06_K_Means_Clustering.ipynb

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      "name": "06 K Means Clustering.ipynb",
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        "# K-Means Clustering\n",
        "\n",
        "# One of the most commonly used methods of clustering is K-means Clustering \n",
        "# K Means allows us to define the required number of clusters\n",
        "# Now we first start by taking an arbitrary number of k. Let’s say we take k=3 \n",
        "# Now to form three groups from the set of data\n",
        "# Algorithm chooses three random points as the centroid \n",
        "# It also computes Euclidean distances from the centroid to all other data points\n",
        "# The algorithm after measuring the distances of all the data points \n",
        "# from the centroid associates each data point with a centroid based on its proximity\n",
        "\n",
        "# Silhouette Score\n",
        "# Clusters are well apart from each other as the silhouette score is closer to 1\n",
        "# Silhouette Coefficient score is a metric used to calculate the goodness of a clustering technique \n",
        "# Its value ranges from -1 to 1.\n",
        "# 1: Means clusters are well apart from each other and clearly distinguished.\n",
        "# 0: Means clusters are indifferent, or we can say that the distance between clusters is not significant.\n",
        "# -1: Means clusters are assigned in the wrong way."
      ],
      "execution_count": 1,
      "outputs": []
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      "source": [
        "# Importing Libraries\n",
        "\n",
        "from sklearn import datasets\n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn.cluster import KMeans\n",
        "from sklearn.datasets import load_iris\n",
        "import numpy as np\n",
        "from sklearn.metrics import silhouette_score\n",
        "import pandas as pd"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
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        "outputId": "af013441-182a-4a39-96f3-ee85e2c83205"
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      "source": [
        "# Loading the Dataset\n",
        "\n",
        "iris = datasets.load_iris()\n",
        "iris_data = pd.DataFrame(iris.data)\n",
        "iris_data.columns = iris.feature_names\n",
        "iris_data['Type']=iris.target\n",
        "iris_data.head()"
      ],
      "execution_count": 3,
      "outputs": [
        {
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>sepal length (cm)</th>\n",
              "      <th>sepal width (cm)</th>\n",
              "      <th>petal length (cm)</th>\n",
              "      <th>petal width (cm)</th>\n",
              "      <th>Type</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>5.1</td>\n",
              "      <td>3.5</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.2</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>4.9</td>\n",
              "      <td>3.0</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.2</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>4.7</td>\n",
              "      <td>3.2</td>\n",
              "      <td>1.3</td>\n",
              "      <td>0.2</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>4.6</td>\n",
              "      <td>3.1</td>\n",
              "      <td>1.5</td>\n",
              "      <td>0.2</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>5.0</td>\n",
              "      <td>3.6</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.2</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
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            ],
            "text/plain": [
              "   sepal length (cm)  sepal width (cm)  ...  petal width (cm)  Type\n",
              "0                5.1               3.5  ...               0.2     0\n",
              "1                4.9               3.0  ...               0.2     0\n",
              "2                4.7               3.2  ...               0.2     0\n",
              "3                4.6               3.1  ...               0.2     0\n",
              "4                5.0               3.6  ...               0.2     0\n",
              "\n",
