assignment7-06.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Untitled7.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyPog5VEmG36b6ueRslwXRlI",
      "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/dlguswn3659/class-MachineLearning/blob/master/assignment7-06.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aWciEeRVYExZ",
        "colab_type": "code",
        "outputId": "315daa32-d096-4d80-df28-70a326350a25",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        }
      },
      "source": [
        "%matplotlib inline\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import matplotlib as mpl\n",
        "import seaborn as sns\n",
        "import matplotlib.animation as animation\n",
        "from scipy import stats \n",
        "from mpl_toolkits.mplot3d import Axes3D\n",
        "from sklearn.datasets.samples_generator import make_regression \n",
        "import csv\n",
        "import math\n",
        "# from google.colab import files\n",
        "\n",
        "# uploaded = files.upload()\n",
        "\n",
        "data    = np.genfromtxt(\"data-nonlinear.txt\", delimiter=',')\n",
        "\n",
        "pointX  = data[:, 0]\n",
        "pointY  = data[:, 1]\n",
        "label   = data[:, 2]\n",
        "\n",
        "pointX0 = pointX[label == 0]\n",
        "pointY0 = pointY[label == 0]\n",
        "\n",
        "pointX1 = pointX[label == 1]\n",
        "pointY1 = pointY[label == 1]\n",
        "\n",
        "# plt.figure()\n",
        "# plt.scatter(pointX0, pointY0, c='b')\n",
        "# plt.scatter(pointX1, pointY1, c='r')\n",
        "# plt.tight_layout()\n",
        "# plt.gca().set_aspect('equal', adjustable='box')\n",
        "# plt.show()"
      ],
      "execution_count": 28,
      "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"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "58zKkl42YJtc",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "X = pointX #전체 x\n",
        "y = np.array(pointY,dtype=float)\n",
        "label = np.array(label,dtype=float)\n",
        "# print(len(y))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qf2fl-SPHcvh",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def g_function(X, y, theta, it, i):\n",
        "  result = 0\n",
        "  for m in range(0, 10): \n",
        "    for n in range(0, 10):\n",
        "      result = result + theta[m*10 + n][it]*(X[i]**m)*(y[i]**n)\n",
        "\n",
        "  return result\n",
        "  # return  (theta[0][it] + theta[1][it]*X[i] + theta[2][it]*y[i] + theta[3][it]*X[i]*X[i] +\n",
        "  #         theta[4][it]*X[i]*y[i] + theta[5][it]*y[i]*y[i] + theta[6][it]*X[i]*X[i]*X[i] + theta[7][it]*X[i]*X[i]*y[i] +\n",
        "  #         theta[8][it]*X[i]*y[i]*y[i] + theta[9][it]*y[i]*y[i]*y[i] + theta[10][it]*X[i]*X[i]*X[i]*X[i] + theta[11][it]*X[i]*X[i]*X[i]*y[i] +\n",
        "  #         theta[12][it]*X[i]*X[i]*y[i]*y[i] + theta[13][it]*X[i]*y[i]*y[i]*y[i] + theta[14][it]*y[i]*y[i]*y[i]*y[i] \n",
        "  #         #  + theta[15][it]*X[i]*X[i]*X[i]*X[i]*X[i]\n",
        "  #          )"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xW6_W-uWHeGe",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def gradient_descent(X,y,label,theta,learning_rate,iterations, controller):\n",
        "    \n",
        "    m = len(y)\n",
        "\n",
        "    cost_history = np.zeros(iterations)\n",
        "    theta_history = np.zeros((iterations,100))\n",
        "    \n",
        "    differential_g_function = np.zeros(100)\n",
        "\n",
        "    for it in range(iterations):\n",
        "        print(it)\n",
        "        pred = 0\n",
        "        preds = np.zeros(100)\n",
        "        sum_theta = 0\n",
        "\n",
        "        for i in range(0, m):\n",
        "          for p in range(0, 10): \n",
        "            for n in range(0, 10):\n",
        "              differential_g_function[p*10 + n] = (X[i]**p)*(y[i]**n)\n",
        "          # print(i)\n",
        "          #cost 함수\n",
        "          # print('100바퀴 이거 오래걸리나?')\n",
