K_in_K_means_Clustering.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "K_in_K_means_Clustering.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "display_name": "Python 2",
      "language": "python",
      "name": "python2"
    }
  },
  "cells": [
    {
      "metadata": {
        "id": "trW1sWcKVC1_",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "from sklearn import datasets\n",
        "from sklearn.cluster import KMeans\n",
        "import matplotlib.pyplot as plt\n",
        "import matplotlib.patches as mpatches\n",
        "import sklearn.metrics as sm\n",
        "import math\n",
        "%matplotlib inline"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "d4YFcA9QVC2F",
        "colab_type": "code",
        "outputId": "3a5e8940-8fcd-4cae-d90e-e91d7e5d4a02",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 2617
        }
      },
      "cell_type": "code",
      "source": [
        "iris = datasets.load_iris()\n",
        "print iris.data"
      ],
      "execution_count": 2,
      "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",
            " [5.4 3.9 1.7 0.4]\n",
            " [4.6 3.4 1.4 0.3]\n",
            " [5.  3.4 1.5 0.2]\n",
            " [4.4 2.9 1.4 0.2]\n",
            " [4.9 3.1 1.5 0.1]\n",
            " [5.4 3.7 1.5 0.2]\n",
            " [4.8 3.4 1.6 0.2]\n",
            " [4.8 3.  1.4 0.1]\n",
            " [4.3 3.  1.1 0.1]\n",
            " [5.8 4.  1.2 0.2]\n",
            " [5.7 4.4 1.5 0.4]\n",
            " [5.4 3.9 1.3 0.4]\n",
            " [5.1 3.5 1.4 0.3]\n",
            " [5.7 3.8 1.7 0.3]\n",
            " [5.1 3.8 1.5 0.3]\n",
            " [5.4 3.4 1.7 0.2]\n",
            " [5.1 3.7 1.5 0.4]\n",
            " [4.6 3.6 1.  0.2]\n",
            " [5.1 3.3 1.7 0.5]\n",
            " [4.8 3.4 1.9 0.2]\n",
            " [5.  3.  1.6 0.2]\n",
            " [5.  3.4 1.6 0.4]\n",
            " [5.2 3.5 1.5 0.2]\n",
            " [5.2 3.4 1.4 0.2]\n",
            " [4.7 3.2 1.6 0.2]\n",
            " [4.8 3.1 1.6 0.2]\n",
            " [5.4 3.4 1.5 0.4]\n",
            " [5.2 4.1 1.5 0.1]\n",
            " [5.5 4.2 1.4 0.2]\n",
            " [4.9 3.1 1.5 0.2]\n",
            " [5.  3.2 1.2 0.2]\n",
            " [5.5 3.5 1.3 0.2]\n",
            " [4.9 3.6 1.4 0.1]\n",
            " [4.4 3.  1.3 0.2]\n",
            " [5.1 3.4 1.5 0.2]\n",
            " [5.  3.5 1.3 0.3]\n",
            " [4.5 2.3 1.3 0.3]\n",
            " [4.4 3.2 1.3 0.2]\n",
            " [5.  3.5 1.6 0.6]\n",
            " [5.1 3.8 1.9 0.4]\n",
            " [4.8 3.  1.4 0.3]\n",
            " [5.1 3.8 1.6 0.2]\n",
            " [4.6 3.2 1.4 0.2]\n",
            " [5.3 3.7 1.5 0.2]\n",
            " [5.  3.3 1.4 0.2]\n",
            " [7.  3.2 4.7 1.4]\n",
            " [6.4 3.2 4.5 1.5]\n",
            " [6.9 3.1 4.9 1.5]\n",
            " [5.5 2.3 4.  1.3]\n",
            " [6.5 2.8 4.6 1.5]\n",
            " [5.7 2.8 4.5 1.3]\n",
            " [6.3 3.3 4.7 1.6]\n",
            " [4.9 2.4 3.3 1. ]\n",
            " [6.6 2.9 4.6 1.3]\n",
            " [5.2 2.7 3.9 1.4]\n",
            " [5.  2.  3.5 1. ]\n",
            " [5.9 3.  4.2 1.5]\n",
            " [6.  2.2 4.  1. ]\n",
            " [6.1 2.9 4.7 1.4]\n",
            " [5.6 2.9 3.6 1.3]\n",
            " [6.7 3.1 4.4 1.4]\n",
            " [5.6 3.  4.5 1.5]\n",
            " [5.8 2.7 4.1 1. ]\n",
            " [6.2 2.2 4.5 1.5]\n",
            " [5.6 2.5 3.9 1.1]\n",
            " [5.9 3.2 4.8 1.8]\n",
            " [6.1 2.8 4.  1.3]\n",
            " [6.3 2.5 4.9 1.5]\n",
            " [6.1 2.8 4.7 1.2]\n",
            " [6.4 2.9 4.3 1.3]\n",
            " [6.6 3.  4.4 1.4]\n",
            " [6.8 2.8 4.8 1.4]\n",
            " [6.7 3.  5.  1.7]\n",
            " [6.  2.9 4.5 1.5]\n",
            " [5.7 2.6 3.5 1. ]\n",
            " [5.5 2.4 3.8 1.1]\n",
            " [5.5 2.4 3.7 1. ]\n",
            " [5.8 2.7 3.9 1.2]\n",
            " [6.  2.7 5.1 1.6]\n",
            " [5.4 3.  4.5 1.5]\n",
            " [6.  3.4 4.5 1.6]\n",
            " [6.7 3.1 4.7 1.5]\n",
            " [6.3 2.3 4.4 1.3]\n",
            " [5.6 3.  4.1 1.3]\n",
            " [5.5 2.5 4.  1.3]\n",
