Agglomerative_Hierarchical_Clustering.ipynb

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      "authorship_tag": "ABX9TyMBmDEpzi0MpXLTdpCHufaw",
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    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
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    "language_info": {
      "name": "python"
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
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      "source": [
        "<a href=\"https://colab.research.google.com/github/SampMark/Machine-Learn/blob/main/Agglomerative_Hierarchical_Clustering.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# **Agrupamento Hierárquico Aglomerativo** (_Agglomerative Hierarchical Clustering_)\n",
        "\n",
        "\n",
        "O Agrupamento Hierárquico (_Hierarchical Clustering_) é um método de aprendizado de máquina não supervisionado que organiza os dados em uma hierarquia de clusters, representada visualmente por meio de um dendrograma. Essa abordagem é particularmente útil para analisar dados e identificar padrões, sem a necessidade de especificar previamente o número de clusters desejados.\n",
        "\n",
        "Existem dois tipos principais de Agrupamento Hierárquico:\n",
        "\n",
        "* **Divisivo** (_top-down_): Este método inicia com todos os pontos de dados agrupados em um único cluster e, de forma progressiva, o divide em clusters menores. O processo continua até que cada ponto de dado seja tratado como um cluster individual.\n",
        "\n",
        "* **Aglomerativo** (_bottom-up_): neste caso, cada ponto de dado começa como um cluster individual. Os clusters são então mesclados iterativamente, formando grupos progressivamente maiores, até que todos os pontos pertençam a um único cluster.\n",
        "\n",
        "## **Etapas do Algoritmo Aglomerativo**\n",
        "\n",
        "1. **Inicialização**: cada ponto de dado é tratado como um cluster individual.\n",
        "\n",
        "2. **Cálculo da Matriz de Distâncias/Proximidade**: uma matriz é criada para armazenar as distâncias entre todos os pares de clusters.\n",
        "\n",
        "3. **Combinação de Clusters**: ocorre a mesclagem dos dois clusters mais próximos, com base na matriz de proximidade, que são combinados em um novo cluster.\n",
        "\n",
        "4. **Atualização da Matriz de Distâncias**: a matriz de distâncias/proximidade é recalculada para refletir as distâncias entre o novo cluster formado e os clusters restantes.\n",
        "\n",
        "5. **Repetição**: as etapas de mesclagem e atualização são repetidas iterativamente até que o número desejado de clusters seja alcançado ou até que todos os pontos estejam agrupados em um único cluster.\n",
        "\n",
        "Essa sequência de etapas constrói uma hierarquia de agrupamentos, que pode ser visualizada em um dendrograma, permitindo explorar a estrutura dos dados em diferentes níveis.\n",
        "\n",
        "## **Aplicações e Considerações**\n",
        "\n",
        "O Agrupamento Hierárquico Aglomerativo é amplamente utilizado em diversas áreas, incluindo:\n",
        "* **Biologia**: análise de genes e classificar espécies com características similares.\n",
        "* **Marketing**: para segmentar clientes e personalizar campanhas de marketing.\n",
        "* **Redução de Dimensionalidade**: identificação de padrões em grandes conjuntos de dados, por exmplo, para análise de imagens e reconhecimento de padrões.\n",
        "\n",
        "Uma vantagem significativa deste método é não ser necessário especificar previamente o número de clusters; a hierarquia completa permite ao analista escolher o nível de granularidade apropriado.\n",
        "\n",
        "Entretanto, pode ser computacionalmente intensivo para conjuntos de dados muito grandes, com complexidade de tempo geralmente em torno de O(n³) e requisitos de memória de Ω(n²)."