              "[5 rows x 5 columns]"
            ]
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      "source": [
        "# Preparing Data\n",
        "# Here we have the target variable ‘Type’. \n",
        "# We need to remove the target variable, used to work in an unsupervised learning \n",
        "# The iloc function is used to get the features we require. \n",
        "# We also use .values function to get an array of the dataset. \n",
        "# Note : We transformed the dataset to an array so that we can plot the graphs of the clusters\n",
        "\n",
        "iris_X = iris_data.iloc[:, [0, 1, 2,3]].values\n",
        "print(iris_X[:5,:]) # Printing First 5 Rows"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[5.1 3.5 1.4 0.2]\n",
            " [4.9 3.  1.4 0.2]\n",
            " [4.7 3.2 1.3 0.2]\n",
            " [4.6 3.1 1.5 0.2]\n",
            " [5.  3.6 1.4 0.2]]\n"
          ],
          "name": "stdout"
        }
      ]
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      "source": [
        "# Now we will separate the target variable from the original dataset \n",
        "# And again convert it to an array by using numpy\n",
        "iris_Y = iris_data['Type']\n",
        "iris_Y = np.array(iris_Y)\n",
        "print(iris_Y)\n",
        "# Frequency count of the Output clusters\n",
        "unique, counts = np.unique(iris_Y, return_counts=True)\n",
        "freq_1 = dict(zip(unique, counts))\n",
        "freq_1"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[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 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
            " 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2\n",
            " 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n",
            " 2 2]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{0: 50, 1: 50, 2: 50}"
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          "execution_count": 5
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        "outputId": "5db5429e-c899-47f5-e49c-169ebee2f3d2"
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      "source": [
        "# Filtering Setosa\n",
        "\n",
        "Setosa = iris_data['Type'] == 0\n",
        "print(\"Filtering Setosa, True means its Setosa and False means Non Setosa\")\n",
        "print(Setosa.head())\n",
        "print(\"Top 6 Rows of Setosa\")\n",
        "Setosa_v2 = iris_data[Setosa]\n",
        "print(Setosa_v2[Setosa_v2.columns[0:2]].head())\n",
        "print(\"Last 6 Rows of Setosa\")\n",
        "print(Setosa_v2[Setosa_v2.columns[0:2]].tail())"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Filtering Setosa, True means its Setosa and False means Non Setosa\n",
            "0    True\n",
            "1    True\n",
            "2    True\n",
            "3    True\n",
            "4    True\n",
            "Name: Type, dtype: bool\n",
            "Top 6 Rows of Setosa\n",
            "   sepal length (cm)  sepal width (cm)\n",
            "0                5.1               3.5\n",
            "1                4.9               3.0\n",
            "2                4.7               3.2\n",
            "3                4.6               3.1\n",
            "4                5.0               3.6\n",
            "Last 6 Rows of Setosa\n",
            "    sepal length (cm)  sepal width (cm)\n",
            "45                4.8               3.0\n",
            "46                5.1               3.8\n",
            "47                4.6               3.2\n",
            "48                5.3               3.7\n",
            "49                5.0               3.3\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
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        "id": "_wOmXWLJWzq5",
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        "outputId": "18dc097b-34e7-45a2-f9e4-0631c88c3a3c"
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      "source": [
        "# Filtering Setosa for 2D Plot \n",
        "\n",
        "print(\"Setosa for 2D Plot\")\n",
        "print(\"X Axis points\")\n",
        "print(iris_X[iris_Y == 0,0])\n",
        "print(\"Y Axis Points\")\n",
        "print(iris_X[iris_Y == 0,1])\n",
        "print('\\n')\n",