            " [5.5 2.6 4.4 1.2]\n",
            " [6.1 3.  4.6 1.4]\n",
            " [5.8 2.6 4.  1.2]\n",
            " [5.  2.3 3.3 1. ]\n",
            " [5.6 2.7 4.2 1.3]\n",
            " [5.7 3.  4.2 1.2]\n",
            " [5.7 2.9 4.2 1.3]\n",
            " [6.2 2.9 4.3 1.3]\n",
            " [5.1 2.5 3.  1.1]\n",
            " [5.7 2.8 4.1 1.3]\n",
            " [6.3 3.3 6.  2.5]\n",
            " [5.8 2.7 5.1 1.9]\n",
            " [7.1 3.  5.9 2.1]\n",
            " [6.3 2.9 5.6 1.8]\n",
            " [6.5 3.  5.8 2.2]\n",
            " [7.6 3.  6.6 2.1]\n",
            " [4.9 2.5 4.5 1.7]\n",
            " [7.3 2.9 6.3 1.8]\n",
            " [6.7 2.5 5.8 1.8]\n",
            " [7.2 3.6 6.1 2.5]\n",
            " [6.5 3.2 5.1 2. ]\n",
            " [6.4 2.7 5.3 1.9]\n",
            " [6.8 3.  5.5 2.1]\n",
            " [5.7 2.5 5.  2. ]\n",
            " [5.8 2.8 5.1 2.4]\n",
            " [6.4 3.2 5.3 2.3]\n",
            " [6.5 3.  5.5 1.8]\n",
            " [7.7 3.8 6.7 2.2]\n",
            " [7.7 2.6 6.9 2.3]\n",
            " [6.  2.2 5.  1.5]\n",
            " [6.9 3.2 5.7 2.3]\n",
            " [5.6 2.8 4.9 2. ]\n",
            " [7.7 2.8 6.7 2. ]\n",
            " [6.3 2.7 4.9 1.8]\n",
            " [6.7 3.3 5.7 2.1]\n",
            " [7.2 3.2 6.  1.8]\n",
            " [6.2 2.8 4.8 1.8]\n",
            " [6.1 3.  4.9 1.8]\n",
            " [6.4 2.8 5.6 2.1]\n",
            " [7.2 3.  5.8 1.6]\n",
            " [7.4 2.8 6.1 1.9]\n",
            " [7.9 3.8 6.4 2. ]\n",
            " [6.4 2.8 5.6 2.2]\n",
            " [6.3 2.8 5.1 1.5]\n",
            " [6.1 2.6 5.6 1.4]\n",
            " [7.7 3.  6.1 2.3]\n",
            " [6.3 3.4 5.6 2.4]\n",
            " [6.4 3.1 5.5 1.8]\n",
            " [6.  3.  4.8 1.8]\n",
            " [6.9 3.1 5.4 2.1]\n",
            " [6.7 3.1 5.6 2.4]\n",
            " [6.9 3.1 5.1 2.3]\n",
            " [5.8 2.7 5.1 1.9]\n",
            " [6.8 3.2 5.9 2.3]\n",
            " [6.7 3.3 5.7 2.5]\n",
            " [6.7 3.  5.2 2.3]\n",
            " [6.3 2.5 5.  1.9]\n",
            " [6.5 3.  5.2 2. ]\n",
            " [6.2 3.4 5.4 2.3]\n",
            " [5.9 3.  5.1 1.8]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "Rh9Z066QVC2N",
        "colab_type": "code",
        "outputId": "e58758f7-ecb1-49a2-d4d2-e430f29b01ee",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "cell_type": "code",
      "source": [
        "print iris.target_names"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "['setosa' 'versicolor' 'virginica']\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "qKg8TSAlVC2Q",
        "colab_type": "code",
        "outputId": "0deef164-5851-41fb-9d6a-3c2e7d5f2b19",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 104
        }
      },
      "cell_type": "code",
      "source": [
        "print iris.target"
      ],
      "execution_count": 4,
      "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"
        }
      ]
    },
    {
      "metadata": {
        "id": "wv6CtqUUVC2U",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "x = pd.DataFrame(iris.data, columns=['Sepal Length', 'Sepal Width', \n",
        "                                     'Petal Length', 'Petal Width'])\n",
        "y = pd.DataFrame(iris.target, columns=['Target'])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "BAUnuoN7VC2W",
        "colab_type": "code",
        "outputId": "139c2d66-18d8-4069-f66b-ff057f81b26b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 202
        }
      },
      "cell_type": "code",
      "source": [
        "x.head()"
      ],
      "execution_count": 6,
      "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>Sepal Length</th>\n",
              "      <th>Sepal Width</th>\n",
              "      <th>Petal Length</th>\n",
              "      <th>Petal Width</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",
              "    </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",
              "    </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",
              "    </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",
