K_means.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "K-means.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyNPPRxrP1nWZ67KG3WtCTEE",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/m607stars/Machine-Learning-Algorithms/blob/master/K_means.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7B8gZC81MnzZ"
      },
      "source": [
        "# Importing Libraries and data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "B904sF6IKuxU",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e7723c3f-9657-45cf-ef65-339226aa8109"
      },
      "source": [
        "#We import the necessary libraries \n",
        "\n",
        "import sys\n",
        "import numpy as np\n",
        "import pandas as pd \n",
        "import matplotlib.pyplot as plt  \n",
        "\n",
        "\n",
        "from sklearn.cluster import KMeans    #To implement KMeans\n",
        "from math import sqrt\n",
        "from sklearn.datasets.samples_generator import make_blobs   #To generate random datapoints "
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/sklearn/utils/deprecation.py:144: FutureWarning: The sklearn.datasets.samples_generator module is  deprecated in version 0.22 and will be removed in version 0.24. The corresponding classes / functions should instead be imported from sklearn.datasets. Anything that cannot be imported from sklearn.datasets is now part of the private API.\n",
            "  warnings.warn(message, FutureWarning)\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oJcMJ7i2cyiU"
      },
      "source": [
        "# Making Random Dataset "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6OPGbc0lMMgA",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "266bb551-8f1d-4caa-b67a-242c282441c8"
      },
      "source": [
        "#We give the centroids as 4, and no. of datapoints as 300\n",
        "#We also take the standard deviation of clusters as 0.9 so that the datapoints are not easily separable\n",
        "X, y_true = make_blobs(n_samples=300, centers=4,\n",
        "                       cluster_std=0.90, random_state=0)    \n",
        "plt.scatter(X[:, 0], X[:, 1], s=50)                  #We plot the datapoints "
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7ff08a022710>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 22
        },
        {
          "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": "markdown",
      "metadata": {
        "id": "LIPMQ58tc8O_"
      },
      "source": [
        "# Finding Optimum Clusters \n",
        "We need to first find the optimum clusters as we can't always guess how many classes would be there in dataset. So we do this by finding the inertia of the KMeans algorithm applied by setting the value of groups from 1 to 20. For larger datasets, one can even do the calculations for as large as 50 different classes. After getting the inertia of all the different number of clusters, we  then see the maximum percent change for all the values starting from 1. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gZ_ofEQxOaNz",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 340
        },
        "outputId": "d2a58c07-b410-4940-8206-7ddfcd44d8d8"
      },
      "source": [
        "inertia_values = []    #Initialize an empty list \n",
        "\n",
        "#For finding the inertia of KMeans for different number of clusters (here 20)\n",
        "for i in range (1,20):\n",
        "  m = KMeans(n_clusters=i)     #store  KMeans in m\n",
        "  m.fit(X)                     #Fit the data\n",
        "  inertia_values.append(m.inertia_)   #Append the inertia into the list inertia_values\n",
        "\n",
        "#print Inertia_values\n",
        "inertia_values"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[3079.6849468163646,\n",
              " 1429.3077585140034,\n",
              " 795.3236124003193,\n",
              " 454.3778700005048,\n",
              " 401.4544706029594,\n",
              " 351.7148170504679,\n",
              " 309.23746248987425,\n",
              " 279.85245512702625,\n",
              " 241.49375625904983,\n",
              " 219.6856269579497,\n",
              " 200.67444954725406,\n",
              " 184.25231038542174,\n",
              " 171.5930017567952,\n",
              " 158.8476669434603,\n",
              " 149.0759406083931,\n",
              " 140.5961919422749,\n",
              " 132.12385577599244,\n",
              " 121.74902338340388,\n",
              " 116.71731896922452]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Cl6euiuaUGqT",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 638
        },
        "outputId": "c08e98ab-c341-473d-8f67-c343700a81e0"
      },
      "source": [
        "#We Convert the inertia_values into dataframe for plottinf it easily\n",
        "df = pd.DataFrame({'Cluster':range(1,20),'inertia_values':inertia_values})  \n",
        "df"
      ],
      "execution_count": null,
      "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>Cluster</th>\n",
              "      <th>inertia_values</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1</td>\n",
              "      <td>3079.684947</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>2</td>\n",
              "      <td>1429.307759</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>3</td>\n",