      ],
      "metadata": {
        "id": "raz5KXvwtQKv"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Instalando e importando as bibliotecas necessárias**\n",
        "\n",
        "---\n",
        "\n"
      ],
      "metadata": {
        "id": "ddii_Phdvolu"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "!pip install matplotlib pandas numpy scipy scikit-learn"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "IQLNqtuIp-cB",
        "outputId": "85e6323a-c04b-4d2b-9ad7-e21e944794e6"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Requirement already satisfied: matplotlib in /usr/local/lib/python3.10/dist-packages (3.10.0)\n",
            "Requirement already satisfied: pandas in /usr/local/lib/python3.10/dist-packages (2.2.2)\n",
            "Requirement already satisfied: numpy in /usr/local/lib/python3.10/dist-packages (1.26.4)\n",
            "Requirement already satisfied: scipy in /usr/local/lib/python3.10/dist-packages (1.13.1)\n",
            "Requirement already satisfied: scikit-learn in /usr/local/lib/python3.10/dist-packages (1.6.0)\n",
            "Requirement already satisfied: contourpy>=1.0.1 in /usr/local/lib/python3.10/dist-packages (from matplotlib) (1.3.1)\n",
            "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.10/dist-packages (from matplotlib) (0.12.1)\n",
            "Requirement already satisfied: fonttools>=4.22.0 in /usr/local/lib/python3.10/dist-packages (from matplotlib) (4.55.3)\n",
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            "Requirement already satisfied: packaging>=20.0 in /usr/local/lib/python3.10/dist-packages (from matplotlib) (24.2)\n",
            "Requirement already satisfied: pillow>=8 in /usr/local/lib/python3.10/dist-packages (from matplotlib) (11.1.0)\n",
            "Requirement already satisfied: pyparsing>=2.3.1 in /usr/local/lib/python3.10/dist-packages (from matplotlib) (3.2.1)\n",
            "Requirement already satisfied: python-dateutil>=2.7 in /usr/local/lib/python3.10/dist-packages (from matplotlib) (2.8.2)\n",
            "Requirement already satisfied: pytz>=2020.1 in /usr/local/lib/python3.10/dist-packages (from pandas) (2024.2)\n",
            "Requirement already satisfied: tzdata>=2022.7 in /usr/local/lib/python3.10/dist-packages (from pandas) (2024.2)\n",
            "Requirement already satisfied: joblib>=1.2.0 in /usr/local/lib/python3.10/dist-packages (from scikit-learn) (1.4.2)\n",
            "Requirement already satisfied: threadpoolctl>=3.1.0 in /usr/local/lib/python3.10/dist-packages (from scikit-learn) (3.5.0)\n",
            "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.10/dist-packages (from python-dateutil>=2.7->matplotlib) (1.17.0)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "from scipy.cluster import hierarchy\n",
        "from scipy.spatial import distance_matrix\n",
        "from matplotlib import pyplot as plt\n",
        "from sklearn.cluster import AgglomerativeClustering\n",
        "from sklearn.datasets import make_blobs\n",
        "from sklearn.metrics import silhouette_score"
      ],
      "metadata": {
        "id": "RwOCxy_op7kn"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Gerando um DataSet aleatório com a Classe `make_blobs`**\n",
        "\n",
        "---\n",
        "Configuração inicial dos parâmetros em make_blobs:\n",
        "\n",
        "* `n_samples`: número total de pontos divididos igualmente entre os clusters (número entre 10 a 1500).\n",
        "\n",
        "* `centers`: locais fixos dos centros (ex. `centers = [[1,1], [2,5]]`) na  matriz de coordenadas (x, y) para gerar os centros ou número de centros a serem gerados (opção de 1 a 10 centros).\n",
        "\n",
        "* `cluster_std`: desvio padrão dos clusters, quanto maior o número, mais distantes os clusters (um número entre 0,5 e 1,5)."