        "# For Setosa in Target Column i.e, iris_Y = 0 \n",
        "# In other word it should range from (0,0) to (0,1)\n",
        "plt.scatter(iris_X[iris_Y == 0, 0], iris_X[iris_Y == 0, 1], \n",
        "            s = 80, c = 'orange', label = 'Iris-setosa')\n",
        "plt.xlim([4.5,8])\n",
        "plt.ylim([2,4.5])"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Setosa for 2D Plot\n",
            "X Axis points\n",
            "[5.1 4.9 4.7 4.6 5.  5.4 4.6 5.  4.4 4.9 5.4 4.8 4.8 4.3 5.8 5.7 5.4 5.1\n",
            " 5.7 5.1 5.4 5.1 4.6 5.1 4.8 5.  5.  5.2 5.2 4.7 4.8 5.4 5.2 5.5 4.9 5.\n",
            " 5.5 4.9 4.4 5.1 5.  4.5 4.4 5.  5.1 4.8 5.1 4.6 5.3 5. ]\n",
            "Y Axis Points\n",
            "[3.5 3.  3.2 3.1 3.6 3.9 3.4 3.4 2.9 3.1 3.7 3.4 3.  3.  4.  4.4 3.9 3.5\n",
            " 3.8 3.8 3.4 3.7 3.6 3.3 3.4 3.  3.4 3.5 3.4 3.2 3.1 3.4 4.1 4.2 3.1 3.2\n",
            " 3.5 3.6 3.  3.4 3.5 2.3 3.2 3.5 3.8 3.  3.8 3.2 3.7 3.3]\n",
            "\n",
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(2.0, 4.5)"
            ]
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          "execution_count": 7
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          "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": "vN6l86eLnvni",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 395
        },
        "outputId": "7e3da435-4a6c-4dd3-9c64-d7ace5871eae"
      },
      "source": [
        "# Filtering Versicolour\n",
        "\n",
        "Versi = iris_data['Type'] == 1\n",
        "print(\"Filtering Versicolour, True means its Versicolour and False means Non Versicolour\")\n",
        "print(Versi.head())\n",
        "print(\"Top 6 Rows of Versicolour\")\n",
        "Versi_v2 = iris_data[Versi]\n",
        "print(Versi_v2[Versi_v2.columns[0:2]].head())\n",
        "print(\"Last 6 Rows of Versicolour\")\n",
        "print(Versi_v2[Versi_v2.columns[0:2]].tail())"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Filtering Versicolour, True means its Versicolour and False means Non Versicolour\n",
            "0    False\n",
            "1    False\n",
            "2    False\n",
            "3    False\n",
            "4    False\n",
            "Name: Type, dtype: bool\n",
            "Top 6 Rows of Versicolour\n",
            "    sepal length (cm)  sepal width (cm)\n",
            "50                7.0               3.2\n",
            "51                6.4               3.2\n",
            "52                6.9               3.1\n",
            "53                5.5               2.3\n",
            "54                6.5               2.8\n",
            "Last 6 Rows of Versicolour\n",
            "    sepal length (cm)  sepal width (cm)\n",
            "95                5.7               3.0\n",
            "96                5.7               2.9\n",
            "97                6.2               2.9\n",
            "98                5.1               2.5\n",
            "99                5.7               2.8\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "M7mb70sXnTMg",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 485
        },
        "outputId": "a524287e-b85b-4b2e-ca44-817e942c4b4a"
      },
      "source": [
        "# Filtering Versicolour for 2D Plot \n",
        "\n",
        "print(\"Versicolour for 2D Plot\")\n",
        "print(\"X Axis points\")\n",
        "print(iris_X[iris_Y == 1,0])\n",
        "print(\"Y Axis Points\")\n",
        "print(iris_X[iris_Y == 1,1])\n",
        "print('\\n')\n",
        "plt.scatter(iris_X[iris_Y == 1, 0], iris_X[iris_Y == 1, 1], \n",
        "            s = 80, c = 'yellow', label = 'Iris-versicolour')\n",
        "\n",
        "plt.xlim([4.5,8])\n",
        "plt.ylim([2,4.5])"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Versicolour for 2D Plot\n",
            "X Axis points\n",
            "[7.  6.4 6.9 5.5 6.5 5.7 6.3 4.9 6.6 5.2 5.  5.9 6.  6.1 5.6 6.7 5.6 5.8\n",
            " 6.2 5.6 5.9 6.1 6.3 6.1 6.4 6.6 6.8 6.7 6.  5.7 5.5 5.5 5.8 6.  5.4 6.\n",
            " 6.7 6.3 5.6 5.5 5.5 6.1 5.8 5.  5.6 5.7 5.7 6.2 5.1 5.7]\n",
            "Y Axis Points\n",
            "[3.2 3.2 3.1 2.3 2.8 2.8 3.3 2.4 2.9 2.7 2.  3.  2.2 2.9 2.9 3.1 3.  2.7\n",
            " 2.2 2.5 3.2 2.8 2.5 2.8 2.9 3.  2.8 3.  2.9 2.6 2.4 2.4 2.7 2.7 3.  3.4\n",