              "      <td>795.323612</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>4</td>\n",
              "      <td>454.377870</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>5</td>\n",
              "      <td>401.454471</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>6</td>\n",
              "      <td>351.714817</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>7</td>\n",
              "      <td>309.237462</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>8</td>\n",
              "      <td>279.852455</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>9</td>\n",
              "      <td>241.493756</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>10</td>\n",
              "      <td>219.685627</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>11</td>\n",
              "      <td>200.674450</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>12</td>\n",
              "      <td>184.252310</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>13</td>\n",
              "      <td>171.593002</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>14</td>\n",
              "      <td>158.847667</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>15</td>\n",
              "      <td>149.075941</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>16</td>\n",
              "      <td>140.596192</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>17</td>\n",
              "      <td>132.123856</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>18</td>\n",
              "      <td>121.749023</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>19</td>\n",
              "      <td>116.717319</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "    Cluster  inertia_values\n",
              "0         1     3079.684947\n",
              "1         2     1429.307759\n",
              "2         3      795.323612\n",
              "3         4      454.377870\n",
              "4         5      401.454471\n",
              "5         6      351.714817\n",
              "6         7      309.237462\n",
              "7         8      279.852455\n",
              "8         9      241.493756\n",
              "9        10      219.685627\n",
              "10       11      200.674450\n",
              "11       12      184.252310\n",
              "12       13      171.593002\n",
              "13       14      158.847667\n",
              "14       15      149.075941\n",
              "15       16      140.596192\n",
              "16       17      132.123856\n",
              "17       18      121.749023\n",
              "18       19      116.717319"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BKPzlZmPV2RF",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "adfabb41-9575-4cb0-95ef-170f5430388b"
      },
      "source": [
        "#We plot the inertia_values\n",
        "plt.scatter(df['Cluster'],df['inertia_values'])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f1831683710>"
            ]
          },
          "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": "markdown",
      "metadata": {
        "id": "VbA-IGpLYd2t"
      },
      "source": [
        "We have optimum 4 clusters since the maximum difference in the slope of the curve occurs at x=4 i.e. 4 clusters. We can interpret this as the max change of the first derivative of the curve i.e. the second derivative must be zero"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mF7RnSGTe330"
      },
      "source": [
        "# K-Means Implementation using sklearn library"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sa8J_VJWfc5T",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e38f4358-c227-4c7a-e082-6f8d8b8b5256"
      },
      "source": [
        "#We now implement the K-means Clustering algorithm for 4 clusters as obtained from the previous cell \n",
        "\n",
        "model = KMeans(n_clusters=4)   #store  KMeans in model\n",
        "model.fit(X)                   #Fit the data\n",
        "y_pred = model.predict(X)      #Predict the Y-values\n",
        "\n",
        "y_pred"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([2, 1, 0, 1, 3, 3, 2, 0, 1, 1, 2, 1, 0, 1, 3, 0, 0, 3, 2, 2, 3, 3,\n",
              "       0, 2, 2, 2, 3, 0, 2, 0, 1, 1, 0, 1, 1, 1, 1, 1, 2, 3, 0, 2, 1, 0,\n",
              "       2, 2, 1, 2, 1, 3, 2, 3, 1, 3, 3, 2, 1, 2, 1, 3, 1, 0, 1, 2, 2, 2,\n",
              "       1, 3, 1, 2, 0, 0, 1, 2, 2, 1, 2, 0, 3, 1, 3, 0, 3, 3, 1, 0, 3, 0,\n",
              "       1, 1, 0, 3, 1, 2, 2, 0, 3, 3, 0, 2, 1, 3, 1, 3, 0, 3, 3, 0, 1, 0,\n",
              "       2, 2, 3, 1, 3, 0, 1, 3, 3, 0, 2, 3, 2, 3, 3, 3, 3, 2, 3, 2, 1, 2,\n",
              "       2, 3, 1, 2, 2, 1, 2, 1, 1, 2, 0, 2, 0, 2, 1, 0, 1, 1, 1, 0, 0, 0,\n",
              "       3, 2, 1, 2, 3, 0, 1, 0, 0, 3, 0, 2, 2, 0, 3, 0, 0, 1, 3, 0, 2, 1,\n",
              "       3, 3, 0, 2, 3, 0, 2, 2, 0, 0, 0, 0, 3, 1, 2, 2, 0, 0, 2, 2, 2, 0,\n",
              "       2, 1, 0, 2, 3, 2, 0, 2, 2, 1, 0, 1, 0, 2, 0, 0, 1, 2, 2, 3, 3, 0,\n",
              "       1, 3, 3, 2, 3, 2, 2, 1, 1, 0, 0, 1, 0, 3, 2, 0, 3, 2, 1, 2, 3, 0,\n",
              "       3, 1, 1, 1, 1, 2, 2, 0, 0, 2, 3, 0, 2, 2, 0, 3, 3, 1, 0, 0, 2, 3,\n",
              "       1, 2, 0, 1, 0, 3, 3, 2, 2, 3, 3, 3, 3, 0, 1, 1, 3, 3, 0, 3, 3, 3,\n",