      ],
      "metadata": {
        "id": "0DmmaFKpv9HA"
      }
    },
    {
      "cell_type": "markdown",
      "source": [],
      "metadata": {
        "id": "mK5rZLHUwPcr"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 44,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 569
        },
        "id": "yp5qJFx5p4ns",
        "outputId": "e92145b9-5125-4f1c-f4f2-67ba54d474be"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ],
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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# Configurações iniciais para make_blobs\n",
        "n_samples = 50\n",
        "centers = [[4, 4], [-2, -1], [1, 1], [10, 4]]\n",
        "cluster_std = 0.9\n",
        "\n",
        "# Gerando os dados\n",
        "X1, y1 = make_blobs(n_samples=n_samples, centers=centers, cluster_std=cluster_std, random_state=42)\n",
        "\n",
        "# Visualização dos dados aleatórios\n",
        "plt.figure(figsize=(8, 6))\n",
        "plt.scatter(X1[:, 0], X1[:, 1], c='purple') # cmap='viridis', marker='o', edgecolor='k'\n",
        "plt.title('Clusters gerados usando a Classe make_blobs', fontsize=14)\n",
        "plt.xlabel('Feature 1', fontsize=12)\n",
        "plt.ylabel('Feature 2', fontsize=12)\n",
        "# plt.grid(True, linestyle='--', alpha=0.7)\n",
        "# plt.colorbar(label='Clusters reais')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Modelando o Agrupamento Hierárquico Aglomerativo**\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "Vamos iniciar o processo de agrupamento com os pontos de dados aleatórios sugeridos acima, utilizando a classe `AgglomerativeClustering`, que tem como parâmetros:\n",
        "\n",
        "* `n_clusters`: define o número de clusters que desejamos formar e, consequentemente, o número de centroides a serem gerados.\n",
        "\n",
        "* `linkage`: determina o critério de ligação que será usado, o qual define a medida de distância utilizada entre os conjuntos de observações. O algoritmo irá mesclar os pares de clusters que minimizam essa distância.\n",
        "\n",
        "Antes, é necessário esclarecer melhor sobre os critérios de ligação existentes no Scikit-Learn, disponíveis para o critério `linkage`.\n",
        "\n",
        "### **Escolha dos Critério de Ligação**\n",
        "\n",
        "Os métodos de ligação definem como calcular a distância entre dois clusters durante o processo de agrupamento. Cada método possui características específicas que influenciam a forma como os clusters são combinados.\n",
        "\n",
        "* **Ligação Única** (`linkage='single'`): a distância entre dois clusters é definida como a menor distância entre quaisquer dois pontos nos clusters.\n",
        "  * Tende a formar clusters em cadeias, conectando pontos próximos sequencialmente.\n",
        "  É mais sensível a ruídos e outliers.\n",
        "\n",
        "* **Ligação Completa** (`linkage='complete'`): a distância entre dois clusters é definida como a maior distância entre quaisquer dois pontos nos clusters.\n",
        "  * Gera clusters mais compactos e esféricos, porém é menos sensível a _outliers_ em comparação à ligação única.\n",
        "\n",
        "* **Ligação Média** (`linkage='average'`): a distância entre dois clusters é definida como a distância média entre todos os pares de pontos nos clusters.\n",
        "  * Considera a distribuição geral dos pontos no cluster, sendo um bom equilíbrio entre os métodos de ligação única e completa.\n",
        "\n",
        "* **Ligação Centróide** (`linkage='ward'`): a distância entre dois clusters é a distância entre os centróides (médias dos pontos) de cada cluster. Esse método minimiza a soma dos quadrados das diferenças internas ao cluster.\n",
        "  * É mais eficiente computacionalmente, mas pode gerar resultados inconsistentes, como inversão de hierarquia."
