{
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "**Concept: Hierarchical Clustering**\n",
        "\n",
        "Hierarchical clustering is a method of cluster analysis that seeks to build a hierarchy of clusters.  There are two main types:\n",
        "\n",
        "*   **Agglomerative (bottom-up):** This is the more common type. It starts with each data point as its own cluster and iteratively merges the closest pairs of clusters until only one cluster remains.\n",
        "*   **Divisive (top-down):** This approach starts with all data points in one cluster and recursively splits it into smaller clusters.\n",
        "\n",
        "We'll focus on **agglomerative hierarchical clustering** in this explanation.\n",
        "\n",
        "**Steps Involved (Agglomerative):**\n",
        "\n",
        "1.  **Initialization:** Each data point is treated as an individual cluster.\n",
        "2.  **Distance Calculation:** Calculate the distance between each pair of clusters. Common distance metrics include:\n",
        "    *   Euclidean distance\n",
        "    *   Manhattan distance\n",
        "    *   Cosine similarity\n",
        "3.  **Cluster Merging:** Merge the two closest clusters based on a linkage criterion. Linkage criteria determine the distance between sets of observations as a function of the pairwise distances between observations. Common linkage criteria are:\n",
        "    *   **Single Linkage:** The distance between two clusters is the shortest distance between any point in one cluster and any point in the other cluster.\n",
        "    *   **Complete Linkage:** The distance between two clusters is the longest distance between any point in one cluster and any point in the other cluster.\n",
        "    *   **Average Linkage:** The distance between two clusters is the average distance between all pairs of points from the two clusters.\n",
        "    *   **Ward Linkage:** Minimizes the total within-cluster variance. At each step, the pair of clusters with the smallest increase in total within-cluster variance after merging is chosen.\n",
        "4.  **Iteration:** Repeat steps 2 and 3 until all data points are merged into a single cluster.\n",
        "5.  **Dendrogram:** The result is often visualized using a dendrogram, a tree-like diagram that shows the hierarchy of cluster merges and the distances at which they occurred.\n",
        "\n",
        "**Code and Explanation**\n",
        "\n",
        "**1. Import Libraries**"
      ],
      "metadata": {
        "id": "QHC-YRJjcLpL"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.cluster.hierarchy import dendrogram, linkage\n",
        "from sklearn.cluster import AgglomerativeClustering\n",
        "from sklearn.datasets import make_blobs"
      ],
      "outputs": [],
      "execution_count": null,
      "metadata": {
        "id": "HkuPX9K_cLpO"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**2. Generate Sample Data**\n",
        "\n",
        "We'll use `make_blobs` from `scikit-learn` to create some synthetic data for demonstration."
      ],
      "metadata": {
        "id": "ciumtb84cLpP"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "X, y = make_blobs(n_samples=15, centers=4, random_state=42, cluster_std=1.5)\n",
        "\n",
        "# Visualize the generated data\n",
        "plt.scatter(X[:, 0], X[:, 1], s=50)\n",
        "plt.title(\"Generated Data Points\")\n",
        "plt.xlabel(\"Feature 1\")\n",
        "plt.ylabel(\"Feature 2\")\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ],
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "MV68CN4mcLpP",
        "outputId": "666fa082-f7e6-457a-b16b-688c7bfa2f77"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**3. Calculate the Linkage Matrix**\n",
        "\n",
        "We'll use the `linkage` function from `scipy.cluster.hierarchy` to compute the linkage matrix, which encodes the hierarchical clustering."
      ],
      "metadata": {
        "id": "2oJXVHzScLpP"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Calculate the linkage matrix using 'ward' linkage (you can try other methods)\n",
        "Z = linkage(X, method='ward')"
      ],
      "outputs": [],
      "execution_count": null,
      "metadata": {
        "id": "A68zt0imcLpQ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**4. Plot the Dendrogram**"
      ],
      "metadata": {
        "id": "J1XcR-oicLpQ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Plot the dendrogram\n",
        "plt.figure(figsize=(10, 5))\n",
        "plt.title(\"Hierarchical Clustering Dendrogram\")\n",
        "plt.xlabel(\"Data Point Index\")\n",
        "plt.ylabel(\"Distance\")\n",
        "dendrogram(Z, leaf_rotation=90., leaf_font_size=8.)\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ],
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "6SaWr4YOcLpQ",
        "outputId": "a625b0a6-9163-4dec-c3c0-fe39305aa920"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Explanation of the Dendrogram:**\n",
        "\n",
        "*   **X-axis:** Represents the data points (initially as individual clusters).\n",
        "*   **Y-axis:** Represents the distance at which clusters are merged.\n",
        "*   **Branches:** Show how clusters are merged. The height of a branch indicates the distance between the merged clusters.\n",
        "\n",
        "**5. Perform Agglomerative Clustering**\n",
        "\n",
        "Now, we'll use `AgglomerativeClustering` from `scikit-learn` to actually perform the clustering and assign cluster labels to our data points."