              "       1, 0, 1, 0, 3, 3, 1, 1, 1, 3, 3, 0, 1, 2], dtype=int32)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "N6ZOCgPAQ9qj",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0c1358a8-509c-4261-b82a-a61b08d39dc1"
      },
      "source": [
        "#Count the number of y_predicted values for each class\n",
        "pd.Series(y_pred).value_counts()  "
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2    78\n",
              "3    75\n",
              "0    74\n",
              "1    73\n",
              "dtype: int64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wm6x7vegV-sh",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "31bddc84-c83d-45b4-918f-b537cfb5d714"
      },
      "source": [
        "#Plot the predicted classes and centroids of clusters \n",
        "plt.scatter(X[:, 0], X[:, 1], c=y_pred)   #plotting the data points\n",
        "centers = model.cluster_centers_          #storing the centroids in centers\n",
        "plt.scatter(centers[:, 0], centers[:, 1],color='red')   #plotting centres"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7ff081778f98>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 26
        },
        {
          "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": "markdown",
      "metadata": {
        "id": "SGRn42FAelE1"
      },
      "source": [
        "# Algorithm from scratch"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kZos_DkugLUF"
      },
      "source": [
        "The algorithm of k-means clustering is based on the simple premise of Euclidean distances. Initially, we need to take the no. of clusters and the dataframe from the user. \r\n",
        "\r\n",
        "Step 1 - Randomly assign 'k' centroids i.e. k = no. of clusters\r\n",
        "\r\n",
        "Step 2 - Calculate the Euclidean distance between data-points and each of the  centroids. Assign the centroid having minimum distance to the datapoint\r\n",
        "\r\n",
        "Step 3 - Calcuate mean variance\r\n",
        "\r\n",
        "Step 4 - The mean of each of the clusters are the new centorids. Repeat step 2 with these new centroids. \r\n",
        "\r\n",
        "Step 5 - Repeat the above procedure until the mean variance of the newly assigned centroids is less than the previous mean variance. \r\n",
        "\r\n",
        "Note- ALthough the algorithm does not fit that nicely as optimization is not done. The main motive was the implementation of the algo giving considerable results."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hbatQUtrxzBN",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 419
        },
        "outputId": "68695c89-f50a-42d4-a24f-6933efd117fd"
      },
      "source": [
        "# We make a pandas dataframe out of the randomly generated dataset and name it as df.\n",
        "# The columns are named x and y based on their respective coordinates.\n",
        "# Another column 'clusters' is introduced indicating the cluster the datapoint belongs to\n",
        "\n",
        "df = pd.DataFrame(X, columns = ['x', 'y']) \n",
        "df['Clusters']=np.nan\n",
        "df"
      ],
      "execution_count": 3,
      "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>x</th>\n",
              "      <th>y</th>\n",
              "      <th>Clusters</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.227652</td>\n",
              "      <td>2.755707</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>-1.496359</td>\n",
              "      <td>7.196705</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1.244684</td>\n",
              "      <td>5.497535</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>-0.903797</td>\n",
              "      <td>7.804642</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0.879393</td>\n",
              "      <td>2.389981</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>295</th>\n",
              "      <td>1.932913</td>\n",
              "      <td>1.920866</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>296</th>\n",
              "      <td>2.749879</td>\n",
              "      <td>1.638817</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>297</th>\n",
              "      <td>0.170350</td>\n",
              "      <td>4.652000</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>298</th>\n",
              "      <td>1.178346</td>\n",
              "      <td>7.768928</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>299</th>\n",
              "      <td>-1.923734</td>\n",
              "      <td>2.665562</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>300 rows × 3 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "            x         y  Clusters\n",
              "0    0.227652  2.755707       NaN\n",
              "1   -1.496359  7.196705       NaN\n",
              "2    1.244684  5.497535       NaN\n",
              "3   -0.903797  7.804642       NaN\n",
              "4    0.879393  2.389981       NaN\n",
              "..        ...       ...       ...\n",
              "295  1.932913  1.920866       NaN\n",
              "296  2.749879  1.638817       NaN\n",
              "297  0.170350  4.652000       NaN\n",
              "298  1.178346  7.768928       NaN\n",
              "299 -1.923734  2.665562       NaN\n",
              "\n",
              "[300 rows x 3 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Qppuy3zxKqX7"