      ],
      "metadata": {
        "id": "vDKRFmRuwe60"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Configuração do agrupamento hierárquico\n",
        "n_clusters = 4  # Número de clusters desejados\n",
        "linkage_method = 'average'  # Método de ligação entre clusters\n",
        "\n",
        "# Criação do modelo\n",
        "agglom = AgglomerativeClustering(n_clusters=n_clusters, linkage=linkage_method)\n",
        "\n",
        "# Ajustando o modelo\n",
        "agglom.fit(X1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 80
        },
        "id": "SiDWyoAlqE9O",
        "outputId": "ff240aba-4a6b-451a-b3ce-88ca1e533390"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "AgglomerativeClustering(linkage='average', n_clusters=4)"
            ],
            "text/html": [
              "<style>#sk-container-id-3 {\n",
              "  /* Definition of color scheme common for light and dark mode */\n",
              "  --sklearn-color-text: #000;\n",
              "  --sklearn-color-text-muted: #666;\n",
              "  --sklearn-color-line: gray;\n",
              "  /* Definition of color scheme for unfitted estimators */\n",
              "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
              "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
              "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
              "  --sklearn-color-unfitted-level-3: chocolate;\n",
              "  /* Definition of color scheme for fitted estimators */\n",
              "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
              "  --sklearn-color-fitted-level-1: #d4ebff;\n",
              "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
              "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
              "\n",
              "  /* Specific color for light theme */\n",
              "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
              "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
              "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
              "  --sklearn-color-icon: #696969;\n",
              "\n",
              "  @media (prefers-color-scheme: dark) {\n",
              "    /* Redefinition of color scheme for dark theme */\n",
              "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
              "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
              "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
              "    --sklearn-color-icon: #878787;\n",
              "  }\n",
              "}\n",
              "\n",
              "#sk-container-id-3 {\n",
              "  color: var(--sklearn-color-text);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 pre {\n",
              "  padding: 0;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 input.sk-hidden--visually {\n",
              "  border: 0;\n",
              "  clip: rect(1px 1px 1px 1px);\n",
              "  clip: rect(1px, 1px, 1px, 1px);\n",
              "  height: 1px;\n",
              "  margin: -1px;\n",
              "  overflow: hidden;\n",
              "  padding: 0;\n",
              "  position: absolute;\n",
              "  width: 1px;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-dashed-wrapped {\n",
              "  border: 1px dashed var(--sklearn-color-line);\n",
              "  margin: 0 0.4em 0.5em 0.4em;\n",
              "  box-sizing: border-box;\n",
              "  padding-bottom: 0.4em;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-container {\n",
              "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
              "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
              "     so we also need the `!important` here to be able to override the\n",
              "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
              "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
              "  display: inline-block !important;\n",
              "  position: relative;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-text-repr-fallback {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              "div.sk-parallel-item,\n",
              "div.sk-serial,\n",
              "div.sk-item {\n",
              "  /* draw centered vertical line to link estimators */\n",
              "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
              "  background-size: 2px 100%;\n",
              "  background-repeat: no-repeat;\n",
              "  background-position: center center;\n",
              "}\n",
              "\n",
              "/* Parallel-specific style estimator block */\n",
              "\n",
              "#sk-container-id-3 div.sk-parallel-item::after {\n",
              "  content: \"\";\n",
              "  width: 100%;\n",
              "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
