25VgwYN9OCDD2rkyJHav3+/Vq1apdatW9u6RgAAgHwrVLiZMWOGUlNTJUkTJkxQamqqPv30U9WtW5d3SgEAALsqVLipXbu25c9ly5ZVVFSUzQoCAAC4E4Wac1O7dm399ddf2dovXrxoFXwAAACKWqHCTVxcnDIzM7O1p6WlKSEh4Y6LAgAAKKwCPZZat26d5c8bNmyQh4eHZT0zM1MxMTHy8/OzWXEAAAAFVaBwExoaKunvb/4eMGCA1TYHBwf5+flp+vTpNisOAACgoAoUbrKysiRJtWrV0o4dO1S5cuW7UhQAAEBhFerdUidOnMjWdvHiRZUvX/5O6wEAALgjhZpQPG3aNH366aeW9b59+6pixYry8fHR3r17bVYcAABAQRUq3ERFRcnX11eStHHjRn377bdav369unXrppdfftmmBQIAABREoR5LJSYmWsLNF198oX79+qlz587y8/PTvffea9MCAQAACqJQd24qVKigU6dOSZLWr1+vkJAQSZLZbM7x828AAACKSqHu3Dz88MN67LHHVLduXf3111/q1q2bJGn37t3y9/e3aYEAAAAFUahwM3PmTPn5+enUqVN688035ebmJkk6ffq0nnvuOZsWCAAAUBCFCjcODg4aNWpUtvaXXnrpjgsCAAC4E/kON+vWrVO3bt3k4OBg9TUMOXnooYfuuDAAAIDCyHe4CQ0NVWJiojw9PS1fw5ATk8nEpGIAAGA3+Q43N7564dY/AwAAFCcFnnOTlZWl6OhorVq1SnFxcTKZTKpdu7b69OmjJ598UiaT6W7UCQAAkC8F+pwbs9mshx56SM8884wSEhLUqFEjNWzYUHFxcQoPD1fv3r3vVp0AAAD5UqA7N9HR0dqyZYtiYmJ03333WW377rvvFBoaqg8++EBhYWE2LRIAACC/CnTn5uOPP9arr76aLdhIUqdOnfTf//5XH330kc2KAwAAKKgChZt9+/apa9euuW7v1q0b3woOAADsqkDh5vz58/Ly8sp1u5eXly5cuJDv423ZskU9e/ZUtWrVZDKZtGbNmjz7x8bGymQyZVsSExPz/ZoAAMDYChRuMjMzVaZM7tN0SpcurevXr+f7eJcvX1ZQUJDmzJlTkDJ05MgRnT592rJ4enoWaH8AAGBcBZpQbDabFR4eLicnpxy3p6WlFejFu3XrZvnSzYLw9PRU+fLlC7wfAAAwvgKFmwEDBty2T1G8U6pJkyZKS0tTYGCgxo8fr7Zt2+baNy0tzSp0paSk3PX6AACA/RQo3CxZsuRu1ZEvVatWVVRUlFq0aKG0tDQtXLhQHTt21E8//aRmzZrluE9kZKQmTJhQxJUCAAB7KdS3gttLvXr1VK9ePct6mzZtdOzYMc2cOVMffvhhjvtERERoxIgRlvWUlBT5+vre9VoBAIB9lKhwk5NWrVpp69atuW53cnLKdY4QAAAwngK9W6o42rNnj6pWrWrvMgAAQDFh1zs3qampOnr0qGX9xIkT2rNnjypWrKgaNWooIiJCCQkJ+uCDDyRJs2bNUq1atdSwYUNdu3ZNCxcu1HfffadvvvnGXqcAAACKGbuGm507d1p9lcONuTEDBgxQdHS0Tp8+rfj4eMv29PR0jRw5UgkJCXJ1dVXjxo317bff5vh1EAAA4J/JruGmY8eOMpvNuW6Pjo62Wh89erRGjx59l6sCAAAlWYmfcwMAAHAzwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUwg0AADAUu4abLVu2qGfPnqpWrZpMJpPWrFlz231iY2PVrFkzOTk5yd/fX9HR0Xe9TgAAUHLYNdxcvnxZQUFBmjNnTr76nzhxQt27d9d9992nPXv2aPjw4XrmmWe0YcOGu1wpAAAoKcrY88W7deumbt265bt/VFSUatWqpenTp0uSGjRooK1bt2rmzJnq0qXL3SoTAACUICVqzs327dsVEhJi1dalSxdt3749133S0tKUkpJitQAAAOMqUeEmMTFRXl5eVm1eXl5KSUnR1atXc9wnMjJSHh4elsXX17coSgUAAHZSosJNYURERCg5OdmynDp1yt4lAQCAu8iuc24KytvbW0lJSVZtSUlJcnd3l4uLS477ODk5ycnJqSjKAwAAxUCJunMTHBysmJgYq7aNGzcqODjYThUBAIDixq7hJjU1VXv27NGePXsk/f1W7z179ig+Pl7S34+UwsLCLP2HDBmi48ePa/To0Tp8+LDmzp2rzz77TC