              "    </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",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   Sepal Length  Sepal Width  Petal Length  Petal Width\n",
              "0           5.1          3.5           1.4          0.2\n",
              "1           4.9          3.0           1.4          0.2\n",
              "2           4.7          3.2           1.3          0.2\n",
              "3           4.6          3.1           1.5          0.2\n",
              "4           5.0          3.6           1.4          0.2"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "metadata": {
        "id": "BVPTp2I7VC2a",
        "colab_type": "code",
        "outputId": "aed33b83-3f48-4474-ae8a-d0c2a1383d8f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 202
        }
      },
      "cell_type": "code",
      "source": [
        "y.head()"
      ],
      "execution_count": 7,
      "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>Target</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   Target\n",
              "0       0\n",
              "1       0\n",
              "2       0\n",
              "3       0\n",
              "4       0"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        }
      ]
    },
    {
      "metadata": {
        "id": "u3bbNKsLVC2h",
        "colab_type": "code",
        "outputId": "5c8918ed-01b6-4312-a9b8-b796f5c03734",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 69
        }
      },
      "cell_type": "code",
      "source": [
        "iris_k_mean_model = KMeans(n_clusters=3)\n",
        "iris_k_mean_model.fit(x)"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "KMeans(algorithm='auto', copy_x=True, init='k-means++', max_iter=300,\n",
              "    n_clusters=3, n_init=10, n_jobs=None, precompute_distances='auto',\n",
              "    random_state=None, tol=0.0001, verbose=0)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        }
      ]
    },
    {
      "metadata": {
        "id": "HfuX5GSGVC2k",
        "colab_type": "code",
        "outputId": "3df9864d-c650-481d-8b19-3527acacf392",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 104
        }
      },
      "cell_type": "code",
      "source": [
        "print iris_k_mean_model.labels_"
      ],
      "execution_count": 9,
      "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 2 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 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 2 2 1 2 2 2 2\n",
            " 2 2 1 1 2 2 2 2 1 2 1 2 1 2 2 1 1 2 2 2 2 2 1 2 2 2 2 1 2 2 2 1 2 2 2 1 2\n",
            " 2 1]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "vaE5OgXTVC2n",
        "colab_type": "code",
        "outputId": "7b506b46-c6f6-475e-bf5d-951c98e47658",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 69
        }
      },
      "cell_type": "code",
      "source": [
        "print iris_k_mean_model.cluster_centers_"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[5.006      3.428      1.462      0.246     ]\n",
            " [5.9016129  2.7483871  4.39354839 1.43387097]\n",
            " [6.85       3.07368421 5.74210526 2.07105263]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "TmM4GZ0rVC2q",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "predictedY = np.choose(iris_k_mean_model.labels_, [0, 1, 2]).astype(np.int64)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "B-tclK4-VC2w",
        "colab_type": "code",
        "outputId": "5cfe143e-467d-4de1-cc92-11255a13902f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "cell_type": "code",
      "source": [
        "sm.accuracy_score(predictedY, y['Target'])"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.8933333333333333"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        }
      ]
    },
    {
      "metadata": {
        "id": "0_S4OvLtVC20",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Interpretation of Confusion Matrix\n",
        "Correctly identifed all 0 classes as 0’s\n",
        "correctly classified 48 class 1’s but miss-classified 2 class 1’s as class 2\n",
        "correctly classified 36 class 2’s but miss-classified 14 class 2’s as class 1"