            " 3.1 2.3 3.  2.5 2.6 3.  2.6 2.3 2.7 3.  2.9 2.9 2.5 2.8]\n",
            "\n",
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(2.0, 4.5)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        },
        {
          "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": "qD2TL0cwocaN",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 395
        },
        "outputId": "918206d2-f559-4b30-ef24-34f592af6d99"
      },
      "source": [
        "# Filtering Virginica\n",
        "\n",
        "Virginica = iris_data['Type'] == 2\n",
        "print(\"Filtering Virginica, True means its Virginica and False means Non Virginica\")\n",
        "print(Virginica.head())\n",
        "print(\"Top 6 Rows of Virginica\")\n",
        "Virginica_v2 = iris_data[Virginica]\n",
        "print(Virginica_v2[Virginica_v2.columns[0:2]].head())\n",
        "print(\"Last 6 Rows of Virginica\")\n",
        "print(Virginica_v2[Virginica_v2.columns[0:2]].tail())"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Filtering Virginica, True means its Virginica and False means Non Virginica\n",
            "0    False\n",
            "1    False\n",
            "2    False\n",
            "3    False\n",
            "4    False\n",
            "Name: Type, dtype: bool\n",
            "Top 6 Rows of Virginica\n",
            "     sepal length (cm)  sepal width (cm)\n",
            "100                6.3               3.3\n",
            "101                5.8               2.7\n",
            "102                7.1               3.0\n",
            "103                6.3               2.9\n",
            "104                6.5               3.0\n",
            "Last 6 Rows of Virginica\n",
            "     sepal length (cm)  sepal width (cm)\n",
            "145                6.7               3.0\n",
            "146                6.3               2.5\n",
            "147                6.5               3.0\n",
            "148                6.2               3.4\n",
            "149                5.9               3.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wsnoGdx0objs",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 485
        },
        "outputId": "6083470d-eded-4d07-cd6d-f42529c933d6"
      },
      "source": [
        "# Filtering Virginica for 2D Plot\n",
        "\n",
        "print(\"Virginica for 2D Plot\")\n",
        "print(\"X Axis points\")\n",
        "print(iris_X[iris_Y == 2,0])\n",
        "print(\"Y Axis Points\")\n",
        "print(iris_X[iris_Y == 2,1])\n",
        "print('\\n')\n",
        "plt.scatter(iris_X[iris_Y == 2, 0], iris_X[iris_Y == 2, 1], \n",
        "            s = 80, c = 'green', label = 'Iris-virginica')\n",
        "plt.xlim([4.5,8])\n",
        "plt.ylim([2,4.5])"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Virginica for 2D Plot\n",
            "X Axis points\n",
            "[6.3 5.8 7.1 6.3 6.5 7.6 4.9 7.3 6.7 7.2 6.5 6.4 6.8 5.7 5.8 6.4 6.5 7.7\n",
            " 7.7 6.  6.9 5.6 7.7 6.3 6.7 7.2 6.2 6.1 6.4 7.2 7.4 7.9 6.4 6.3 6.1 7.7\n",
            " 6.3 6.4 6.  6.9 6.7 6.9 5.8 6.8 6.7 6.7 6.3 6.5 6.2 5.9]\n",
            "Y Axis Points\n",
            "[3.3 2.7 3.  2.9 3.  3.  2.5 2.9 2.5 3.6 3.2 2.7 3.  2.5 2.8 3.2 3.  3.8\n",
            " 2.6 2.2 3.2 2.8 2.8 2.7 3.3 3.2 2.8 3.  2.8 3.  2.8 3.8 2.8 2.8 2.6 3.\n",
            " 3.4 3.1 3.  3.1 3.1 3.1 2.7 3.2 3.3 3.  2.5 3.  3.4 3. ]\n",
            "\n",
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(2.0, 4.5)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        },
        {
          "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": "HCShLm9HUWHn",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "outputId": "80dcebe9-3c2d-4b27-ca0c-6482ae05ba19"
      },
      "source": [
        "# Visualise Classes all at once\n",
        "\n",
        "# In this Iris dataset, we have three classes (0,1,2)\n",
        "# We visualise these classes in a 2-D graph \n",
        "# This will help us in comparing the original classes with the clusters created \n",
        "# Plot the three type of flowers on a graph\n",
        "\n",
        "plt.scatter(iris_X[iris_Y == 0, 0], iris_X[iris_Y == 0, 1], \n",
