hierarchical_clustering.ipynb

{
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  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "hierarchical clustering.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyPhOik5SbkS4KrYK6sMRuCA"
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "##Hierarchical Clustering\n",
        "There are two types of hierarchical clustering: Agglomerative and Divisive. In the former, data points are clustered using a bottom-up approach starting with individual data points, while in the latter top-down approach is followed where all the data points are treated as one big cluster and the clustering process involves dividing the one big cluster into several small clusters."
      ],
      "metadata": {
        "id": "u3OFYh70gmUl"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "####Steps to Perform Hierarchical Clustering\n",
        "Following are the steps involved in agglomerative clustering:\n",
        "\n",
        "- At the start, treat each data point as one cluster. Therefore, the number of clusters at the start will be K, while K is an integer representing the number of data points.\n",
        "- Form a cluster by joining the two closest data points resulting in K-1 clusters.\n",
        "- Form more clusters by joining the two closest clusters resulting in K-2 clusters.\n",
        "- Repeat the above three steps until one big cluster is formed.\n",
        "- Once single cluster is formed, dendrograms are used to divide into multiple clusters depending upon the problem. We will study the concept of dendrogram in detail in an upcoming section.\n",
        "\n",
        "There are different ways to find distance between the clusters. The distance itself can be Euclidean or Manhattan distance. Following are some of the options to measure distance between two clusters:\n",
        "\n",
        "- Measure the distance between the closes points of two clusters.\n",
        "- Measure the distance between the farthest points of two clusters.\n",
        "- Measure the distance between all possible combination of points between the two clusters and take the mean."
      ],
      "metadata": {
        "id": "6-DsbGzkgtY6"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "057FHgxpgiqZ"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "\n",
        "X = np.array([[5,3],\n",
        "    [10,15],\n",
        "    [15,12],\n",
        "    [24,10],\n",
        "    [30,30],\n",
        "    [85,70],\n",
        "    [71,80],\n",
        "    [60,78],\n",
        "    [70,55],\n",
        "    [80,91],])"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "labels = range(1, 11)\n",
        "plt.figure(figsize=(10, 7))\n",
        "plt.subplots_adjust(bottom=0.1)\n",
        "plt.scatter(X[:,0],X[:,1], label='True Position')\n",
        "\n",
        "for label, x, y in zip(labels, X[:, 0], X[:, 1]):\n",
        "    plt.annotate(\n",
        "        label,\n",
        "        xy=(x, y), xytext=(-3, 3),\n",
        "        textcoords='offset points', ha='right', va='bottom')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 441
        },
        "id": "_v1xeKIFhLKc",
        "outputId": "9d0ae7ac-cc44-488c-9d1c-a7000fa665be"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x504 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.cluster.hierarchy import dendrogram, linkage\n",
        "from matplotlib import pyplot as plt\n",
        "\n",
        "linked = linkage(X, 'single')\n",
        "\n",
        "labelList = range(1, 11)\n",
        "\n",
        "plt.figure(figsize=(10, 7))\n",
        "dendrogram(linked,\n",
        "            orientation='top',\n",
        "            labels=labelList,\n",
        "            distance_sort='descending',\n",
        "            show_leaf_counts=True)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 431
        },
        "id": "L-LaBjJDhmJI",
        "outputId": "79f0587d-8503-4145-f9bd-e9fc34ddea01"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x504 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "J1P6HQFzhttw"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}