              "  flex-grow: 1;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-parallel {\n",
              "  display: flex;\n",
              "  align-items: stretch;\n",
              "  justify-content: center;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  position: relative;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-parallel-item {\n",
              "  display: flex;\n",
              "  flex-direction: column;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-parallel-item:first-child::after {\n",
              "  align-self: flex-end;\n",
              "  width: 50%;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-parallel-item:last-child::after {\n",
              "  align-self: flex-start;\n",
              "  width: 50%;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-parallel-item:only-child::after {\n",
              "  width: 0;\n",
              "}\n",
              "\n",
              "/* Serial-specific style estimator block */\n",
              "\n",
              "#sk-container-id-3 div.sk-serial {\n",
              "  display: flex;\n",
              "  flex-direction: column;\n",
              "  align-items: center;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  padding-right: 1em;\n",
              "  padding-left: 1em;\n",
              "}\n",
              "\n",
              "\n",
              "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
              "clickable and can be expanded/collapsed.\n",
              "- Pipeline and ColumnTransformer use this feature and define the default style\n",
              "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
              "*/\n",
              "\n",
              "/* Pipeline and ColumnTransformer style (default) */\n",
              "\n",
              "#sk-container-id-3 div.sk-toggleable {\n",
              "  /* Default theme specific background. It is overwritten whether we have a\n",
              "  specific estimator or a Pipeline/ColumnTransformer */\n",
              "  background-color: var(--sklearn-color-background);\n",
              "}\n",
              "\n",
              "/* Toggleable label */\n",
              "#sk-container-id-3 label.sk-toggleable__label {\n",
              "  cursor: pointer;\n",
              "  display: flex;\n",
              "  width: 100%;\n",
              "  margin-bottom: 0;\n",
              "  padding: 0.5em;\n",
              "  box-sizing: border-box;\n",
              "  text-align: center;\n",
              "  align-items: start;\n",
              "  justify-content: space-between;\n",
              "  gap: 0.5em;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 label.sk-toggleable__label .caption {\n",
              "  font-size: 0.6rem;\n",
              "  font-weight: lighter;\n",
              "  color: var(--sklearn-color-text-muted);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 label.sk-toggleable__label-arrow:before {\n",
              "  /* Arrow on the left of the label */\n",
              "  content: \"▸\";\n",
              "  float: left;\n",
              "  margin-right: 0.25em;\n",
              "  color: var(--sklearn-color-icon);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 label.sk-toggleable__label-arrow:hover:before {\n",
              "  color: var(--sklearn-color-text);\n",
              "}\n",
              "\n",
              "/* Toggleable content - dropdown */\n",
              "\n",
              "#sk-container-id-3 div.sk-toggleable__content {\n",
              "  max-height: 0;\n",
              "  max-width: 0;\n",
              "  overflow: hidden;\n",
              "  text-align: left;\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-toggleable__content.fitted {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-toggleable__content pre {\n",
              "  margin: 0.2em;\n",
              "  border-radius: 0.25em;\n",
              "  color: var(--sklearn-color-text);\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-toggleable__content.fitted pre {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
              "  /* Expand drop-down */\n",
              "  max-height: 200px;\n",
              "  max-width: 100%;\n",
              "  overflow: auto;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
              "  content: \"▾\";\n",
              "}\n",
              "\n",
              "/* Pipeline/ColumnTransformer-specific style */\n",
              "\n",
              "#sk-container-id-3 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Estimator-specific style */\n",
              "\n",
              "/* Colorize estimator box */\n",
              "#sk-container-id-3 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-label label.sk-toggleable__label,\n",
              "#sk-container-id-3 div.sk-label label {\n",
              "  /* The background is the default theme color */\n",
