HW5_1_A_badinit.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "HW5-1-A.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": [],
      "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/yh08037/Introduction-to-Intelligent-Systems/blob/master/HW5_1_A_badinit.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sesRPeytWFjU",
        "colab_type": "text"
      },
      "source": [
        "# Lab 5-1  K-means\n",
        "## A) Clustering some synthetic data"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EuFggZMcAOg8",
        "colab_type": "text"
      },
      "source": [
        "### Loading data and Initialization"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XOXSgk_WWA1h",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "\n",
        "name_file = \"./data_kmeans.txt\"\n",
        "\n",
        "columns = ['x1', 'x2']\n",
        "\n",
        "x = np.asarray(pd.read_csv(name_file, names=columns, sep='\\t'))\n",
        "\n",
        "I, N = x.shape\n",
        "\n",
        "K = 3  # given\n",
        "\n",
        "y = np.zeros((I, 1))\n",
        "\n",
        "mu = np.random.uniform(-1, 9, (N, K))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jSrc90XnAKFl",
        "colab_type": "text"
      },
      "source": [
        "### Definition of distortion function"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tm3nV8xylo3e",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def distortion(x, mu):\n",
        "    \n",
        "    result = 0.\n",
        "    \n",
        "    _I = x.shape[0]\n",
        "    _K = mu.shape[1]\n",
        "    \n",
        "    for i in range(_I):\n",
        "        tmp = []\n",
        "        for k in range(_K):\n",
        "            tmp.append(np.linalg.norm(x[i]-mu[:, k]) ** 2)\n",
        "        _argmin = np.argmin(tmp)\n",
        "        for k in range(_K):\n",
        "            if k == _argmin:\n",
        "                result += tmp[_argmin]\n",
        "    return result"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VPRLZZxhAGZO",
        "colab_type": "text"
      },
      "source": [
        "### Training the model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XIdilhQWe02B",
        "colab_type": "code",
        "outputId": "9a5ff604-1255-46d1-f783-582d1e6d4e2c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "source": [
        "J_previous = 0.\n",
        "J_present = 0.\n",
        "\n",
        "epsilon = 0.0001\n",
        "cnt = 0\n",
        "\n",
        "mu_list = []\n",
        "\n",
        "while cnt < 1 or abs(J_present - J_previous) > epsilon:\n",
        "    for i in range(I):\n",
        "        tmp = []\n",
        "        for k in range(0, K):\n",
        "            tmp.append(np.linalg.norm(x[i]-mu[:, k]))\n",
        "        y[i] = np.argmin(tmp)\n",
        "\n",
        "    for k in range(K):\n",
        "        cnt1 = 0\n",
        "        mu[:, k] = np.zeros(N)\n",
        "        for i in range(I):\n",
        "            if y[i, 0] == k:\n",
        "                mu[:, k] += x[i]\n",
        "                cnt1 += 1\n",
        "        if cnt1 > 0:\n",
        "            mu[:, k] /= cnt1\n",
        "    \n",
        "    J_previous = J_present\n",
        "    J_present = distortion(x, mu)\n",
        "    cnt += 1\n",
        "    \n",
        "    print('iteration', cnt)\n",
        "    print(\"mu_k\\n\", (mu[0, 0], mu[1, 0]),'\\n', (mu[0, 1], mu[1, 1]),'\\n', (mu[0, 2], mu[1, 2]))\n",
        "    print('distortion\\n', J_present)\n",
        "    print()\n",
        "    \n",
        "    mu_list.append(mu.copy())\n",
        "    \n",
        "plt.rcParams[\"figure.figsize\"] = (10, 6)\n",
        "    \n",
        "\n",
        "plt.title('Trained model')        \n",
        "plt.plot(x[(y==0)[:,0]][:,0], x[(y==0)[:,0]][:,1], 'ro', label='cluster 0')\n",
        "plt.plot(x[(y==1)[:,0]][:,0], x[(y==1)[:,0]][:,1], 'bo', label='cluster 1')\n",
        "plt.plot(x[(y==2)[:,0]][:,0], x[(y==2)[:,0]][:,1], 'go', label='cluster 2')\n",
        "\n",
        "for i in range(cnt):\n",
        "    plt.plot(mu_list[i][0, 0], mu_list[i][1, 0], 'kx', markersize = 10)\n",
        "    plt.plot(mu_list[i][0, 1], mu_list[i][1, 1], 'kx', markersize = 10)\n",
        "    plt.plot(mu_list[i][0, 2], mu_list[i][1, 2], 'kx', markersize = 10)\n",
        "    \n",
        "plt.plot([mu_list[i][0][0] for i in range(cnt)], [mu_list[i][1][0] for i in range(cnt)], 'k')\n",
        "plt.plot([mu_list[i][0][1] for i in range(cnt)], [mu_list[i][1][1] for i in range(cnt)], 'k')\n",
