k_means.ipynb

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      "name": "k_means.ipynb",
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        "<a href=\"https://colab.research.google.com/github/gabifc/machine_learning_dell/blob/main/k_means.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "cell_type": "markdown",
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      "source": [
        "Olá, seja bem-vindo!\n",
        "Durante este curso, você aprendeu sobre “clusterização”, a técnica de\n",
        "Machine Learning que faz parte do aprendizado não supervisionado, também\n",
        "conhecida como “análise de agrupamentos”, está lembrado? Então, nesta aula, será\n",
        "abordado um dos mais renomados algoritmos não hierárquicos na análise de\n",
        "clusters, o algoritmo K-means. Ficou curioso para saber como funciona? Vamos lá!\n",
        "Para agrupar dados não rotulados e que possuem características\n",
        "semelhantes, diversos sistemas utilizam a clusterização. Para realizar essa tarefa,\n",
        "existem vários algoritmos, sendo um dos mais simples e populares algoritmos de\n",
        "clustering, o K-means, que você, agora, vai conhecer e entender como funciona.\n",
        "Inicialmente, vamos falar sobre a definição do K-means. Ele é um algoritmo\n",
        "não hierárquico, que tem o objetivo de agrupar os dados em k clusters diferentes.\n",
        "Para entender como o K-means funciona é preciso, primeiro, definir o conceito de\n",
        "centróide de um cluster.\n",
        "Um centróide representa o centro de um cluster e é obtido pelo valor médio\n",
        "dos dados que estão dentro desse cluster. Assim, o algoritmo K-means encontra,\n",
        "iterativamente, o centróide de cada cluster através de uma medida de distância, de forma que cada cluster contenha os dados, cuja distância entre eles e o centróide\n",
        "seja mínima. O algoritmo K-means pode ser representado pelas seguintes etapas:\n",
        "1 - Divida os dados em k grupos com centróides criadas aleatoriamente\n",
        "2 - repita até que a condição seja satisfeita:\n",
        "3 - | calcule a distância de cada objeto ao centróide\n",
        "|\n",
        "4 - | atribuir o objeto para o grupo com menor distância ao centróide\n",
        "|\n",
        "5 - | atualize o centróide de cada grupo\n",
        "\n",
        "Graficamente, as etapas podem ser expressas da seguinte forma: Os passos\n",
        "do algoritmo K-means estão ligados por setas e cada passo é ilustrado por três\n",
        "grupos de círculos, representando os dados, com um símbolo de + colorido.\n",
        "No primeiro passo, o da “Inicialização de meio”, o grupo à esquerda tem um\n",
        "símbolo de + azul, o da direita tem um símbolo de + em vermelho e o de cima tem\n",
        "um símbolo de + verde. Todos os grupos são da cor cinza.\n",
        "No segundo passo, o da “Atribuição de grupo”, os grupos agora estão\n",
        "coloridos e estão divididos por três linhas. À esquerda, sobre um fundo azul, há o\n",
        "grupo azul com o + azul. À direita, sobre um fundo vermelho, existe o grupo\n",
        "vermelho com o + vermelho. Em cima, sobre um fundo verde, encontra-se o grupo\n",
        "verde com o + verde. Alguns círculos de um grupo cruzam parcialmente a linha do\n",
        "outro grupo.\n",
        "No terceiro passo, o da “Atualização de meio”, as linhas e os fundos\n",
        "sumiram, mas os grupos ainda mantêm a mesma posição do passo 2, com alguns círculos de um grupo próximo de outro. Sobre esse passo, há um símbolo de\n",
        "atualização.\n",
        "No quarto passo, o da “Convergência”, os grupos estão claramente\n",
        "separados entre si, sem nenhum círculo de um grupo se aproximando de outro.  \n",
        "O algoritmo realizará esses passos até que uma condição de parada seja\n",
        "satisfeita. Essa condição de parada é conhecida como convergência, e pode ser\n",
        "representada, por exemplo, pela soma do erro quadrático, do inglês SSE (Sum of\n",
        "Squared Errors). Ele representa a soma das diferenças ao quadrado, entre cada\n",
        "observação e a média do grupo em um conjunto de dados.  \n",
        "Na literatura, um dos métodos mais populares de encontrar o valor de k é o\n",
        "método Elbow, que consiste em plotar a variância dos dados em função do número\n",
        "de clusters. Desse modo, a partir do ponto em que os valores de k crescem e os\n",
        "valores de variância não mudam de forma significativa, esse ponto é o melhor valor\n",
        "para k.\n",
        "Sendo assim, o método Elbow, também conhecido como método do\n",
        "cotovelo, cujo apelido se deve, além da tradução literal de Elbow ser “cotovelo”, à\n",
        "curva formada por ele também lembra o formato de um cotovelo.\n",
        "A representação gráfica desse método é formada por dois eixos. O eixo Y, na\n",
        "vertical, representa a variância. O eixo X, na horizontal, representa o número de\n",
        "clusters. Ao lado, há a letra k. No gráfico, existe uma linha com vários pontos\n",
        "vermelhos que se assemelha a um cotovelo. No quarto ponto, na “dobra” do\n",
        "cotovelo, encontra-se uma seta com a mensagem “Valor de k pelo método Elbow”.  \n",
        "Agora, de forma prática, no ambiente do jupyter, você vai aplicar o algoritmo\n",
        "K-means, usando a biblioteca scikit-learn em um conjunto de dados, tudo bem?  \n",
        "Para isso, utilize uma base de dados criada para fins didáticos, que\n",
        "representa informações básicas dos clientes de um shopping. Depois, use o\n",
        "algoritmo K-means para identificar possíveis grupos de clientes."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VA-D9ELJBM3P"