              "  color: var(--sklearn-color-text-on-default-background);\n",
              "}\n",
              "\n",
              "/* On hover, darken the color of the background */\n",
              "#sk-container-id-3 div.sk-label:hover label.sk-toggleable__label {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "/* Label box, darken color on hover, fitted */\n",
              "#sk-container-id-3 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Estimator label */\n",
              "\n",
              "#sk-container-id-3 div.sk-label label {\n",
              "  font-family: monospace;\n",
              "  font-weight: bold;\n",
              "  display: inline-block;\n",
              "  line-height: 1.2em;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-label-container {\n",
              "  text-align: center;\n",
              "}\n",
              "\n",
              "/* Estimator-specific */\n",
              "#sk-container-id-3 div.sk-estimator {\n",
              "  font-family: monospace;\n",
              "  border: 1px dotted var(--sklearn-color-border-box);\n",
              "  border-radius: 0.25em;\n",
              "  box-sizing: border-box;\n",
              "  margin-bottom: 0.5em;\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-estimator.fitted {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "/* on hover */\n",
              "#sk-container-id-3 div.sk-estimator:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-estimator.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
              "\n",
              "/* Common style for \"i\" and \"?\" */\n",
              "\n",
              ".sk-estimator-doc-link,\n",
              "a:link.sk-estimator-doc-link,\n",
              "a:visited.sk-estimator-doc-link {\n",
              "  float: right;\n",
              "  font-size: smaller;\n",
              "  line-height: 1em;\n",
              "  font-family: monospace;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  border-radius: 1em;\n",
              "  height: 1em;\n",
              "  width: 1em;\n",
              "  text-decoration: none !important;\n",
              "  margin-left: 0.5em;\n",
              "  text-align: center;\n",
              "  /* unfitted */\n",
              "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-unfitted-level-1);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link.fitted,\n",
              "a:link.sk-estimator-doc-link.fitted,\n",
              "a:visited.sk-estimator-doc-link.fitted {\n",
              "  /* fitted */\n",
              "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-fitted-level-1);\n",
              "}\n",
              "\n",
              "/* On hover */\n",
              "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
              ".sk-estimator-doc-link:hover,\n",
              "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
              ".sk-estimator-doc-link:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
              ".sk-estimator-doc-link.fitted:hover,\n",
              "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
              ".sk-estimator-doc-link.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "/* Span, style for the box shown on hovering the info icon */\n",
              ".sk-estimator-doc-link span {\n",
              "  display: none;\n",
              "  z-index: 9999;\n",
              "  position: relative;\n",
              "  font-weight: normal;\n",
              "  right: .2ex;\n",
              "  padding: .5ex;\n",
              "  margin: .5ex;\n",
              "  width: min-content;\n",
              "  min-width: 20ex;\n",
              "  max-width: 50ex;\n",
              "  color: var(--sklearn-color-text);\n",
              "  box-shadow: 2pt 2pt 4pt #999;\n",
              "  /* unfitted */\n",
              "  background: var(--sklearn-color-unfitted-level-0);\n",
              "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link.fitted span {\n",
              "  /* fitted */\n",
              "  background: var(--sklearn-color-fitted-level-0);\n",
              "  border: var(--sklearn-color-fitted-level-3);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link:hover span {\n",
              "  display: block;\n",
              "}\n",
              "\n",
              "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
              "\n",
              "#sk-container-id-3 a.estimator_doc_link {\n",
              "  float: right;\n",
              "  font-size: 1rem;\n",
              "  line-height: 1em;\n",
              "  font-family: monospace;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  border-radius: 1rem;\n",
              "  height: 1rem;\n",
              "  width: 1rem;\n",
              "  text-decoration: none;\n",
              "  /* unfitted */\n",
              "  color: var(--sklearn-color-unfitted-level-1);\n",