      ],
      "metadata": {
        "id": "ZjutRgWdcLpQ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Perform agglomerative clustering with a specified number of clusters (e.g., 3)\n",
        "cluster = AgglomerativeClustering(n_clusters=4, linkage='ward') # Remove affinity argument\n",
        "labels = cluster.fit_predict(X)"
      ],
      "outputs": [],
      "execution_count": null,
      "metadata": {
        "id": "oKRHCof5cLpR"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**6. Visualize the Clusters**"
      ],
      "metadata": {
        "id": "eOkAoge9cLpR"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Visualize the clustered data\n",
        "plt.scatter(X[:, 0], X[:, 1], c=labels, s=50, cmap='viridis')\n",
        "plt.title(\"Data Points After Agglomerative Clustering\")\n",
        "plt.xlabel(\"Feature 1\")\n",
        "plt.ylabel(\"Feature 2\")\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ],
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "hx5eWhERcLpR",
        "outputId": "01b91e06-0a4d-4ba7-e110-9fcbef7a1073"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Explanation of the Cluster Visualization:**\n",
        "\n",
        "*   Each color represents a different cluster.\n",
        "*   The points with the same color belong to the same cluster.\n",
        "\n",
        "**Determining the Number of Clusters**\n",
        "\n",
        "You can use the dendrogram to help you decide on the number of clusters. Look for large vertical distances where merges happen. These distances suggest a natural separation between clusters.\n",
        "\n",
        "**Example using other linkage method**"
      ],
      "metadata": {
        "id": "nGfdkyHscLpR"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#Calculate linkage matrix using \"complete\" linkage\n",
        "Z_complete = linkage(X, method='complete')\n",
        "\n",
        "#Plot the dendrogram for \"complete\" linkage\n",
        "plt.figure(figsize=(10,5))\n",
        "plt.title(\"Hierarchical clustering with complete linkage\")\n",
        "plt.xlabel(\"Data point index\")\n",
        "plt.ylabel(\"Distance\")\n",
        "dendrogram(Z_complete, leaf_rotation=90., leaf_font_size=8.)\n",
        "plt.show()\n",
        "\n",
        "#Perform aglomerative clustering with \"complete\" linkage\n",
        "cluster_complete = AgglomerativeClustering(n_clusters=4, linkage='complete')  # Remove affinity='euclidean'\n",
        "labels_complete = cluster_complete.fit_predict(X)\n",
        "\n",
        "#Visualize the clusters for \"complete\" linkage\n",
        "plt.scatter(X[:, 0], X[:, 1], c=labels_complete, s=50, cmap='viridis')\n",
        "plt.title(\"Data point after aglomerative clustering (complete linkage)\")\n",
        "plt.xlabel(\"Feature 1\")\n",
        "plt.ylabel(\"Feature 2\")\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ],
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 942
        },
        "id": "5tvdNSPCcLpS",
        "outputId": "929d3242-5dfe-438e-f398-b78ee2512e55"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "In this example, we used the `complete` linkage method instead of `ward`. The dendrogram and cluster visualization demonstrate the difference in clustering results when using different linkage methods.\n",
        "\n",
        "**Conclusion**\n",
        "\n",
        "This step-by-step guide, along with the code and visualizations, should provide a solid foundation for your students to understand hierarchical clustering. Encourage them to experiment with different linkage methods, distance metrics, and datasets to get a better feel for how the algorithm works in practice. Remember to relate these concepts back to real-world examples to make them more relatable. Please let me know if you have any other questions."
      ],
      "metadata": {
        "id": "-AQMvj_mcLpS"
      }
    }
  ],
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}