      ]
    },
    {
      "metadata": {
        "id": "1zFTfx7bVC21",
        "colab_type": "code",
        "outputId": "f21afa14-6c0e-4d8d-ba3a-3c3e315feffe",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 69
        }
      },
      "cell_type": "code",
      "source": [
        "sm.confusion_matrix(predictedY, y['Target'])"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[50,  0,  0],\n",
              "       [ 0, 48, 14],\n",
              "       [ 0,  2, 36]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 13
        }
      ]
    },
    {
      "metadata": {
        "id": "jHrk6RzPVC24",
        "colab_type": "code",
        "outputId": "8b47b214-0bee-4d16-a8d3-15f910a5b8ce",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "cell_type": "code",
      "source": [
        "x.shape"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(150, 4)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        }
      ]
    },
    {
      "metadata": {
        "id": "sjHPljyCVfR9",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "dist_points_from_cluster_center = []\n",
        "K = range(1,10)\n",
        "for no_of_clusters in K:\n",
        "  k_model = KMeans(n_clusters=no_of_clusters)\n",
        "  k_model.fit(x)\n",
        "  dist_points_from_cluster_center.append(k_model.inertia_)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "C_Aa4J-_WJKY",
        "colab_type": "code",
        "outputId": "316d2d1f-ff25-49ff-8ee4-91e601597742",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 173
        }
      },
      "cell_type": "code",
      "source": [
        "dist_points_from_cluster_center"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[681.3706,\n",
              " 152.34795176035792,\n",
              " 78.85144142614601,\n",
              " 57.25600931571815,\n",
              " 46.44618205128205,\n",
              " 39.066035353535355,\n",
              " 34.40900974025974,\n",
              " 30.254402675826597,\n",
              " 27.811546962762637]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 20
        }
      ]
    },
    {
      "metadata": {
        "id": "U6Ff9KHIX_tL",
        "colab_type": "code",
        "outputId": "38243610-dbac-4405-fbdb-954333e21808",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "cell_type": "code",
      "source": [
        "plt.plot(K, dist_points_from_cluster_center)"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fd8426be550>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 21
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXUAAAD4CAYAAAATpHZ6AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQlTqIiIl5P8DuHH8H+fzx1sAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fd8426e7910>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "HUaX653JWQcg",
        "colab_type": "code",
        "outputId": "11e878d1-4a4b-40c1-c0a8-b8dc72f37ffd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        }
      },
      "cell_type": "code",
      "source": [
        "plt.plot(K, dist_points_from_cluster_center)\n",
        "plt.plot([K[0], K[8]], [dist_points_from_cluster_center[0], \n",
        "                        dist_points_from_cluster_center[8]], 'ro-')\n",
        "plt.show()"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXUAAAD4CAYAAAATpHZ6AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\njvw/rY4b+g7XmBsAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fd84265cc90>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "PwjipbLxWav1",
        "colab_type": "code",
        "outputId": "0c826eb0-45e8-4b96-ba44-cf38b10c73d4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 304
        }
      },
      "cell_type": "code",
      "source": [
        "x = [K[0], K[8]]\n",
        "y = [dist_points_from_cluster_center[0], dist_points_from_cluster_center[8]]\n",
        "\n",
        "# Calculate the coefficients. This line answers the initial question. \n",
        "coefficients = np.polyfit(x, y, 1)\n",
        "\n",
        "# Print the findings\n",
        "print 'a =', coefficients[0]\n",
        "print 'b =', coefficients[1]\n",
        "\n",