              "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 a.estimator_doc_link.fitted {\n",
              "  /* fitted */\n",
              "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-fitted-level-1);\n",
              "}\n",
              "\n",
              "/* On hover */\n",
              "#sk-container-id-3 a.estimator_doc_link:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 a.estimator_doc_link.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-3);\n",
              "}\n",
              "</style><div id=\"sk-container-id-3\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>AgglomerativeClustering(linkage=&#x27;average&#x27;, n_clusters=4)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-3\" type=\"checkbox\" checked><label for=\"sk-estimator-id-3\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow\"><div><div>AgglomerativeClustering</div></div><div><a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.6/modules/generated/sklearn.cluster.AgglomerativeClustering.html\">?<span>Documentation for AgglomerativeClustering</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></div></label><div class=\"sk-toggleable__content fitted\"><pre>AgglomerativeClustering(linkage=&#x27;average&#x27;, n_clusters=4)</pre></div> </div></div></div></div>"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Obtenção dos rótulos dos clusters\n",
        "cluster_labels = agglom.labels_\n",
        "print(f\"Rótulos dos clusters: {cluster_labels}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "yMfpxg-JqITf",
        "outputId": "1550ca5c-7038-40eb-df33-170bde1969d5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Rótulos dos clusters: [2 1 2 1 1 3 1 3 3 3 2 3 3 2 2 0 2 0 0 0 1 1 1 3 2 0 2 0 1 1 2 2 0 0 0 2 1\n",
            " 1 3 1 3 3 0 2 2 3 3 0 0 1]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Visualizando os clusters gerados\n",
        "plt.figure(figsize=(8, 6))\n",
        "plt.scatter(X1[:, 0], X1[:, 1], c=cluster_labels, cmap='viridis', marker='o', edgecolor='k')\n",
        "plt.title(f'Agglomerative Clustering (linkage={linkage_method})', fontsize=14)\n",
        "plt.xlabel('Feature 1', fontsize=10)\n",
        "plt.ylabel('Feature 2', fontsize=10)\n",
        "plt.grid(True, linestyle='--', alpha=0.7)\n",
        "plt.colorbar(label='Clusters')\n",
        "plt.show()\n",
        "\n",
        "# Avaliação com coeficiente de silhueta\n",
        "silhouette_avg = silhouette_score(X1, cluster_labels)\n",
        "print(f\"Coeficiente de silhueta: {silhouette_avg:.2f}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 582
        },
        "id": "0Emfsq5SqKT1",
        "outputId": "ccadcfef-aa6a-48d8-a54e-2bd715772573"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Coeficiente de silhueta: 0.64\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Análise do Coeficiente de Silhueta**\n",
        "\n",
        "Valores de silhueta próximos de 1 indicam clusters bem definidos, valores próximos de 0 indicam sobreposição, e valores negativos indicam pontos atribuídos ao cluster errado."
      ],
      "metadata": {
        "id": "2y31hMHj788c"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Calculando a matriz de distância entre os pontos de dados**\n",
        "\n",
        "\n",
        "Para construir o dendrograma, é necessário primeiro calcular a matriz de distância entre os pontos de dados, com a função `distance_matrix . A matriz irá armazenar as distâncias entre cada par de pontos em um conjunto de dados."
      ],
      "metadata": {
        "id": "NrZ69JNl4hKg"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Calcula a matriz de distância entre os pontos em X1\n",
        "dist_matrix = distance_matrix(X1, X1)\n",
        "\n",
        "# Imprime a matriz de distância\n",
        "print(dist_matrix)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jCVkYVpkqpvJ",
        "outputId": "a7b44f56-875c-48a5-a644-b4475a820218"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.         7.82132806 2.31835717 ... 5.25385395 5.02733535 7.72211735]\n",
            " [7.82132806 0.         8.31836714 ... 2.58756892 3.05368095 0.45960388]\n",
            " [2.31835717 8.31836714 0.         ... 5.79088258 5.26981874 8.09654389]\n",
            " ...\n",
            " [5.25385395 2.58756892 5.79088258 ... 0.         0.78621733 2.46873047]\n",
            " [5.02733535 3.05368095 5.26981874 ... 0.78621733 0.         2.83048346]\n",
            " [7.72211735 0.45960388 8.09654389 ... 2.46873047 2.83048346 0.        ]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Construindo Dendrogramas**\n",
        "\n",
        "---\n",
        "\n",
        "O passo final na análise de agrupamento hierárquico é a criação do dendrograma. Essa representação gráfica ilustra as relações entre os _clusters_ e facilita a visualização da estrutura hierárquica dos dados."