        "            s = 80, c = 'orange', label = 'Iris-setosa')\n",
        "plt.scatter(iris_X[iris_Y == 1, 0], iris_X[iris_Y == 1, 1], \n",
        "            s = 80, c = 'yellow', label = 'Iris-versicolour')\n",
        "plt.scatter(iris_X[iris_Y == 2, 0], iris_X[iris_Y == 2, 1], \n",
        "            s = 80, c = 'green', label = 'Iris-virginica')\n",
        "plt.legend()\n",
        "\n",
        "# Inference : \n",
        "# We find that we have three classes with two types of Iris flowers overlapping each other"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f6285136550>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        },
        {
          "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": "q3vCVatczYBY",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 215
        },
        "outputId": "dfe67d59-8817-407a-9670-d80c14235780"
      },
      "source": [
        "# K Means\n",
        "\n",
        "# Deciding Value of K\n",
        "# The most crucial aspect of K-Means clustering is deciding the value of K\n",
        "# We do this by performing Elbow Analysis \n",
        "\n",
        "wcss=[]\n",
        "for i in range(1, 11):\n",
        "    kmeans = KMeans(n_clusters = i, init = 'k-means++', max_iter = 300,\n",
        "                    n_init = 10, random_state = 0)\n",
        "    kmeans.fit(iris_X)\n",
        "    wcss.append(kmeans.inertia_)\n",
        "\n",
        "print('Within Cluster Sum of Square (WCSS) for 10 Clusters')\n",
        "wcss\n",
        "\n",
        "# Inference : \n",
        "# Cluster 1 means only one cluster, inshort variance of the dataset\n",
        "# Variance in Cluster 1 = 681\n",
        "# Cluster 2 means two cluster i.e, Variance in Cluster 2 = 152\n",
        "# Same way for Variance in Cluster 3 = 78\n",
        "# Vairance in Cluster is also knows as Within Cluster Sum of Square (WCSS)\n",
        "# Normally as we increase number of clusters, within Sum of Square will decrease "
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Within Cluster Sum of Square (WCSS) for 10 Clusters\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[681.3706,\n",
              " 152.34795176035792,\n",
              " 78.85144142614601,\n",
              " 57.25600931571815,\n",
              " 46.44618205128205,\n",
              " 39.03998724608725,\n",
              " 34.299712121212124,\n",
              " 30.014398496240602,\n",
              " 28.036906353450473,\n",
              " 26.53452922077922]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Hq6c3GLBzw9o",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 313
        },
        "outputId": "c5cafa52-6763-4900-b728-081c0ee9aa3c"
      },
      "source": [
        "# We now plot the WCSS obtained \n",
        "\n",
        "# WCSS or within-cluster sum of squares is a measure of \n",
        "# how internally coherent the clusters are K-Means tries to minimize this criterion\n",
        "\n",
        "plt.plot(range(1, 11), wcss)\n",
        "plt.title('The elbow method')\n",
        "plt.xlabel('Number of clusters')\n",
        "plt.ylabel('WCSS')\n",
        "\n",
        "# Inference : \n",
        "# In the elbow graph, we look for the points where the drop falls and the line smoothens out\n",
        "# In the above graph, this happens for k=3. \n",
        "# Another way of understanding this is that we note the point at which the WCSS is less \n",
        "# and try to find the number of clusters for our dataset. \n",
        "# We see that at the number of clusters = 3, WCSS is less than 100, which is good for us. \n",
        "# So we take k =3.\n",
        "# We will check Silhouette Coefficient also for 3 and 4 Clusters respectively"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'WCSS')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        },
        {
          "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": "lTHnXGs90GGq",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 125
        },
        "outputId": "6ee16ec6-19cb-4a25-9445-deffc6e6eab6"
      },
      "source": [
        "# Running K-Means Model\n",
        "\n",
        "# We now run K-Means clustering for obtaining a 3 cluster solution.\n",
        "cluster_Kmeans = KMeans(n_clusters=3)\n",