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
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        "outputId": "54d32884-1bbd-4f18-c293-3c6c436098ad"
      },
      "source": [
        "# Leitura dos dados\n",
        "df = pd.read_csv('Mall_Customers.csv')\n",
        "df.head()\n"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
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              "\n",
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              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>CustomerID</th>\n",
              "      <th>Gender</th>\n",
              "      <th>Age</th>\n",
              "      <th>Annual Income (k$)</th>\n",
              "      <th>Spending Score (1-100)</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1</td>\n",
              "      <td>Male</td>\n",
              "      <td>19</td>\n",
              "      <td>15</td>\n",
              "      <td>39</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>2</td>\n",
              "      <td>Male</td>\n",
              "      <td>21</td>\n",
              "      <td>15</td>\n",
              "      <td>81</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>3</td>\n",
              "      <td>Female</td>\n",
              "      <td>20</td>\n",
              "      <td>16</td>\n",
              "      <td>6</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>4</td>\n",
              "      <td>Female</td>\n",
              "      <td>23</td>\n",
              "      <td>16</td>\n",
              "      <td>77</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>5</td>\n",
              "      <td>Female</td>\n",
              "      <td>31</td>\n",
              "      <td>17</td>\n",
              "      <td>40</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   CustomerID  Gender  Age  Annual Income (k$)  Spending Score (1-100)\n",
              "0           1    Male   19                  15                      39\n",
              "1           2    Male   21                  15                      81\n",
              "2           3  Female   20                  16                       6\n",
              "3           4  Female   23                  16                      77\n",
              "4           5  Female   31                  17                      40"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "LpJ2N7QVGi64",
        "outputId": "b173e84b-49fb-4120-fa1d-3957c8cd425b"
      },
      "source": [
        "#tamanho do dataframe - quantidade de registros\n",
        "df.shape"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(200, 5)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "irsZwCp7Gq2_",
        "outputId": "3cc2b179-a7a0-448d-cb8f-c371cf9c7282"
      },
      "source": [
        "# verificar dados nulos - retorna a soma dos dados nulos na tabela\n",
        "df.isnull().sum()"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "CustomerID                0\n",
              "Gender                    0\n",
              "Age                       0\n",
              "Annual Income (k$)        0\n",
              "Spending Score (1-100)    0\n",
              "dtype: int64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
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          "height": 294
        },
        "id": "9-L4QPCzGxpm",
        "outputId": "162d7a05-8d0a-46a8-d415-0cb80e760a2a"
      },
      "source": [
        "# informações estatísticas\n",
        "df.describe()"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
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              "\n",
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              "    }\n",
              "\n",
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>CustomerID</th>\n",
              "      <th>Age</th>\n",
              "      <th>Annual Income (k$)</th>\n",
              "      <th>Spending Score (1-100)</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>count</th>\n",
              "      <td>200.000000</td>\n",
              "      <td>200.000000</td>\n",
              "      <td>200.000000</td>\n",
              "      <td>200.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>100.500000</td>\n",
              "      <td>38.850000</td>\n",
              "      <td>60.560000</td>\n",
              "      <td>50.200000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>std</th>\n",
              "      <td>57.879185</td>\n",
              "      <td>13.969007</td>\n",
              "      <td>26.264721</td>\n",
              "      <td>25.823522</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>min</th>\n",
              "      <td>1.000000</td>\n",
              "      <td>18.000000</td>\n",
              "      <td>15.000000</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25%</th>\n",
              "      <td>50.750000</td>\n",
              "      <td>28.750000</td>\n",
              "      <td>41.500000</td>\n",
              "      <td>34.750000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>50%</th>\n",
              "      <td>100.500000</td>\n",
              "      <td>36.000000</td>\n",
              "      <td>61.500000</td>\n",
              "      <td>50.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>75%</th>\n",
              "      <td>150.250000</td>\n",
              "      <td>49.000000</td>\n",
              "      <td>78.000000</td>\n",
              "      <td>73.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>max</th>\n",
              "      <td>200.000000</td>\n",
              "      <td>70.000000</td>\n",
              "      <td>137.000000</td>\n",
