5.Logistic Regression.ipynb

{
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  "metadata": {
    "colab": {
      "name": "assignment05.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sQy9EvTe1J6q",
        "colab_type": "text"
      },
      "source": [
        "### **0. Preparation**\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YgZQmLLx1HWI",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import copy\n",
        "import math\n",
        "import csv\n",
        "from collections import deque\n",
        "from google.colab import files\n",
        "from mpl_toolkits.mplot3d import Axes3D\n",
        "from matplotlib import cm\n",
        "from matplotlib.ticker import LinearLocator, FormatStrFormatter"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oDTD9ppr1OAX",
        "colab_type": "text"
      },
      "source": [
        "### **1. Input Data**\n",
        "load the training data file ('data.txt')  \n",
        "each row $\\{ (x^{(i)}, y^{(i)}, l^{(i)}) \\}$ of the data consists of a 2-dimensional point $(x, y)$ with its label $l$  \n",
        "$x, y \\in \\mathbb{R}$ and $l \\in \\{0, 1\\}$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XjbPUG9E1Tie",
        "colab_type": "code",
        "outputId": "5441abcc-0df0-4f72-f90f-7cdd8a343fb9",
        "colab": {
          "resources": {
            "http://localhost:8080/nbextensions/google.colab/files.js": {
              "data": 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              "ok": true,
              "headers": [
                [
                  "content-type",
                  "application/javascript"
                ]
              ],
              "status": 200,
              "status_text": ""
            }
          },
          "base_uri": "https://localhost:8080/",
          "height": 78
        }
      },
      "source": [
        "uploaded = files.upload()"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "\n",
              "     <input type=\"file\" id=\"files-024b39a7-871f-4c64-aff1-9ea06835a666\" name=\"files[]\" multiple disabled />\n",
              "     <output id=\"result-024b39a7-871f-4c64-aff1-9ea06835a666\">\n",
              "      Upload widget is only available when the cell has been executed in the\n",
              "      current browser session. Please rerun this cell to enable.\n",
              "      </output>\n",
              "      <script src=\"/nbextensions/google.colab/files.js\"></script> "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Saving data.txt to data.txt\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MFaPtak-zpwW",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 501
        },
        "outputId": "1788b170-80bb-4fb0-ba3b-ae38a94232d4"
      },
      "source": [
        "data = np.genfromtxt(\"data.txt\", delimiter=',')\n",
        "x = data[:, 0]\n",
        "y = data[:, 1]\n",
        "label = data[:, 2]\n",
        "x_label0 = x[label == 0]\n",
        "x_label1 = x[label == 1]\n",
        "y_label0 = y[label == 0]\n",
        "y_label1 = y[label == 1]\n",
        "\n",
        "print(\"Plotting the training data\")\n",
        "plt.figure(figsize=(8, 8))\n",
        "plt.scatter(x_label0, y_label0, alpha=0.3, c='b')\n",
        "plt.scatter(x_label1, y_label1, alpha=0.3, c='r')\n",
        "plt.show()\n",
        "\n",
        "#print(len(x)) #100\n",
        "#print(type(x))\n",
        "#print(y_label0)\n",
        "#print(type(x_label0))"
      ],
      "execution_count": 108,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Plotting the training data\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 576x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Cw4DKfx74hAg",
        "colab_type": "text"
      },
      "source": [
        "### **2. Logistic Regression**\n",
        "1) Linear Model\n",
        "<br>\n",
        "$\\ z = \\theta_0 + \\theta_1x + \\theta_2y  $  \n",
        "$\\sigma(z) = \\frac{1}{1 + \\exp(-z)}$\n",
        "<br>  \n",
        "2) Objective Function\n",
        "<br>\n",
        "$\\ J(\\theta_0, \\theta_1, \\theta_2) = \\frac{1}{m} \\sum_{i=1}^m ( - l^{(i)} \\log(\\sigma(z^{(i)})) - (1 - l^{(i)}) \\log(1 - \\sigma(z^{(i)}))  )$\n",
        "<br>  \n",
        "3) Gradient Descent\n",
        "<br>\n",
        "$\\ \\theta_0^{(t+1)} = \\theta_0^{(t)} - \\alpha \\frac{1}{m} \\sum_{i=1}^{m} (\\sigma(z^{(i)}) - l^{(i)})$  \n",
        "$\\ \\theta_1^{(t+1)} = \\theta_1^{(t)} - \\alpha \\frac{1}{m} \\sum_{i=1}^{m} (\\sigma(z^{(i)}) - l^{(i)}) x^{(i)}$  \n",
        "$\\ \\theta_2^{(t+1)} = \\theta_2^{(t)} - \\alpha \\frac{1}{m} \\sum_{i=1}^{m} (\\sigma(z^{(i)}) - l^{(i)}) y^{(i)}$  \n",
        "<br>\n",
        "4) HyperParameters Setting\n",
        "<br>\n",
        "$\\ \\theta_0^{(0)} = -10$  \n",
        "$\\ \\theta_1^{(0)} = 20$  \n",
        "$\\ \\theta_2^{(0)} = -10$\n",
        "<br>\n",
        "$\\ lr = 2*10^{-2}$\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "b8ZdZ71zkyiN",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def sigmoidFunction(z):\n",