        "          pred = pred + ((-1)*label[i]*math.log(1/(1 + math.exp((-1)*g_function(X, y, theta, it, i))))-((1-label[i])*math.log(1 + (-1)*(1/(1 + math.exp((-1)*g_function(X, y, theta, it, i)))))))\n",
        "          \n",
        "          #  σ(z)   =    (1/(1 + math.exp((-1)*(theta[0][it] + theta[1][it]*X[i] + theta[2][it]*y[i]))))\n",
        "\n",
        "          #theta함수\n",
        "          for j in range(0, 100):\n",
        "            preds[j] = preds[j] + ((1/(1 + math.exp((-1)*g_function(X, y, theta, it, i)))) - label[i])*differential_g_function[j]\n",
        "            # (y[i]**(j%10))\n",
        "        \n",
        "        for i in range(0, 100):\n",
        "          theta[i][it + 1] = theta[i][it] - learning_rate*((1/m)*preds[i] + controller*theta[i][it])\n",
        "          # print(theta[i][it])\n",
        "        # print('100바퀴 이거 오래걸리나?')\n",
        "\n",
        "        for i in range(0, 100):\n",
        "          theta_history[it][i] = theta[i][it]\n",
        "\n",
        "        for p in range(0, 10): \n",
        "          for n in range(0, 10):\n",
        "            sum_theta = sum_theta + (theta[p*10 + n][it]**2)\n",
        "            # print(theta[p*10 + n][it]**2)\n",
        "\n",
        "        # print(controller)\n",
        "        # print(sum_theta)\n",
        "        # print(pred)\n",
        "        cost_history[it]  = (1/m) * pred + (controller/2)*sum_theta\n",
        "        print(cost_history[it])\n",
        "        \n",
        "    return theta, cost_history, theta_history"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3DHApwKLHfn1",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 15563
        },
        "outputId": "aba27b65-a1c6-4802-ebb2-2d870ffdde3a"
      },
      "source": [
        "lr =0.5\n",
        "n_iter = 150\n",
        "\n",
        "theta = np.zeros((150, n_iter + 1))\n",
        "theta2 = np.zeros((150, n_iter + 1))  \n",
        "theta3 = np.zeros((150, n_iter + 1))  \n",
        "\n",
        "X_b = np.c_[np.ones((len(X),0)),X]\n",
        "X_b = np.array(X_b,dtype=float)\n",
        "# print(X_b.shape)\n",
        "# print(X_b.dtype)\n",
        "# print(y.dtype)\n",
        "control_lambda1 = 0.00000001\n",
        "theta,cost_history,theta_history = gradient_descent(X_b,y,label,theta,lr,n_iter, control_lambda1)\n",
        "\n",
        "control_lambda2 = 1\n",
        "theta2,cost_history2,theta_history2 = gradient_descent(X_b,y,label,theta,lr,n_iter, control_lambda2)\n",
        "\n",
        "lr =0.0001\n",
        "control_lambda3 = 1000\n",
        "theta3,cost_history3,theta_history3 = gradient_descent(X_b,y,label,theta,lr,n_iter, control_lambda3)"
      ],
      "execution_count": 32,
      "outputs": [
        {
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          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fO0weclTHhcP",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 515
        },
        "outputId": "f88f6d9d-2e6e-4074-df92-e657d65fc3c6"
      },
      "source": [
        "fig,ax = plt.subplots(figsize=(12,8))\n",
        "\n",
        "print(cost_history[1])\n",
        "\n",
        "ax.set_ylabel('J(Theta)')\n",
        "ax.set_xlabel('Iterations')\n",
        "_=ax.plot(range(n_iter),cost_history,'b.', color = 'red')\n",
        "_=ax.plot(range(n_iter),cost_history2,'b.', color = 'green')\n",
        "_=ax.plot(range(n_iter),cost_history3,'b.', color = 'blue')"
      ],
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.6843243600903024\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lGWP5Xo5YObd",
        "colab_type": "code",
        "outputId": "db35ad86-9a17-4397-ae24-453dde6edb74",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "%pylab inline \n",
        "import numpy as np \n",
        "import pandas as pd \n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Populating the interactive namespace from numpy and matplotlib\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4DzEGNiHYO6s",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def sigmoid(z): \n",