        "model_kmeans = cluster_Kmeans.fit(iris_X)\n",
        "pred_kmeans = model_kmeans.labels_\n",
        "print(pred_kmeans)\n",
        "\n",
        "# Frequency count of the Output clusters\n",
        "unique, counts = np.unique(pred_kmeans, return_counts=True)\n",
        "dict(zip(unique, counts))"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
            " 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 2 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 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 2 2 2 0 2 2 2 2\n",
            " 2 2 0 0 2 2 2 2 0 2 0 2 0 2 2 0 0 2 2 2 2 2 0 2 2 2 2 0 2 2 2 0 2 2 2 0 2\n",
            " 2 0]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{0: 62, 1: 50, 2: 38}"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mezxq4Fx030O",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "outputId": "ec5c8599-8597-431d-f83e-adbae4fcf774"
      },
      "source": [
        "# Visualizing Output\n",
        "\n",
        "print('Original Cluster Frequency')\n",
        "print(freq_1)\n",
        "# Frequency count of the Output clusters\n",
        "unique, counts = np.unique(pred_kmeans, return_counts=True)\n",
        "print('K Means Output Cluster Frequency')\n",
        "print(dict(zip(unique, counts)))\n",
        "# Silhouette Score\n",
        "print('Silhouette Score for 3 Clusters')\n",
        "print(silhouette_score(iris_X,pred_kmeans))\n",
        "print(\"\\n\")\n",
        "\n",
        "# In the above output we got value labels: ‘0’, ‘1’  and ‘2’\n",
        "# For a better understanding, we can visualize these clusters.\n",
        "\n",
        "plt.scatter(iris_X[pred_kmeans == 0, 0], iris_X[pred_kmeans == 0, 1], \n",
        "            s = 80, c = 'orange', label = 'Iris-setosa')\n",
        "plt.scatter(iris_X[pred_kmeans == 1, 0], iris_X[pred_kmeans == 1, 1], \n",
        "            s = 80, c = 'yellow', label = 'Iris-versicolour')\n",
        "plt.scatter(iris_X[pred_kmeans == 2, 0], iris_X[pred_kmeans == 2, 1], \n",
        "            s = 80, c = 'green', label = 'Iris-virginica')\n",
        "plt.legend()\n",
        "\n",
        "# Inference : \n",
        "# When compared to the original classes we find that the observations of the class label \n",
        "# \"1\" has been correctly formed into a separate well-defined cluster\n",
        "# however, for the other two classes, clusters are not as correct. \n",
        "# This is mainly because, in the original dataset, these two class labels were overlapping each other \n",
        "# which makes it difficult for the clustering algorithm as it works best for clear neat separate observations. \n",
        "# Still, the clusters have been formed, more or less correctly\n",
        "# Silhouette Score = 0.55 which is not bad enough (should be tend to 1)"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Original Cluster Frequency\n",
            "{0: 50, 1: 50, 2: 50}\n",
            "K Means Output Cluster Frequency\n",
            "{0: 62, 1: 50, 2: 38}\n",
            "Silhouette Score for 3 Clusters\n",
            "0.5528190123564091\n",
            "\n",
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f62856794a8>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 16
        },
        {
          "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": "jXNotcalLWmu",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        },
        "outputId": "c25c27a7-f909-439b-f719-d04cb139dfec"
      },
      "source": [
        "# If we take 4 Cluster to Check Silhouetter Score\n",
        "cluster_Kmeans = KMeans(n_clusters=4)\n",
        "model_kmeans = cluster_Kmeans.fit(iris_X)\n",
        "labels_1 = model_kmeans.labels_\n",
        "print(\"Silhouette Score for 4 Cluster\")\n",
        "print(silhouette_score(iris_X,labels_1))\n",
        "\n",
        "# Inference : \n",
        "# As we can observe Score is 0.49 (decrease so reject 4 Cluster)\n",
        "# Optimal number of cluster=3 as its silhouette score is greater than that of 4 clusters"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Silhouette Score for 4 Cluster\n",
            "0.49721766487109686\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}