+99JI9ygcAAMWQXcPNzp071bRpUzVt2lSSNGLECDVt2lRjx46VJJ0+fdoSdCSpVq1a+vLLL7Vx40YFBQVp+vTpWrhwIW8DBwAAFnadc9OxY0eZzeZct+f06cMdO3bU7t2772JVAACgJCtRc24AAABuh3ADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMpViEmzlz5sjPz0/Ozs6699579fPPP+faNzo6WiaTyWpxdnYuwmoBAEBxZvdw8+mnn2rEiBEaN26cdu3apaCgIHXp0kVnzpzJdR93d3edPn3aspw8ebIIKwYAAMWZ3cPNjBkzNGjQIA0cOFABAQGKioqSq6urFi9enOs+JpNJ3t7elsXLy6sIKwYAAMWZXcNNenq6fvnlF4WEhFjaSpUqpZCQEG3fvj3X/VJTU1WzZk35+vqqV69eOnjwYK5909LSlJKSYrUAAADjsmu4OXfunDIzM7PdefHy8lJiYmKO+9SrV0+LFy/W2rVrtWzZMmVlZalNmzb6448/cuwfGRkpDw8Py+Lr62vz8wAAAMWH3R9LFVRwcLDCwsLUpEkTdejQQatWrVKVKlU0f/78HPtHREQoOTnZspw6daqIKwYAAEWpjD1fvHLlyipdurSSkpKs2pOSkuTt7Z2vYzg4OKhp06Y6evRojtudnJzk5OR0x7UCAICSwa53bhwdHdW8eXPFxMRY2rKyshQTE6Pg4OB8HSMzM1P79+9X1apV71aZAACgBLHrnRtJGjFihAYMGKAWLVqoVatWmjVrli5fvqyBAwdKksLCwuTj46PIyEhJ0sSJE9W6dWv5+/vr4sWLeuutt3Ty5Ek988wz9jwNAABQTNg93Dz66KM6e/asxo4dq8TERDVp0kTr16+3TDKOj49XqVL/d4PpwoULGjRokBITE1WhQgU1b95c27ZtU0BAgL1OAQAAFCN2DzeSNGzYMA0bNizHbbGxsVbrM2fO1MyZM4ugKgAAUBKVuHdLAQAA5IVwAwAADIVwAwAADIVwAwAADIVwAwAADIVwAwAADIVwAwAADIVwAwAADIVwAwAADIVwAwAADIVwAwAADIVwAwAADIVwAwAADIVwAwAADIVwAwAADIVwAwAADIVwAwAADIVwAwAADIVwAwAADIVwAwAADIVwAwAADIVwAwAADIVwAwAADIVwAwAADIVwAwAADIVwAwAADIVwAwAADIVwAwAADIVwAwAADIVwAwAADIVwAwAADIVwAwAADIVwAwAADIVwAwAADIVwAwAADIVwAwAADIVwAwAADIVwAwAADIVwAwAADKVYhJs5c+bIz89Pzs7Ouvfee/Xzzz/n2X/FihWqX7++nJ2d1ahRI3311VdFVCkAACju7B5uPv30U40YMULjxo3Trl27FBQUpC5duujMmTM59t+2bZv69++vp59+Wrt371ZoaKhCQ0N14MCBIq4cAAAUR3YPNzNmzNCgQYM0cOBABQQEKCoqSq6urlq8eHGO/WfPnq2uXbvq5ZdfVoMGDTRp0iQ1a9ZM7733XhFXDgAAiiO7hpv09HT98ssvCgkJsbSVKlVKISEh2r59e477bN++3aq/JHXp0iXX/gAA4J+ljD1f/Ny5c8rMzJSXl5dVu5eXlw4fPpzjPomJiTn2T0xMzLF/Wlqa0tLSLOvJycmSpJSUlDsp/a66kn5dWWlXJP1d53VHu/41lViMo+0wlrbDWNoG42g7JWUsb/zeNpvNt+1bPM/AhiIjIzVhwoRs7b6+vnaopuCqzrJ3BcbAONoOY2k7jKVtMI62UxLG8tKlS/Lw8Mizj13DTeXKlVW6dGklJSVZtSclJcnb2zvHfby9vQvUPyIiQiNGjLCsZ2Vl6fz586pUqZJMJtMdngEAACgKZrNZly5dUrVq1W7b167hxtHRUc2bN1dMTIxCQ0Ml/R0+YmJiNGzYsBz3CQ4OVkxMjIYPH25p27hxo4KDg3Ps7+TkJCcnJ6u28uXL26J8AABQhG53x+YGuz+WGjFihAYMGKAWLVqoVatWmjVrli5fvqyBAwdKksLCwuTj46PIyEhJ0osvvqgOHTpo+vTp6t69uz755BPt3LlTCxYssOdpAACAYsLu4ebRRx/V2bNnNXbsWCUmJqpJkyZav369ZdJwfHy8SpX6vzd1tWnTRsuXL9eYMWP06quvqm7dulqzZo0CAwPtdQoAAKAYMZnzM+0YAACghLD7h/gBAADYEuEGAAAYCuEGAAAYCuEGAAAYCuEGAAAYCuHGTqKjo2UymSyLs7Oz7rnnHg0bNszyCcxxcXFWfW5ePvnkEzufQfGRn7G84dixY3rsscfk6ekpFxcX1a1bV6+99pqdKi9e8jOOf/75p5544gnVq1dP5cqVU/ny5dWqVSstXbo0X9/38k9RkGvyho8++kgmk0lubm5FXG3xlt+xnDJlih566CF5eXnJZDJp/Pjx9iu6GMrPOB4+fFijR49WkyZNVK5cOVWtWlXdu3fXzp077Vx9wdn9c27+6SZOnKhatWrp2rVr2rp1q+bNm6evvvpKBw4csPTp37+/HnzwQav9cvtE5n+yvMbS1dVVe/bsUceOHeXj46ORI0eqUqVKio+P16lTp+xderGS1zieO3dOf/zxhx555BHVqFFDGRkZ2rhxo8LDw3XkyBG98cYb9i6/WLndNXlDamqqRo8erbJly9qx2uLtdmM5ZswYeXt7q2nTptqwYYO9yy228hrHhQsXatGiRerTp4+ee+45JScna/78+WrdurXWr1+vkJAQe5eff2bYxZIlS8ySzDt27LBqHzFihFmSefny5eYTJ06YJZnfeustO1VZMuRnLDMzM82BgYHme++913zlyhU7VVq85Wccc9OjRw9z2bJlzdevX7/bZZYIBR3LV155xVyvXj3z448/bi5btmxRllrs5XcsT5w4YTabzeazZ8+aJZnHjRtXxJUWb/kZx507d5ovXbpktf3cuXPmKlWqmNu2bVuU5d4xHksVM506dZIknThxwqr98uXLSk9Pt0dJJdbNY/nNN9/owIEDGjdunFxcXHTlyhVlZmbaucKSIbdr8mZ+fn66cuUK1+ht5DSWv//+u2bOnKkZM2aoTBlupufXrWPp5+dnx2pKrpvHsXnz5tkei1aqVEnt2rXToUOH7FFeoRFuipljx45J+vuCumHChAlyc3OTs7OzWrZsqW+++cZe5ZUoN4/lt99+K+nvL1Jt0aKFypYtK1dXV/373//W+fPn7VlmsZfTNXn16lWdO3dOcXFxWrp0qZYsWaLg4GC5uLjYq8wSIaexHD58uO67775sj56Rt5zGEgWXn3FMTExU5cqVi6okm+CfCXaWnJysc+fO6dq1a/rhhx80ceJEubi4qEePHsrMzFTnzp3Vu3dv+fj46Pjx45oxY4a6deumdevWqXv37vYuv1jJayyfe+45SVK/fv3UtWtXRUREaO/evYqMjNSpU6e0detWmUwmO59B8ZDXON4we/ZsRUREWNbvv/9+LVmyxB7lFmu3G8svv/xS33zzjfbu3WvnSou//FyXuL2CjuP333+v7du3a8yYMUVc6Z0h3NjZrRO0atasqY8++kg+Pj6SlG1i3JNPPqmAgACNHDmScHOLvMYyNTVVktSyZUstW7ZMktSnTx+5uroqIiJCMTExJWuy3F10u2tS+nuSe4sWLXT27Fl98cUXSkpK0tWrV4u61GIvr7FMT0/XSy+9pCFDhiggIMBOFZYc+bkucXsFGcczZ87oscceU61atTR69OiiKtEmCDd2NmfOHN1zzz0qU6aMvLy8VK9ePatvQb9VxYoVNXDgQE2dOlV//PGHqlevXoTVFm95jeWNxyX9+/e32uexxx5TRESEtm3bRrj5//JzTdasWVM1a9aU9PeYDh48WCEhITpy5AiPpm6S11jOnDlT586d04QJE+xcZclQ0P9XImf5HcfLly+rR48eunTpkrZu3VriPqKAcGNnrVq1UosWLQq0j6+vryTp/PnzhJub5DWW1apVkyR5eXlZtXt6ekqSLly4cHeLK0EKc00+8sgjev/997VlyxZ16dLlLlVW8uQ2lsnJyZo8ebKee+45paSkKCUlRdLfbwk3m82Ki4uTq6ur5fpE4a5LZJefcUxPT9fDDz+sffv2acOGDQoMDCyi6myH2FsCHT9+XJJUpUoVO1dScjRv3lySlJCQYNX+559/SmIs79SNR1LJycl2rqRkuHDhglJTU/Xmm2+qVq1almXlypW6cuWKatWqpcGDB9u7TPwDZWVlKSwsTDExMVq+fLk6dOhg75IKhTs3xdjZs2ez/dJNSEjQ4sWL1bhxY1WtWtVOlZU8vXr10osvvqglS5YoPDzccht24cKFkqQHHnjAnuWVGDldk5K0aNEimUwmNWvWzA5VlTyenp5avXp1tvZ33nlH27dv18cff8zPN+zi+eef16effqr58+fr4Ycftnc5hUa4KcZGjx6tY8eO6f7771e1atUUFxen+fPn6/