        "  g = 1 / (1 + np.exp(-z)) \n",
        "  \n",
        "  return g \n",
        "  \n",
        "# print('sigmoid(10) = %s, sigmoid(-10) = %s, sigmoid(0) = %s' % (sigmoid(10), sigmoid(-10), sigmoid(0)))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dIzxEx3rYP4s",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "416e252c-f38e-46b5-de1f-9b0bef793620"
      },
      "source": [
        "def mapFeature(X1, X2): \n",
        "  degree =  9\n",
        "  #print(X1.shape) \n",
        "  m = np.size(X1) \n",
        "  # out = np.ones(m) \n",
        "  res = [] \n",
        "  \n",
        "  # res.append(out) \n",
        "  \n",
        "  for i in np.arange(0, degree + 1): \n",
        "    for j in np.arange(0, degree + 1): \n",
        "      out1 = (X1 ** i) * (X2 ** j) \n",
        "      res.append(out1) \n",
        "      \n",
        "  return np.array(res).T \n",
        "\n",
        "data = matrix(data)\n",
        "\n",
        "X = data[:, 0:2] \n",
        "y = data[:, 2] \n",
        "\n",
        "X = np.array(X)\n",
        "y = np.array(y)\n",
        "      \n",
        "X_reg = mapFeature(X[:, 0], X[:, 1]) \n",
        "# print(X_reg[0:2, :])\n",
        "print(X_reg.shape)"
      ],
      "execution_count": 63,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(118, 100)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xkjwGxvsYQ7m",
        "colab_type": "code",
        "outputId": "a56dba47-3ef9-479d-af5f-8afea2390807",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 138
        }
      },
      "source": [
        "import scipy.optimize as op \n",
        "\n",
        "def myCostReg(theta, X, y, s_lambda): \n",
        "  \n",
        "  X = matrix(X) \n",
        "\n",
        "  J = 0 \n",
        "  grad = np.zeros(np.size(theta)) \n",
        "  m, n = X.shape \n",
        "  y = y.reshape((m, 1)) \n",
        "  theta = theta.reshape((n, 1)) \n",
        "\n",
        "  theta_0 = theta[0] \n",
        "  theta_j = theta[1:] \n",
        "\n",
        "  theta = np.matrix(theta) \n",
        "  sum_theta_square = np.sum(theta_j ** 2) \n",
        "  predictions = X * theta \n",
        "  sig_term = sigmoid(predictions)\n",
        "\n",
        "  J = 1/m * sum(np.multiply(-y, log(sig_term)) - np.multiply((1 - y), log(1 - sig_term))) + s_lambda / (2 * m) * sum_theta_square \n",
        "  \n",
        "  return J \n",
        "  \n",
        "def myGradientReg(theta, X, y, s_lambda): \n",
        " \n",
        "  X = matrix(X) \n",
        "\n",
        "  J = 0 \n",
        "  grad = np.zeros(np.size(theta)) \n",
        "  m, n = X.shape \n",
        "  y = y.reshape((m, 1)) \n",
        "  theta = theta.reshape((n, 1)) \n",
        "\n",
        "  theta_0 = theta[0] \n",
        "  theta_j = theta[1:] \n",
        " \n",
        "  theta = np.matrix(theta) \n",
        "\n",
        "  predictions = X * theta \n",
        "  sig_term = sigmoid(predictions) \n",
        "\n",
        "  errors = (sig_term - y) \n",
        "\n",
        "  delta_0 = 1/m * errors.T * X[:, 0] \n",
        "\n",
        "  delta = 1/m * errors.T * X[:, 1:]\n",
        "\n",
        "  regular = s_lambda / m * theta_j \n",
        "  delta_j = delta.T + regular \n",
        "  grad[0] = delta_0 \n",
        "  grad[1:] = delta_j.T \n",
        "   \n",
        "  return grad.flatten() \n",
        "   \n",
        "initial_theta = np.zeros((X_reg.shape[1], 1)) \n",
        "\n",
        "s_lambda = 0.00000001\n",
        "Result = op.minimize(fun = myCostReg, x0 = initial_theta, args = (X_reg, y, s_lambda), method = 'TNC', jac = myGradientReg); \n",
        "cost = Result.fun \n",
        "theta = Result.x \n",
        "\n",
        "s_lambda2 = 1 \n",
        "Result2 = op.minimize(fun = myCostReg, x0 = initial_theta, args = (X_reg, y, s_lambda2), method = 'TNC', jac = myGradientReg); \n",
        "cost2 = Result2.fun \n",
        "theta2 = Result2.x \n",
        "\n",