              "      <td>99.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "       CustomerID         Age  Annual Income (k$)  Spending Score (1-100)\n",
              "count  200.000000  200.000000          200.000000              200.000000\n",
              "mean   100.500000   38.850000           60.560000               50.200000\n",
              "std     57.879185   13.969007           26.264721               25.823522\n",
              "min      1.000000   18.000000           15.000000                1.000000\n",
              "25%     50.750000   28.750000           41.500000               34.750000\n",
              "50%    100.500000   36.000000           61.500000               50.000000\n",
              "75%    150.250000   49.000000           78.000000               73.000000\n",
              "max    200.000000   70.000000          137.000000               99.000000"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
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          "height": 279
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        "id": "WfPR1YfhG1l3",
        "outputId": "5e9996df-e8ee-49c3-d3a3-546d0dc0d44a"
      },
      "source": [
        "# gerando gráfico de renda anual versus score do cliente\n",
        "plt.scatter(df['Annual Income (k$)'], df['Spending Score (1-100)'], marker='.')\n",
        "plt.xlabel('Renda Anual [k$]')\n",
        "plt.ylabel('Score (1-100)')\n",
        "plt.show()"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 202
        },
        "id": "USMvtoaMG514",
        "outputId": "6cd17834-b948-492a-c2f4-531bf36a9ff7"
      },
      "source": [
        "# selecionando dados para o agrupamento\n",
        "X = df[['Annual Income (k$)', 'Spending Score (1-100)']]\n",
        "X.head()"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Annual Income (k$)</th>\n",
              "      <th>Spending Score (1-100)</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>15</td>\n",
              "      <td>39</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>15</td>\n",
              "      <td>81</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>16</td>\n",
              "      <td>6</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>16</td>\n",
              "      <td>77</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>17</td>\n",
              "      <td>40</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   Annual Income (k$)  Spending Score (1-100)\n",
              "0                  15                      39\n",
              "1                  15                      81\n",
              "2                  16                       6\n",
              "3                  16                      77\n",
              "4                  17                      40"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "F_B53sf3HiGK"
      },
      "source": [
        "# Importando K-means\n",
        "from sklearn.cluster import KMeans"
      ],
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WogrXUJOH43d"
      },
      "source": [
        "# clusterizando com k = 5\n",
        "modelo_kmeans = KMeans(n_clusters= 5, init='k-means++')"
      ],
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "plm5Kn_PH8AG"
      },
      "source": [
        "y_kmeans= modelo_kmeans.fit_predict(X)"
      ],
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fa48Ns4NIADu",
        "outputId": "2cf63a07-1653-4866-92c0-249682999bf1"
      },
      "source": [
        "print(y_kmeans)"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3\n",
            " 4 3 4 3 4 3 0 3 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
            " 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
            " 0 0 0 0 0 0 0 0 0 0 0 0 2 1 2 0 2 1 2 1 2 0 2 1 2 1 2 1 2 1 2 0 2 1 2 1 2\n",
            " 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1\n",
            " 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "y4yXSDOHIbkw",
        "outputId": "71a0e063-0055-43ca-a9ea-8adda3e39795"
      },
      "source": [
        "# visualizando o primeiro grupo criado\n",
        "print(X[y_kmeans == 0])"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "     Annual Income (k$)  Spending Score (1-100)\n",
            "43                   39                      61\n",
            "46                   40                      55\n",
            "47                   40                      47\n",
            "48                   40                      42\n",
            "49                   40                      42\n",
            "..                  ...                     ...\n",
            "121                  67                      40\n",
            "122                  69                      58\n",
            "126                  71                      35\n",
            "132                  72                      34\n",
            "142                  76                      40\n",
            "\n",
            "[81 rows x 2 columns]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "IsTncIU5Ignv",
        "outputId": "a15ef247-ffd0-4594-dbd6-325aab552b97"
      },
      "source": [
        "# visualizando todos os grupos com loop\n",
        "k_grupos = 5\n",
        "cores = ['r', 'b', 'k', 'y', 'g']\n",
        "for k in range(k_grupos):\n",
        "    cluster = X[y_kmeans == k]\n",
        "    plt.scatter(cluster['Annual Income (k$)'], cluster['Spending Score (1-100)'],\n",
        "                s = 100, c = cores[k], label = f'Cluster {k}')\n",
        "    \n",
        "plt.title('Grupos de clientes')\n",
        "plt.xlabel('Renda Anual (k$)')\n",
        "plt.ylabel('Score (1-100)')\n",
        "plt.grid()\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BGFvvXDGI2Jm"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}