        "plt.plot([mu_list[i][0][2] for i in range(cnt)], [mu_list[i][1][2] for i in range(cnt)], 'k')\n",
        "\n",
        "plt.legend()\n",
        "plt.show()\n",
        "\n",
        "print()\n",
        "print('TRAIN\\t | cluster 0\\t\\t | cluster 1\\t\\t | cluster 2\\t\\t | total')\n",
        "print('--------------------------------------------------------------------------------------------')\n",
        "print('number\\t | %d\\t\\t\\t | %d\\t\\t\\t | %d\\t\\t\\t | %d' %(x[(y==0)[:,0]].shape[0], \n",
        "                                       x[(y==1)[:,0]].shape[0], \n",
        "                                       x[(y==2)[:,0]].shape[0],\n",
        "                                       x.shape[0]))\n",
        "print('--------------------------------------------------------------------------------------------')\n",
        "print('mu_k\\t | (%f, %f)\\t | (%f, %f)\\t | (%f, %f)\\t |' %(mu[0, 0], mu[1, 0],\n",
        "                                                      mu[0, 1], mu[1, 1], \n",
        "                                                      mu[0, 2], mu[1, 2]))"
      ],
      "execution_count": 121,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "iteration 1\n",
            "mu_k\n",
            " (4.159811111111111, 5.109011111111111) \n",
            " (1.8450559782608695, 5.010477173913041) \n",
            " (4.5132127638190935, 1.9557056783919613)\n",
            "distortion\n",
            " 874.3584255746202\n",
            "\n",
            "iteration 2\n",
            "mu_k\n",
            " (3.7134, 5.0888375) \n",
            " (1.738459411764706, 5.0061599999999995) \n",
            " (4.5132127638190935, 1.9557056783919613)\n",
            "distortion\n",
            " 864.4886525762171\n",
            "\n",
            "iteration 3\n",
            "mu_k\n",
            " (3.4452, 5.0571125) \n",
            " (1.616865584415585, 5.007458441558441) \n",
            " (4.5132127638190935, 1.9557056783919613)\n",
            "distortion\n",
            " 860.2752404182435\n",
            "\n",
            "iteration 4\n",
            "mu_k\n",
            " (3.2740466666666674, 5.066586666666666) \n",
            " (1.5346767605633806, 4.999259154929578) \n",
            " (4.5132127638190935, 1.9557056783919613)\n",
            "distortion\n",
            " 858.708282009344\n",
            "\n",
            "iteration 5\n",
            "mu_k\n",
            " (3.2217156250000007, 5.058853124999999) \n",
            " (1.508529710144928, 5.000894202898551) \n",
            " (4.5132127638190935, 1.9557056783919613)\n",
            "distortion\n",
            " 858.43760188858\n",
            "\n",
            "iteration 6\n",
            "mu_k\n",
            " (3.1969454545454554, 5.057854545454545) \n",
            " (1.4953566176470592, 5.000526470588236) \n",
            " (4.5132127638190935, 1.9557056783919613)\n",
            "distortion\n",
            " 858.4055121975753\n",
            "\n",
            "iteration 7\n",
            "mu_k\n",
            " (3.1969454545454554, 5.057854545454545) \n",
            " (1.4953566176470592, 5.000526470588236) \n",
            " (4.5132127638190935, 1.9557056783919613)\n",
            "distortion\n",
            " 858.4055121975753\n",
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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w3XXXobm5GbfeeuuQoMrOt7/9bUyYMAGHDx/GlClT8MUvfjH3nbQhyfonf7W2tmqqap4o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\nRERERGSAQRMRERGRAQZNRERERAb+fxyudOqYQcNYAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "TRAIN\t | cluster 0\t\t | cluster 1\t\t | cluster 2\t\t | total\n",
            "--------------------------------------------------------------------------------------------\n",
            "number\t | 33\t\t\t | 68\t\t\t | 199\t\t\t | 300\n",
            "--------------------------------------------------------------------------------------------\n",
            "mu_k\t | (3.196945, 5.057855)\t | (1.495357, 5.000526)\t | (4.513213, 1.955706)\t |\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5Rs9QGXRAYy3",
        "colab_type": "text"
      },
      "source": [
        "### Generating test data and Prediction"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DbR4acaK-lv9",
        "colab_type": "code",
        "outputId": "5225156d-88c6-47b8-fbb0-323f66bd783b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 460
        }
      },
      "source": [
        "\n",
        "I_test = 100\n",