        "s_lambda3 = 1000\n",
        "Result3 = op.minimize(fun = myCostReg, x0 = initial_theta, args = (X_reg, y, s_lambda3), method = 'TNC', jac = myGradientReg); \n",
        "cost3 = Result3.fun \n",
        "theta3 = Result3.x \n",
        "\n",
        "print(cost)\n",
        "print(cost2)\n",
        "print(cost3)\n",
        "\n",
        "# theta[0] = theta_history[1500][0]\n",
        "# theta[1] = theta_history[1500][1]\n",
        "# theta[2] = theta_history[1500][2]\n",
        "# theta[3] = theta_history[1500][3]\n",
        "# theta[4] = theta_history[1500][4]\n",
        "# theta[5] = theta_history[1500][5]\n",
        "# theta[6] = theta_history[1500][6]\n",
        "# theta[7] = theta_history[1500][7]\n",
        "# theta[8] = theta_history[1500][8]\n",
        "# theta[9] = theta_history[1500][9]\n",
        "# theta[10] = theta_history[1500][10]\n",
        "# theta[11] = theta_history[1500][11]\n",
        "# theta[12] = theta_history[1500][12]\n",
        "# theta[13] = theta_history[1500][13]\n",
        "# theta[14] = theta_history[1500][14]"
      ],
      "execution_count": 64,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.17331609404130785\n",
            "0.5220032740379434\n",
            "0.6919947549477525\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:2: RuntimeWarning: overflow encountered in exp\n",
            "  \n",
            "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:21: RuntimeWarning: divide by zero encountered in log\n",
            "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:21: RuntimeWarning: invalid value encountered in multiply\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "enDqJ7h-YSrX",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def predict(theta, X): \n",
        "  m = matrix(X) \n",
        "  m, n = X.shape \n",
        "  theta = theta.reshape((n, 1)) \n",
        "  theta = matrix(theta) \n",
        "  p = np.zeros((m, 1)) \n",
        "  p = sigmoid(X * theta) >= 0.5; \n",
        "  \n",
        "  return p "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3E805B0vYTR7",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "p = predict(theta, X_reg) \n",
        "p2 = predict(theta2, X_reg) \n",
        "p3 = predict(theta3, X_reg) "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cvnZvkCzYUK1",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def plotBoundary(theta, X, y, line_color): \n",
        "  \n",
        "  if np.size(X, 1) <= 3: \n",
        "    plot_x = np.array([np.min(X[:, 1]) - 2, np.max(X[:, 1] + 2)]) \n",
        "    plot_y = (-1 / theta[2]) * (theta[1] * plot_x + theta[0]) \n",
        "    plot(plot_x, plot_y) \n",
        "    plt.legend(('Admitted', 'Not admitted'), loc='upper right') \n",
        "  \n",
        "  else: \n",
        "\n",
        "    u = linspace(-1, 1.5, 800) \n",
        "    v = linspace(-1, 1.5, 800) \n",
        "    z = np.zeros((np.size(u), np.size(v))) \n",
        "\n",
        "    for i in np.arange(np.size(u)): \n",
        "      for j in np.arange(np.size(v)): \n",
        "        z[i, j] = np.sum(mapFeature(u[i], v[j]) * theta) \n",
        "        \n",
        "        z = z.T \n",
        "\n",
        "    # plt.figure()\n",
        "    # plt.scatter(pointX0, pointY0, c='b')\n",
        "    # plt.scatter(pointX1, pointY1, c='r')\n",
        "    # plt.tight_layout()\n",
        "    # plt.gca().set_aspect('equal', adjustable='box')\n",
        "    plt.contour(u, v, z, colors=line_color) "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eKSIHbgVYU7t",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "00b6e582-c8bb-4c1c-c08c-1b4914d3a251"
      },
      "source": [
        "accuracy_history = np.zeros(150)\n",
        "print(X.shape)\n",
        "print(theta_history[0].shape)\n",
        "\n",
        "# a = np.array([0])\n",
        "\n",
        "for i in range(150):\n",
        "  # theta_history[i].append(0)\n",
        "  p = predict(theta_history[i], X_reg) \n",