        "  result = 1/(1 + math.e**-z)\n",
        "  return result"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3-gCevCjgKyl",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def objectiveFunction(x_data, y_data, class_data, theta_0, theta_1, theta_2):\n",
        "  cost = 0\n",
        "  predictions = deque()\n",
        "  for i in range(0, 100):\n",
        "    estimate = sigmoidFunction(theta_0 + theta_1 * x_data[i] + theta_2 * y_data[i])\n",
        "    #print(\"Estimate\",estimate)\n",
        "    predictions.append((-class_data[i]*np.log10(estimate)) - (1-class_data[i])*np.log10(1-estimate))\n",
        "    #print(\"predictions\",predictions)\n",
        "  cost = np.sum(predictions) / 100\n",
        "  #print(\"Cost\",i,\"번째\",cost)\n",
        "  return cost"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NsaVBnlHiAys",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def gradientDescent(x_data, y_data, class_data, theta_0, theta_1, theta_2):\n",
        "  for i in range(0, 100):\n",
        "    lr = 0.02\n",
        "    estimate = sigmoidFunction(theta_0 + theta_1 * x_data[i] + theta_2 * y_data[i]) - class_data[i]\n",
        "    theta_0 -= lr * estimate / 100\n",
        "    theta_1 -= lr * estimate * x_data[i] / 100\n",
        "    theta_2 -= lr * estimate * y_data[i] / 100\n",
        "  return theta_0, theta_1, theta_2"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nKROWnxQlgsK",
        "colab_type": "code",
        "outputId": "40059984-bef4-4d44-9d13-d5448e09631b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 938
        }
      },
      "source": [
        "def main():\n",
        "  theta_0,theta_1,theta_2 = 100, 20, 10  #Initialization\n",
        "  train_costs = deque()\n",
        "  theta_0s = deque()\n",
        "  theta_1s = deque()\n",
        "  theta_2s = deque()\n",
        "  iters = deque()\n",
        "\n",
        "  for iter in range(0, 600000):\n",
        "    train_value = objectiveFunction(x, y, label, theta_0, theta_1, theta_2)\n",
        "    #train data 수집\n",
        "    train_costs.append(train_value)\n",
        "    theta_0, theta_1, theta_2 = gradientDescent(x, y, label, theta_0, theta_1, theta_2)\n",
        "    #test_value = objectiveFunction(test_data, theta_0, theta_1, theta_2, theta_3)\n",
        "\n",
        "    #data 수집\n",
        "    iters.append(iter)\n",
        "    theta_0s.append(theta_0)\n",
        "    theta_1s.append(theta_1)\n",
        "    theta_2s.append(theta_2)\n",
        "\n",
        "  print(theta_0, theta_1, theta_2)\n",
        "  print(\"Plotting the Estimated Parameters\")\n",
        "  fig = plt.figure()\n",
        "  graph1 = plt.plot(iters, theta_0s, 'r')\n",
        "  graph2 = plt.plot(iters, theta_1s, 'g', linewidth = 3, linestyle=(0, (5, 2, 1, 2)), dash_capstyle='round')\n",
        "  graph3 = plt.plot(iters, theta_2s, 'b')\n",
        "  plt.xlabel('iterations')\n",
        "  plt.ylabel('value')\n",
        "  plt.show()\n",
        "\n",
        "  print(\"Plotting the Training Error\")\n",
        "  plt.plot(iters, train_costs, 'b')\n",
        "  plt.xlabel('iteration')\n",
        "  plt.ylabel('Traing Error')\n",
        "  plt.show()\n",
        "\n",
        "  print(\"Plotting the Obtained Classifer\")\n",
        "  points = np.arange(30,100,0.5)\n",
        "  xs,ys = np.meshgrid(points, points)\n",
        "  z = theta_0 + theta_1 * xs + theta_2 * ys\n",
        "  z = sigmoidFunction(z)\n",
        "\n",
        "  fig = plt.figure()\n",
        "  plt.xlim([30,100])\n",
        "  plt.ylim([30,100])\n",
        "  graph4 = plt.imshow(z, cmap=plt.cm.bwr)\n",
        "  graph5 = plt.scatter(x_label0, y_label0, alpha=0.3, c='b')\n",
        "  graph6 = plt.scatter(x_label1, y_label1, alpha=0.3, c='r')\n",
        "  plt.show()\n",
        "\n",
        "if __name__ == \"__main__\":\n",
        "  main()"
      ],
      "execution_count": 106,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:7: RuntimeWarning: divide by zero encountered in log10\n",
            "  import sys\n",
            "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:7: RuntimeWarning: invalid value encountered in double_scalars\n",
            "  import sys\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "-28.03007647003962 0.2381632703372477 0.23789339324722206\n",
            "Plotting the Estimated Parameters\n"
          ],
          "name": "stdout"
        },
        {
          "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": "stream",
          "text": [
            "Plotting the Training Error\n"
          ],
          "name": "stdout"
        },
        {
          "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": "stream",
          "text": [
            "Plotting the Obtained Classifer\n"
          ],
          "name": "stdout"
        },
        {
          "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"
          }
        }
      ]
    }
  ]
}