Lly5o9e7a9yytRvL299dprr2ns2LHq2rWrQkNDtXfvXr3//vvq37+/WrZsae8SS4QpU6bohx9+UNeuXVWjRg2dP39eK1eu1I4dO/T888/L39/f3iWWCK6urgoNDc3WvmbNGv388885bkPePvzwQ508eVJXrlyRJG3ZskWTJ0+W9PcbMW7MEUPuZs2apblz5yo4OFiurq6WN1/c0Lt37xLzKdqEm2Ksc+fOioqK0pw5c3ThwgWVL19e7du315gxY/gXciGMGTNGFSpU0Lvvvqvhw4dbBR7kT/fu3XXs2DEtXrxYZ8+elbOzsxo3bqwlS5ZowIAB9i4P/2CLFi3S5s2bLeubNm3Spk2bJEn/+te/CDf5sGfPHknS9u3btX379mzbT5w4UWLCjcls5tvuAACAcTChGAAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgAAGArhBgBuMn78eDVp0sTeZQC4A4QbAIUSHh4uk8kkk8kkBwcHeXl56YEHHtDixYuVlZVVoGNFR0erfPnyNqmrY8eOlrqcnZ0VEBCguXPn5nv/UaNGKSYmpkCv6efnp1mzZhWwUgB3C+EGQKF17dpVp0+fVlxcnL7++mvdd999evHFF9WjRw9dv37dbnUNGjRIp0+f1q+//qp+/fpp6NCh+vjjj/O1r5ubmypVqnSXKwRwNxFuABSak5OTvL295ePjo2bNmunVV1/V2rVr9fXXXys6OtrSb8aMGWrUqJHKli0rX19fPffcc0pNTZUkxcbGauDAgUpOTrbccRk/frykv7/puUWLFipXrpy8vb312GOP6cyZM7ety9XVVd7e3qpdu7bGjx+vunXrat26dZKk+Ph49erVS25ubnJ3d1e/fv2UlJRk2ffWx1Lh4eEKDQ3V22+/rapVq6pSpUoaOnSoMjIyJP19p+jkyZN66aWXLPVL0smTJ9WzZ09VqFBBZcuWVcOGDfXVV1/dyXADyCfCDQCb6tSpk4KCgrRq1SpLW6lSpfTOO+/o4MGDWrp0qb777juNHj1aktSmTRvNmjVL7u7uOn36tE6fPq1Ro0ZJkjIyMjRp0iTt3btXa9asUVxcnMLDwwtck4uLi9LT05WVlaVevXrp/Pnz2rx5szZu3Kjjx4/r0UcfzXP/TZs26dixY9q0aZOWLl2q6OhoS3hbtWqVqlevrokTJ1rql6ShQ4cqLS1NW7Zs0f79+zVt2jS5ubkVuHYABVfG3gUAMJ769etr3759lvXhw4db/uzn56fJkydryJAhmjt3rhwdHeXh4SGTySRvb2+r4zz11FOWP9euXVvvvPOOWrZsqdTU1HwFhczMTH388cfat2+fBg8erJiYGO3fv18nTpyQr6+vJOmDDz5Qw4YNtWPHDrVs2TLH41SoUEHvvfeeSpcurfr166t79+6KiYnRoEGDVLFiRZUuXdpyd+mG+Ph49enTR40aNbLUD6BocOcGgM2ZzWbL4xlJ+vbbb3X//ffLx8dH5cqV05NPPqm//vpLV65cyfM4v/zyi3r27KkaNWqoXLly6tChg6S/g0Ne5s6dKzc3N7m4uGjQoEF66aWX9Oyzz+rQoUPy9fW1BBtJCggIUPny5XXo0KFcj9ewYUOVLl3asl61atXbPh574YUXNHnyZLVt21bjxo2zCnsA7i7CDQCbO3TokGrVqiVJiouLU48ePdS4cWOtXLlSv/zyi+bMmSNJSk9Pz/UYly9fVpcuXeTu7q6PPvpIO3bs0OrVq2+7nyQ9/vjj2rNnj06cOKHLly9rxowZKlWq8P+7c3BwsFo3mUy3fUfYM888o+PHj+vJJ5/U/v371aJFC7377ruFrgFA/hFuANjUd999p/3796tPnz6S/r77kpWVpenTp6t169a655579Oeff1rt4+joqMzMTKu2w4cP66+//tLUqVPVrl071a9fP1+TiSXJw8ND/v7+8vHxsQo1DRo00KlTp3Tq1ClL26+//qqLFy8qICCgsKecY/2S5OvrqyFDhmjVqlUaOXKk3n///UK/BoD8I9wAKLS0tDQlJiYqISFBu3bt0htvvKFevXqpR48eCgsLkyT5+/srIyND7777ro4fP64PP/xQUVFRVsfx8/NTamqqYmJidO7cOV25ckU1atSQo6OjZb9169Zp0qRJd1RvSEiIGjVqpMcff1y7du3Szz//rLCwMHXo0EEtWrQo9HH9/Py0ZcsWJSQk6Ny5c5L+nme0YcMGnThxQrt27dKmTZvUoEGDO6ofQP4QbgAU2vr161W1alX5+fmpa9eu2rRpk9555x2tXbvWMkclKChIM2bM0LRp0xQYGKiPPvpIkZGRVsdp06aNhgwZokcffVRVqlTRm2++qSpVqig6OlorVqxQQECApk6dqrfffvuO6jWZTFq7dq0qVKig9u3bKyQkRLVr19ann356R8edOHGi4uLiVKdOHVWpUkXS35OZhw4dqgYNGqhr16665557CvRhggAKz2Q2m832LgIAAMBWuHMDAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAMhXADAAAM5f8BPmRx/EzQ84YAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "linkage_matrix = linkage(distance_matrix, method='complete')\n",
        "\n",
        "dendrogram(linkage_matrix, labels=[f'P{i + 1}' for i in range(len(data))])\n",
        "\n",
        "plt.title('Hierarchical Clustering Dendrogram')\n",
        "plt.xlabel('Data Points')\n",
        "plt.ylabel('Distance')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 511
        },
        "id": "BONIAqQQLICu",
        "outputId": "c7ff316a-9467-492c-f830-f9c5609508ee"
      },
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-33-0ff4b58d6ea0>:1: ClusterWarning: scipy.cluster: The symmetric non-negative hollow observation matrix looks suspiciously like an uncondensed distance matrix\n",
            "  linkage_matrix = linkage(distance_matrix, method='complete')\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "linkage_matrix = linkage(distance_matrix, method='average')\n",
        "\n",
        "dendrogram(linkage_matrix, labels=[f'P{i + 1}' for i in range(len(data))])\n",
        "\n",
        "plt.title('Hierarchical Clustering Dendrogram')\n",
        "plt.xlabel('Data Points')\n",
        "plt.ylabel('Distance')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 511
        },
        "id": "mls-p7R8LZ3F",
        "outputId": "69494dba-2db8-496e-beab-c962b69f47cd"
      },
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-34-7d5190653f9b>:1: ClusterWarning: scipy.cluster: The symmetric non-negative hollow observation matrix looks suspiciously like an uncondensed distance matrix\n",
            "  linkage_matrix = linkage(distance_matrix, method='average')\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "linkage_matrix = linkage(distance_matrix, method='centroid')\n",
        "\n",
        "dendrogram(linkage_matrix, labels=[f'P{i + 1}' for i in range(len(data))])\n",
        "\n",