        "  accuracy_history[i] = np.mean(double(p == y))\n",
        "\n",
        "accuracy_history2 = np.zeros(150)\n",
        "\n",
        "for i in range(150):\n",
        "  p2 = predict(theta_history2[i], X_reg) \n",
        "  accuracy_history2[i] = np.mean(double(p2 == y))\n",
        "\n",
        "accuracy_history3 = np.zeros(150)\n",
        "\n",
        "for i in range(150):\n",
        "  p3 = predict(theta_history3[i], X_reg) \n",
        "  accuracy_history3[i] = np.mean(double(p3 == y))"
      ],
      "execution_count": 68,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(118, 2)\n",
            "(100,)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LG2dPQgVYZ8z",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 497
        },
        "outputId": "7c56950a-d8e9-43ec-99f9-a3e5681b12aa"
      },
      "source": [
        "fig,ax = plt.subplots(figsize=(12,8))\n",
        "\n",
        "ax.set_ylabel('accuracy')\n",
        "ax.set_xlabel('Iterations')\n",
        "_=ax.plot(range(150),accuracy_history,'r.', color = 'red')\n",
        "_=ax.plot(range(150),accuracy_history2,'r.', color = 'green')\n",
        "_=ax.plot(range(150),accuracy_history3,'r.', color = 'blue')"
      ],
      "execution_count": 70,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0IKRmAdgYbM3",
        "colab_type": "code",
        "outputId": "10f66877-b41a-4e53-84a0-c15766913649",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 121
        }
      },
      "source": [
        "# print(\"Train Accuracy:  \", end=' ')\n",
        "# print(accuracy_history[-1]*100, end='%')\n",
        "# print(\"Train Accuracy:  \", end=' ')\n",
        "# print(accuracy_history2[-1]*100, end='%')\n",
        "# print(\"Train Accuracy:  \", end=' ')\n",
        "# print(accuracy_history3[-1]*100, end='%')\n",
        "print(\"Over-fitting Train Accuracy:  \", end=' ')\n",
        "a = np.mean(double(p == y))\n",
        "print(a*100, end='%')\n",
        "print('\\n')\n",
        "print(\"Just-right Train Accuracy:  \", end=' ')\n",
        "a = np.mean(double(p2 == y))\n",
        "print(a*100, end='%')\n",
        "print('\\n')\n",
        "print(\"Under-fitting Train Accuracy:  \", end=' ')\n",
        "a = np.mean(double(p3 == y))\n",
        "print(a*100, end='%')\n",
        "print('\\n')"
      ],
      "execution_count": 71,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Over-fitting Train Accuracy:   82.20338983050848%\n",
            "\n",
            "Just-right Train Accuracy:   61.86440677966102%\n",
            "\n",
            "Under-fitting Train Accuracy:   50.847457627118644%\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "497I76XeYcAl",
        "colab_type": "code",
        "outputId": "0dc7e606-887e-4d81-8ea1-540e22c1ad97",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 301
        }
      },
      "source": [
        "plt.figure()\n",
        "plt.scatter(pointX0, pointY0, c='b')\n",
        "plt.scatter(pointX1, pointY1, c='r')\n",
        "plt.tight_layout()\n",
        "plt.gca().set_aspect('equal', adjustable='box')\n",
        "\n",
        "plotBoundary(theta, X_reg, y, 'red')\n",
        "plotBoundary(theta2, X_reg, y, 'green')\n",
        "plotBoundary(theta3, X_reg, y, 'blue')"
      ],
      "execution_count": 72,
      "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"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pMcbWdbh98uY",
        "colab_type": "text"
      },
      "source": [
        "# **Machine Learning Assignment07** #\n",
        "\n",
        "Name : 이현주\n",
        "\n",
        "Student # : 20184060"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SmK4D4Gm-Owm",
        "colab_type": "text"
      },
      "source": [
        "# **1. Plot the training data [1pt]**\n",
        "\n",
        "- plot the training data points (x,y) with their labels / in colors (blue for label 0 and red for label 1)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ST9tuh7XwCVX",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "outputId": "0d3782e0-31db-4bdc-92b7-b31700258e97"