      ],
      "metadata": {
        "id": "Xi32bti_4UzA"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Configurando os métodos de ligação\n",
        "linkage_methods = ['average', 'complete']\n",
        "\n",
        "# Criando uma figura com subplots lado a lado\n",
        "fig, axes = plt.subplots(1, 2, figsize=(16, 6), sharey=True)\n",
        "\n",
        "for ax, method in zip(axes, linkage_methods):\n",
        "    # Calculando a matriz de ligação\n",
        "    Z = hierarchy.linkage(X1, method)\n",
        "\n",
        "    # Gerando o dendrograma\n",
        "    hierarchy.dendrogram(Z, ax=ax, color_threshold=7)\n",
        "\n",
        "    # Configurando os títulos e rótulos dos eixos\n",
        "    ax.set_title(f'Dendrograma (linkage={method})', fontsize=14)\n",
        "    ax.set_xlabel('Pontos de Dados', fontsize=12)\n",
        "    ax.set_ylabel('Distância', fontsize=12)\n",
        "\n",
        "# Ajustando o espaçamento entre os subplots\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 607
        },
        "id": "FSKscAP42eXy",
        "outputId": "413eb979-db92-4ca1-e9e8-82ba8a1f3b4d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1600x600 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Comparando os dendrogramas**\n",
        "\n",
        "---\n",
        "\n",
        "A análise dos dendrogramas permite entender a estrutura hierárquica dos clusters, identificar o número ideal de clusters e obter insights sobre a similaridade entre os pontos de dados.\n",
        "\n",
        "* **Altura do ramo**: indica a distância entre os clusters que foram mesclados. Ramos mais longos sugerem maior dissimilaridade entre os clusters.\n",
        "\n",
        "* **Ordem de mesclagem**: a ordem em que os clusters são mesclados é representada pela sequência dos ramos no dendrograma.\n",
        "\n",
        "Ao comparar os dois dendrogramas, podemos observar que o critério de ligação `complete` gerou clusters mais distintos em alguns casos, com maior separação entre os grupos. Por outro lado, o método `average` tende a produzir uma estrutura de cluster mais \"suave\", com transições mais graduais entre os grupos.\n",
        "\n",
        "A escolha do método de ligação influencia diretamente na formação dos clusters e deve ser considerada de acordo com o objetivo da análise."
      ],
      "metadata": {
        "id": "rZCzj5D857TN"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Visualização dos dendrogramas para cada critério**\n"
      ],
      "metadata": {
        "id": "oI-A3Eed_E6o"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import os\n",
        "\n",
        "linkage_methods = ['single', 'average', 'complete', 'ward']\n",
        "\n",
        "# Cria um diretório para salvar as imagens, se ele não existir\n",
        "if not os.path.exists('dendrogramas'):\n",
        "    os.makedirs('dendrogramas')\n",
        "\n",
        "for method in linkage_methods:\n",
        "    Z = hierarchy.linkage(X1, method)\n",
        "    plt.figure(figsize=(8, 6))\n",
        "    hierarchy.dendrogram(Z)\n",
        "    plt.title(f'Dendrograma (linkage={method})', fontsize=14)\n",
        "    plt.xlabel('Pontos de Dados')\n",
        "    plt.ylabel('Distância')\n",
        "\n",
        "    # Salva a figura no diretório 'dendrogramas'\n",
        "    plt.savefig(f'dendrogramas/dendrograma_{method}.png')\n",
        "\n",
        "    plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "uazzRFaG8OOa",
        "outputId": "9288b9aa-ecaf-4637-c4ea-d1ee6aab0d54"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Referãncias**\n",
        "\n",
        "  ROKACH, Lior. Hierarchical Clustering.  Department of Computer Science, Ben-Gurion University of the Negev. Beer-Sheva, Israel, 2022. Disponível em: https://www.cs.princeton.edu/courses/archive/fall18/cos324/files/hierarchical-clustering.pdf. Acesso em: 4 jan. 2025.\n",
        "  \n",
        "  SCIKIT-LEARN. AgglomerativeClustering — scikit-learn 1.6.0 documentation. Documentação oficial do Scikit-Learn sobre a classe AgglomerativeClustering, detalhando parâmetros, atributos e exemplos de uso. Disponível em: https://scikit-learn.org/stable/modules/generated/sklearn.cluster.AgglomerativeClustering.html. Acesso em: 8 jan. 2025.\n",
        "\n"
      ],
      "metadata": {
        "id": "_-6KsRNgAXRx"
      }
    }
  ]
}