Clustering.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Clustering.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "LPdfdQ3zodTX",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "from sklearn.preprocessing import normalize\n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn.metrics.pairwise import euclidean_distances\n",
        "import sys"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Dow-2sixm48z",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def kMeans(data, k=2):\n",
        "  st = True\n",
        "  iter = 0\n",
        "  centroids = np.zeros((k, np.size(data,1)))\n",
        "  numOfSamples = len(data)\n",
        "  newData = np.zeros((numOfSamples, np.size(data,1)+1))\n",
        "  randomIndex = np.random.randint(numOfSamples, size=k)\n",
        "  centroids = data[randomIndex,:]\n",
        "  newData[:,:-1] = data\n",
        "\n",
        "  while st:\n",
        "    iter += 1\n",
        "    for i in range(numOfSamples):\n",
        "      EuclideanDis = np.zeros(k)\n",
        "      for j in range(len(centroids)):\n",
        "        EuclideanDis[j] = np.linalg.norm(newData[i,:-1]-centroids[j,:])\n",
        "      cluster = np.argmin(EuclideanDis) + 1\n",
        "      newData[i,-1] = cluster\n",
        "      centroids[cluster-1] = np.mean(newData[newData[:,-1] == cluster, :-1], axis=0)\n",
        "    \n",
        "    if(iter == 50):\n",
        "      st = False\n",
        "\n",
        "  return newData"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "H2vUkdp178FS",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def hierarchicalClustering(data, linkage, numOfClusters):\n",
        "    eucDistances = euclidean_distances(data, data)\n",
        "    np.fill_diagonal(eucDistances,sys.maxsize)\n",
        "    clusters = findClusters(eucDistances, linkage) \n",
        "    clusterIndice = eucDistances.shape[0] - numOfClusters\n",
        "    dataClusters = clusters[clusterIndice]\n",
        "    \n",
        "    return dataClusters"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "r-BHiqTd7_E7",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def findClusters(input, linkage):\n",
        "    clusters = {}\n",
        "    rowIndex = -1\n",
        "    colIndex = -1\n",
        "    indices = list(range(input.shape[0]))\n",
        "        \n",
        "    clusters[0] = indices.copy()\n",
        "\n",
        "    for k in range(1, input.shape[0]):      \n",
        "        result = np.where(input == np.amin(input))\n",
        "        listOfCordinates = list(zip(result[0], result[1]))\n",
        "        cords = []\n",
        "        for cord in listOfCordinates:\n",
        "          if cord[0] < cord[1]:\n",
        "            cords.append(cord)\n",
        "        candidate = cords[np.random.choice(len(cords))]\n",
        "        rowIndex = candidate[1]\n",
        "        colIndex = candidate[0]\n",
        "\n",
        "        if(linkage == \"single\"):\n",
        "            temp = np.minimum(input[colIndex,:], input[rowIndex,:])\n",
        "            input[colIndex,0:colIndex] = temp[0:colIndex]\n",
        "            input[colIndex,colIndex+1:] = temp[colIndex+1:]\n",
        "            input[0:colIndex,colIndex] = temp[0:colIndex]\n",
        "            input[colIndex+1:,colIndex] = temp[colIndex+1:]\n",
        "        elif(linkage == \"complete\"):\n",
        "            temp = np.maximum(input[colIndex,:], input[rowIndex,:])\n",
        "            input[colIndex,0:colIndex] = temp[0:colIndex]\n",
        "            input[colIndex,colIndex+1:] = temp[colIndex+1:]\n",
        "            input[0:colIndex,colIndex] = temp[0:colIndex]\n",
        "            input[colIndex+1:,colIndex] = temp[colIndex+1:]\n",
        "        elif(linkage == \"average\"):\n",
        "            temp = (np.array(input[colIndex,:]) + np.array(input[rowIndex,:])) / 2.0\n",
        "            input[colIndex,0:colIndex] = temp[0:colIndex]\n",
        "            input[colIndex,colIndex+1:] = temp[colIndex+1:]\n",
        "            input[0:colIndex,colIndex] = temp[0:colIndex]\n",
        "            input[colIndex+1:,colIndex] = temp[colIndex+1:]\n",
        "                   \n",
        "        input[rowIndex,:] = sys.maxsize\n",
        "        input[:,rowIndex] = sys.maxsize\n",
        "            \n",
        "        minimum = min(rowIndex,colIndex)\n",
        "        maximum = max(rowIndex,colIndex)\n",
        "        for n in range(len(indices)):\n",
        "            \n",
        "            if(indices[n]==maximum):\n",
        "                indices[n] = minimum\n",
        "        \n",
        "        clusters[k] = indices.copy()\n",
        "\n",
        "    return clusters"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aMtymNRJjgPv",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "data_dir = '/content/gdrive/My Drive/Colab Notebooks/Dataset/'\n",
        "data = np.genfromtxt(data_dir + 'iris.txt', dtype='str')\n",
        "data = np.delete(data, np.size(data,1)-1, 1)\n",
        "data = data.astype(float)"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ox_1X-IKZsN4",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "K = 3\n",
        "sLink = hierarchicalClustering(data,\"single\",K)\n",
        "cLink = hierarchicalClustering(data,\"complete\",K)\n",
        "aLink = hierarchicalClustering(data,\"average\",K)"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kyUZODYCvJNc",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "2e5b83a8-e0a0-4856-ceb2-e41312a00867"
      },
      "source": [
        "hierarchicalMethods = {0: [sLink, 'Sigle-Link'],\n",
        "                       1: [cLink, 'Complete-Link'],\n",
        "                       2: [aLink, 'Average-Link']}\n",
        "\n",
        "for h in range(0,len(hierarchicalMethods)):\n",
        "  newData = np.zeros((len(data), np.size(data,1)+1))\n",
        "  newData[:,:-1] = data\n",
        "  cl = hierarchicalMethods[h][0]\n",
        "  newData[:,-1] = cl\n",
        "  uniqueClusters = np.unique(cl)\n",
        "  separatedByClus = {}\n",
        "  for o in uniqueClusters:\n",
        "    separatedByClus[o] = newData[newData[:,-1] == o, :-1]\n",
        "    temp = np.asarray(separatedByClus[o])\n",
        "    plt.scatter(temp[:,0],temp[:,1])\n",
        "    plt.title(hierarchicalMethods[h][1])\n",
        "  plt.show()\n",
        "\n",
        "cl = kMeans(data, k=K)\n",
        "separatedByClus = {}\n",
        "for i in range(1,K+1):\n",
        "  separatedByClus[i] = cl[cl[:,-1] == i, :-1]\n",
        "  temp = np.asarray(separatedByClus[i])\n",
        "  plt.scatter(temp[:,0],temp[:,1])\n",
        "  plt.title('K-Means')\n",
        "plt.show()"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "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"
          }
        },
        {
          "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"
          }
        },
        {
          "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"
          }
        }
      ]
    }
  ]
}