      },
      "source": [
        "plt.figure()\n",
        "plt.scatter(pointX0, pointY0, c='b')\n",
        "plt.scatter(pointX1, pointY1, c='r')\n",
        "plt.tight_layout()\n",
        "plt.gca().set_aspect('equal', adjustable='box')\n",
        "plt.show()"
      ],
      "execution_count": 73,
      "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"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZqqLOKHkCI_o",
        "colab_type": "text"
      },
      "source": [
        "# **2. Plot the training error with varying regularization parameters[9pt]**\n",
        "\n",
        "- choose a value for λ1 in such a way that over-fitting is demonstrated and plot the training error J(θ) at every iteration of gradient descent until convergence (in red color) [3pt]\n",
        "- choose a value for λ2 in such a way that just-right is demonstrated and plot the training error J(θ) at every iteration of gradient descent until convergence (in green color) [3pt]\n",
        "- choose a value for λ3​ in such a way that under-fitting is demonstrated and plot the training error J(θ) at every iteration of gradient descent until convergence (in blue color) [3pt]\n",
        "- the above three curves should be presented all together in a single figure"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KBxF3w8RwI2j",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 497
        },
        "outputId": "0cc5c3d9-04e9-4d71-91ce-4e70178754ee"
      },
      "source": [
        "fig,ax = plt.subplots(figsize=(12,8))\n",
        "\n",
        "# print(cost_history[1])\n",
        "\n",
        "ax.set_ylabel('J(Theta)')\n",
        "ax.set_xlabel('Iterations')\n",
        "_=ax.plot(range(n_iter),cost_history,'b.', color = 'red')\n",
        "_=ax.plot(range(n_iter),cost_history2,'b.', color = 'green')\n",
        "_=ax.plot(range(n_iter),cost_history3,'b.', color = 'blue')"
      ],
      "execution_count": 74,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mujVAKAmCNjP",
        "colab_type": "text"
      },
      "source": [
        "# **3. Display the values of the chosen regularization parameters[3pt]**\n",
        "\n",
        "- display the value of the chosen λ1 for the demonstration of over-fitting (in red color) [1pt]\n",
        "- display the value of the chosen λ2​ for the demonstration of just-right (in green color) [1pt]\n",
        "- display the value of the chosen λ3 for the demonstration of under-fitting (in blue color) [1pt]"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hZswODjdwQxs",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 121
        },
        "outputId": "3a257620-0ae2-4266-8624-e62db17ed8de"
      },
      "source": [
        "print(\"Over-fitting λ1: 0.00000001 \", end=' ')\n",
        "print('\\n')\n",
        "print(\"Just-right λ2​: 1 \", end=' ')\n",
        "print('\\n')\n",
        "print(\"Under-fitting λ3: 1000 \", end=' ')\n",
        "print('\\n')"
      ],
      "execution_count": 75,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Over-fitting λ1: 0.00000001  \n",
            "\n",
            "Just-right λ2​: 1  \n",
            "\n",
            "Under-fitting λ3: 1000  \n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "W0_y4h3lCOEW",
        "colab_type": "text"
      },
      "source": [
        "# **4. Plot the training accuracy with varying regularization parameters[9pt]**\n",
        "\n",
        "- plot the training accuracy with the chosen λ1 for over-fitting at every iteration of gradient descent until convergence (in red color) [3pt]\n",
        "- plot the training accuracy with the chosen λ2​ for just-right at every iteration of gradient descent until convergence (in green color) [3pt]\n",
        "- plot the training accuracy with the chosen λ3​ for under-fitting at every iteration of gradient descent until convergence (in blue color) [3pt]\n",
        "- the above three curves should be presented all together in a single figure"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-Jyl8j_Gwz5a",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 497