        "\n",
        "N_test = 2\n",
        "\n",
        "x_test = np.hstack((np.random.uniform(-1, 9, (I_test, 1)), np.random.uniform(0, 7, (I_test, 1))))\n",
        "                           \n",
        "y_test = np.zeros((I_test, 1))\n",
        "\n",
        "\n",
        "for i in range(I_test):\n",
        "    tmp = []\n",
        "    for k in range(0, K):\n",
        "        tmp.append(np.linalg.norm(x_test[i]-mu[:, k]))\n",
        "    y_test[i] = np.argmin(tmp)\n",
        "    \n",
        "plt.title('Generated Test Data')\n",
        "plt.plot(x_test[(y_test==0)[:,0]][:,0], x_test[(y_test==0)[:,0]][:,1], 'ro')\n",
        "plt.plot(x_test[(y_test==1)[:,0]][:,0], x_test[(y_test==1)[:,0]][:,1], 'bo')\n",
        "plt.plot(x_test[(y_test==2)[:,0]][:,0], x_test[(y_test==2)[:,0]][:,1], 'go')\n",
        "plt.show()\n",
        "\n",
        "print()\n",
        "print('TEST\\t | cluster 0\\t | cluster 1\\t | cluster 2\\t | total')\n",
        "print('------------------------------------------------------------------------')\n",
        "print('number\\t | %d\\t\\t | %d\\t\\t | %d\\t\\t | %d' %(x_test[(y_test==0)[:,0]].shape[0], \n",
        "                                       x_test[(y_test==1)[:,0]].shape[0], \n",
        "                                       x_test[(y_test==2)[:,0]].shape[0],\n",
        "                                       x_test.shape[0]))\n"
      ],
      "execution_count": 122,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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9rQhNQIrYsBHAGFbXd5+6H3W9qlg9B6Sq1SIkAcilPl9Xf72/63WcRqUJAICK6x7pqnZo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\nJgAAgBz+P6c8nmjb0rxYAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "TEST\t | cluster 0\t | cluster 1\t | cluster 2\t | total\n",
            "------------------------------------------------------------------------\n",
            "number\t | 24\t\t | 26\t\t | 50\t\t | 100\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sCB2Ah0kAvM5",
        "colab_type": "text"
      },
      "source": [
        "### Ploting train / test data and decision boundary"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RHAV_hJCNbi7",
        "colab_type": "code",
        "outputId": "a64258c8-1b8b-4592-9c74-0b23fe1e3bc9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 762
        }
      },
      "source": [
        "X, Y = np.meshgrid(np.linspace(-1, 9, 100), np.linspace(0, 7, 70))\n",
        "\n",
        "Z = np.empty((70, 100))\n",
        "\n",
        "for i in range(70):\n",
        "    for j in range(100):\n",
        "        tmp = []\n",
        "        for k in range(0, K):\n",
        "            tmp.append(np.linalg.norm(np.asarray([X[i, j], Y[i, j]]) - mu[:, k]))\n",
        "        Z[i, j] = np.argmin(tmp)\n",
        "        \n",
        "        \n",
        "plt.title('Train Data and Traind Decision Boundary')    \n",
        "plt.contour(X, Y, Z, colors='grey')       \n",
        "plt.plot(x[(y==0)[:,0]][:,0], x[(y==0)[:,0]][:,1], 'ro', label='cluster 0')\n",
        "plt.plot(x[(y==1)[:,0]][:,0], x[(y==1)[:,0]][:,1], 'bo', label='cluster 1')\n",
        "plt.plot(x[(y==2)[:,0]][:,0], x[(y==2)[:,0]][:,1], 'go', label='cluster 2')\n",
        "plt.legend()\n",
        "plt.show()\n",
        "\n",
        "\n",
        "plt.title('Test Data and Trained Decision Boundary')\n",
        "plt.contour(X, Y, Z, colors='grey') \n",
        "plt.plot(x_test[(y_test==0)[:,0]][:,0], x_test[(y_test==0)[:,0]][:,1], 'ro', label='cluster 0')\n",
        "plt.plot(x_test[(y_test==1)[:,0]][:,0], x_test[(y_test==1)[:,0]][:,1], 'bo', label='cluster 1')\n",
        "plt.plot(x_test[(y_test==2)[:,0]][:,0], x_test[(y_test==2)[:,0]][:,1], 'go', label='cluster 2')\n",
        "plt.show()"
      ],
      "execution_count": 123,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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lS5fw9NNPe9egcMV8HCKysfck7du3z/AxIoIRI0YguX09GB1JSUkYOHBgW49+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\n8GjXFjCpBF9bDmxB3k/yIH4skPeTPGw5sEXpeC09LXGzTMD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A1gHY7+ywiIiIiNwlaaZJ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\nRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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QSkr8jwXwFzyZk5Xeo2R67GkiiheRzEPiL3giikMMmiyAM7spIiKdh+R0AlVVgMejXTJg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\nSZIkNbA0SZIkNbA0SZIkNbA0SZIkNfgFew6GzRetOFoAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}