      },
      "source": [
        "# We define a function to randomly geenrate 'k' centroids from the dataframe 'df'\r\n",
        "# This function returns centroids dataframe which only contains the co-ordinates of the centroids\r\n",
        "\r\n",
        "def clustering(df,k):\r\n",
        "  centroids = df.sample(n=k)   #Select any k random points from the dataset\r\n",
        "  centroids = centroids.drop(columns='Clusters')    \r\n",
        "  return centroids"
      ],
      "execution_count": 15,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "T1Hnk2o6PTH3"
      },
      "source": [
        "# This function asssigns each of data point to any one of the 'k' centroids\r\n",
        "\r\n",
        "def assigning_clusters(centroids,df):\r\n",
        "  for i in range(len(df)):         \r\n",
        "    sum = []\r\n",
        "    for j in range(len(centroids)):           \r\n",
        "      sum.append((df.iat[i,0]-centroids.iat[j,0])**2 + (df.iat[i,1]-centroids.iat[j,1])**2)        #Calculating distance from each of the centroids\r\n",
        "    df.iat[i, 2] = sum.index(min(sum))   #Assigning the point to that centroid from which the distance is minimum\r\n",
        "  return (df)"
      ],
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "E8P1bcxuTuj4"
      },
      "source": [
        "# variance function is used to calculate the mean variance of all the datapoints\r\n",
        "\r\n",
        "def variance(df,centroids):\r\n",
        "  varaince_mean = sys.maxsize         #We initialize the varaince_mean with the maximum integer\r\n",
        "  # We now calulcate the variance for each of the datapoint. It is the square of the Euclidean distance between datapoint and its assigned centroid\r\n",
        "  for i in range(len(df)):            \r\n",
        "    varaince_mean = varaince_mean + (df.iat[i,0]-centroids.iat[int(df.iat[i,2]),0])**2 + (df.iat[i,1]-centroids.iat[int(df.iat[i,2]),1])**2\r\n",
        "  varaince_mean = varaince_mean/len(df)    #We caluclate the mean\r\n",
        "  return varaince_mean"
      ],
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9lyE1-bFVIKG"
      },
      "source": [
        "# Here, we integrate all the above defined functions into our final k_means\r\n",
        "\r\n",
        "def k_means(df,k):\r\n",
        "  centroids = clustering(df,k)                 #Randomly create the centroids\r\n",
        "  df = assigning_clusters(centroids,df)        #Assign the centroids\r\n",
        "  current_variance = variance(df,centroids)    #We caluclate the current varaince using the randomly assigned centroids\r\n",
        "  previous_variance = sys.maxsize              #for the first iteration, we just initialize the previous_variance to maximum integer\r\n",
        "  # In k means we have to iterate i.e. take the mean of the clusters until the variance starts to increase.\r\n",
        "  #  Hence we have compared the previous variance with the current one.\r\n",
        "  while (current_variance < previous_variance):\r\n",
        "    previous_variance = variance(df,centroids)\r\n",
        "    df = assigning_clusters(centroids,df)      #We form the clusters of datapoints\r\n",
        "    means = df.groupby('Clusters')             #We group the datapoints by clusters\r\n",
        "    centroids = means.mean()                   #The mean of the clusters so formed are the new centroids\r\n",
        "    current_variance = variance(df,centroids)  #The variance is calculated.\r\n",
        "  return centroids,df"
      ],
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zDR_1EJvWVr6",
        "outputId": "8232b6d7-0ad8-4f31-dae1-27f0ec343d12"
      },
      "source": [
        "# We call the k_means function and print the dataframe with the updated clusters\r\n",
        "centers,dataframe = k_means(df,4)\r\n",
        "print(dataframe)"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "            x         y  Clusters\n",
            "0    0.227652  2.755707       1.0\n",
            "1   -1.496359  7.196705       3.0\n",
            "2    1.244684  5.497535       2.0\n",
            "3   -0.903797  7.804642       3.0\n",
            "4    0.879393  2.389981       1.0\n",
            "..        ...       ...       ...\n",
            "295  1.932913  1.920866       2.0\n",
            "296  2.749879  1.638817       2.0\n",
            "297  0.170350  4.652000       3.0\n",
            "298  1.178346  7.768928       2.0\n",
            "299 -1.923734  2.665562       0.0\n",
            "\n",
            "[300 rows x 3 columns]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ix-n4GSnej-s",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "05320a3d-3409-4b53-fcba-5721f2515608"
      },
      "source": [
        "#Plot the predicted classes and centroids of clusters\r\n",
        "plt.scatter(df['x'], df['y'],c=df['Clusters'])   #plotting the data points\r\n",
        "plt.scatter(centers['x'], centers['y'],color='red')   #plotting centres"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7ff08a0a1c18>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 21
        },
        {
          "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": "xRRAxCQ7XbyW"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}