        "plt.title('Hierarchical Clustering Dendrogram')\n",
        "plt.xlabel('Data Points')\n",
        "plt.ylabel('Distance')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 511
        },
        "id": "PUxlKTMfLfNf",
        "outputId": "b2fc678a-d98f-4468-a57c-fc09f94ee5c3"
      },
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-35-1d05c294bdd7>:1: ClusterWarning: scipy.cluster: The symmetric non-negative hollow observation matrix looks suspiciously like an uncondensed distance matrix\n",
            "  linkage_matrix = linkage(distance_matrix, method='centroid')\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "linkage_matrix = linkage(distance_matrix, method='ward')\n",
        "\n",
        "dendrogram(linkage_matrix, labels=[f'P{i + 1}' for i in range(len(data))])\n",
        "\n",
        "plt.title('Hierarchical Clustering Dendrogram')\n",
        "plt.xlabel('Data Points')\n",
        "plt.ylabel('Distance')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 511
        },
        "id": "qBnc9Do2Li-p",
        "outputId": "3a20d9cb-a1e6-41d2-ddfa-1ee7d073e66b"
      },
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-36-96cb8af3d3b4>:1: ClusterWarning: scipy.cluster: The symmetric non-negative hollow observation matrix looks suspiciously like an uncondensed distance matrix\n",
            "  linkage_matrix = linkage(distance_matrix, method='ward')\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "linkage_matrix = linkage(distance_matrix, method='median')\n",
        "\n",
        "dendrogram(linkage_matrix, labels=[f'P{i + 1}' for i in range(len(data))])\n",
        "\n",
        "plt.title('Hierarchical Clustering Dendrogram')\n",
        "plt.xlabel('Data Points')\n",
        "plt.ylabel('Distance')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 511
        },
        "id": "Au67myxcMOca",
        "outputId": "d12d2e80-9de4-4a9f-daa5-f7c0a4f46e42"
      },
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-37-c96a84b0fb69>:1: ClusterWarning: scipy.cluster: The symmetric non-negative hollow observation matrix looks suspiciously like an uncondensed distance matrix\n",
            "  linkage_matrix = linkage(distance_matrix, method='median')\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}