        },
        "outputId": "a8db5a7c-22b4-463a-dde6-892540576b90"
      },
      "source": [
        "fig,ax = plt.subplots(figsize=(12,8))\n",
        "\n",
        "ax.set_ylabel('accuracy')\n",
        "ax.set_xlabel('Iterations')\n",
        "_=ax.plot(range(150),accuracy_history,'r.', color = 'red')\n",
        "_=ax.plot(range(150),accuracy_history2,'r.', color = 'green')\n",
        "_=ax.plot(range(150),accuracy_history3,'r.', color = 'blue')"
      ],
      "execution_count": 76,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nv_zAWupCOVI",
        "colab_type": "text"
      },
      "source": [
        "# **5. Display the final training accuracy with varying regularization parameters[3pt]**\n",
        "\n",
        "- display the final training accuracy obtained with the chosen λ1​ for over-fitting in number (%) at convergence (in red color) [1pt]\n",
        "- display the final training accuracy obtained with the chosen λ2​ for just-right in number (%) at convergence (in green color) [1pt]\n",
        "- display the final training accuracy obtained with the chosen λ3​ for under-fitting in number (%) at convergence (in blue color) [1pt]"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gXFrCD9vw6OG",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 121
        },
        "outputId": "b1f0ba74-f311-4414-9502-8117fe2b74eb"
      },
      "source": [
        "print(\"Over-fitting Train Accuracy:  \", end=' ')\n",
        "a = np.mean(double(p == y))\n",
        "print(a*100, end='%')\n",
        "print('\\n')\n",
        "print(\"Just-right Train Accuracy:  \", end=' ')\n",
        "a = np.mean(double(p2 == y))\n",
        "print(a*100, end='%')\n",
        "print('\\n')\n",
        "print(\"Under-fitting Train Accuracy:  \", end=' ')\n",
        "a = np.mean(double(p3 == y))\n",
        "print(a*100, end='%')\n",
        "print('\\n')"
      ],
      "execution_count": 77,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Over-fitting Train Accuracy:   82.20338983050848%\n",
            "\n",
            "Just-right Train Accuracy:   61.86440677966102%\n",
            "\n",
            "Under-fitting Train Accuracy:   50.847457627118644%\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MokllgPaCOmA",
        "colab_type": "text"
      },
      "source": [
        "# **6. Plot the optimal classifier with varying regularization parameters superimposed on the training data[9pt]**\n",
        "\n",
        "- plot the boundary of the optimal classifier with the chosen λ1​ for over-fitting at convergence (in red color) [3pt]\n",
        "- plot the boundary of the optimal classifier with the chosen λ2 for just-right at convergence (in green color) [3pt]\n",
        "- plot the boundary of the optimal classifier with the chosen λ3​ for under-fitting at convergence (in blue color) [3pt]\n",
        "- the boundary of the classifier is defined by {(x,y)∣σ(g(x,y;θ))=0.5}={(x,y)∣g(x,y;θ)=0}\n",
        "- the boundaries of the classifiers with different regularization parameters should be presented with the training data points (x,y) with their labels lll in colors (blue for label 0 and red for label 1)\n",
        "- you can use contour function in python3"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zgkpwx8OxEWv",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 301
        },
        "outputId": "234b3079-93f3-4afe-f762-008342c5057f"
      },
      "source": [
        "plt.figure()\n",
        "plt.scatter(pointX0, pointY0, c='b')\n",
        "plt.scatter(pointX1, pointY1, c='r')\n",
        "plt.tight_layout()\n",
        "plt.gca().set_aspect('equal', adjustable='box')\n",
        "\n",
        "plotBoundary(theta, X_reg, y, 'red')\n",
        "plotBoundary(theta2, X_reg, y, 'green')\n",
        "plotBoundary(theta3, X_reg, y, 'blue')"
      ],
      "execution_count": 78,
      "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"
          }
        }
      ]
    }
  ]
}