        "# Let's compute the values of the line...\n",
        "polynomial = np.poly1d(coefficients)\n",
        "x_axis = np.linspace(0,9,100)\n",
        "y_axis = polynomial(x_axis)\n",
        "\n",
        "# ...and plot the points and the line\n",
        "plt.plot(x_axis, y_axis)\n",
        "plt.grid('on')\n",
        "plt.show()"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "a = -81.69488162965469\n",
            "b = 763.0654816296545\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXUAAAD8CAYAAACINTRsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRxTqIiJ+RKEuIuJHFOoiIn7k/wNZ/1+P+x96rwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fd8425e7ad0>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "sou1tiClZPe5",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "# Function to find distance\n",
        "# https://www.geeksforgeeks.org/perpendicular-distance-\n",
        "# between-a-point-and-a-line-in-2-d/\n",
        "def calc_distance(x1, y1, a, b, c):\n",
        "  d = abs((a * x1 + b * y1 + c)) / (math.sqrt(a * a + b * b))\n",
        "  return d"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "fxtz0AxyeS2k",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "# (y1 – y2)x + (x2 – x1)y + (x1y2 – x2y1) = 0\n",
        "# https://bobobobo.wordpress.com/2008/01/07/solving-linear-equations-ax-by-c-0/\n",
        "a = dist_points_from_cluster_center[0] - dist_points_from_cluster_center[8]\n",
        "b = K[8] - K[0]\n",
        "c1 = K[0] * dist_points_from_cluster_center[8]\n",
        "c2 = K[8] * dist_points_from_cluster_center[0]\n",
        "c = c1 - c2"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "eZonpVr8dn6Q",
        "colab_type": "code",
        "outputId": "1e90e7e2-da73-486b-84e4-c9be62d814eb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 173
        }
      },
      "cell_type": "code",
      "source": [
        "dist_points_from_cluster_center"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[681.3706,\n",
              " 152.34795176035792,\n",
              " 78.85144142614601,\n",
              " 57.25600931571815,\n",
              " 46.44618205128205,\n",
              " 39.066035353535355,\n",
              " 34.40900974025974,\n",
              " 30.254402675826597,\n",
              " 27.811546962762637]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 27
        }
      ]
    },
    {
      "metadata": {
        "id": "ugKut730ZPiZ",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "distance_of_points_from_line = []\n",
        "for k in range(9):\n",
        "  distance_of_points_from_line.append(\n",
        "      calc_distance(K[k], dist_points_from_cluster_center[k], a, b, c))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "dlB2XhCafBic",
        "colab_type": "code",
        "outputId": "5e4b9a66-8eba-4b2a-9781-55f240eeb798",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 173
        }
      },
      "cell_type": "code",
      "source": [
        "distance_of_points_from_line"
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[0.0,\n",
              " 5.475180929378972,\n",
              " 5.3748348978572755,\n",
              " 4.639232539954151,\n",
              " 3.771617053485105,\n",
              " 2.862023127414809,\n",
              " 1.9190988745841675,\n",
              " 0.9700251433117231,\n",
              " 0.0]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 30
        }
      ]
    },
    {
      "metadata": {
        "id": "7PWrEAMEYvMC",
        "colab_type": "code",
        "outputId": "64ed1528-0171-4584-9550-6d047bb6a455",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "cell_type": "code",
      "source": [
        "plt.plot(K, distance_of_points_from_line)"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fd8426e7e50>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 32
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWkAAAD4CAYAAAAuNhccAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nVNIiIi6mkhYRcTGVtIiIi/1/0zuOuqiqBgsAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fd8425a9e90>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}