Z30G0D/Logistic_regression_ex2

## Logistic_regression_ex2
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 2- Andrew NG Machine Learning Course\n",
    "## Hey all!\n",
    "This is the second task from Andrew NG course of machine learning concerning simple **logistic** regression.\n",
    "I implemented the exercise in python but the original implementation is in MATLAB.\n",
    "feel free to review my work through tomer@nahshoh.net.\n",
    "The task is locate <a href=\"https://github.com/jdwittenauer/ipython-notebooks/blob/master/exercises/ML/ex1.pdf\">here</a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import os\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "path = os.getcwd() + '/\\Exercise2\\ex2\\ex2data1.txt'\n",
    "data = pd.read_csv(path, header=None, names=['Exam 1', 'Exam 2', 'Admitted'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<bound method NDFrame.head of        Exam 1     Exam 2  Admitted\n",
       "0   34.623660  78.024693         0\n",
       "1   30.286711  43.894998         0\n",
       "2   35.847409  72.902198         0\n",
       "3   60.182599  86.308552         1\n",
       "4   79.032736  75.344376         1\n",
       "5   45.083277  56.316372         0\n",
       "6   61.106665  96.511426         1\n",
       "7   75.024746  46.554014         1\n",
       "8   76.098787  87.420570         1\n",
       "9   84.432820  43.533393         1\n",
       "10  95.861555  38.225278         0\n",
       "11  75.013658  30.603263         0\n",
       "12  82.307053  76.481963         1\n",
       "13  69.364589  97.718692         1\n",
       "14  39.538339  76.036811         0\n",
       "15  53.971052  89.207350         1\n",
       "16  69.070144  52.740470         1\n",
       "17  67.946855  46.678574         0\n",
       "18  70.661510  92.927138         1\n",
       "19  76.978784  47.575964         1\n",
       "20  67.372028  42.838438         0\n",
       "21  89.676776  65.799366         1\n",
       "22  50.534788  48.855812         0\n",
       "23  34.212061  44.209529         0\n",
       "24  77.924091  68.972360         1\n",
       "25  62.271014  69.954458         1\n",
       "26  80.190181  44.821629         1\n",
       "27  93.114389  38.800670         0\n",
       "28  61.830206  50.256108         0\n",
       "29  38.785804  64.995681         0\n",
       "..        ...        ...       ...\n",
       "70  32.722833  43.307173         0\n",
       "71  64.039320  78.031688         1\n",
       "72  72.346494  96.227593         1\n",
       "73  60.457886  73.094998         1\n",
       "74  58.840956  75.858448         1\n",
       "75  99.827858  72.369252         1\n",
       "76  47.264269  88.475865         1\n",
       "77  50.458160  75.809860         1\n",
       "78  60.455556  42.508409         0\n",
       "79  82.226662  42.719879         0\n",
       "80  88.913896  69.803789         1\n",
       "81  94.834507  45.694307         1\n",
       "82  67.319257  66.589353         1\n",
       "83  57.238706  59.514282         1\n",
       "84  80.366756  90.960148         1\n",
       "85  68.468522  85.594307         1\n",
       "86  42.075455  78.844786         0\n",
       "87  75.477702  90.424539         1\n",
       "88  78.635424  96.647427         1\n",
       "89  52.348004  60.769505         0\n",
       "90  94.094331  77.159105         1\n",
       "91  90.448551  87.508792         1\n",
       "92  55.482161  35.570703         0\n",
       "93  74.492692  84.845137         1\n",
       "94  89.845807  45.358284         1\n",
       "95  83.489163  48.380286         1\n",
       "96  42.261701  87.103851         1\n",
       "97  99.315009  68.775409         1\n",
       "98  55.340018  64.931938         1\n",
       "99  74.775893  89.529813         1\n",
       "\n",
       "[100 rows x 3 columns]>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's visualize the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x27c61c01cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "admitted = pd.DataFrame(data.loc[data['Admitted'].isin([1])])\n",
    "not_admitted = pd.DataFrame(data.loc[data['Admitted'].isin([0])])\n",
    "\n",
    "fig = plt.figure()\n",
    "ax1 = fig.add_subplot(111)\n",
    "ax1.scatter(admitted['Exam 1'],admitted['Exam 2'], s=10, c='r', label='Admitted', marker='o')\n",
    "ax1.scatter(not_admitted['Exam 1'],not_admitted['Exam 2'], s=10, c='b', label = 'Not admitted', marker='^')\n",
    "plt.legend(loc='lower left');\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nice, Ok now we can see our data more clearly. It is possible to have a decision boundary between the two different classes we got.Next we are asked to implement the sigmoid function (activation). Let's implement it)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(z):\n",
    "    \"\"\"sigmoid function\"\"\"\n",
    "    return 1/(1+np.exp(-z))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's a nice warmup exercise, let's continue with the cost function and gradients."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def costfunction(theta, X, y):\n",
    "    hypo = sigmoid(theta * X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def costfunction1(theta, X, y):\n",
    "    theta = np.matrix(theta)\n",
    "    X = np.matrix(X)\n",
    "    y = np.matrix(y)\n",
    "    hypo = X * theta.T# Hypothesis of the linear regression-> inserting to a sigmoid turns it to logistic regression\n",
    "    first = np.multiply(-y, np.log(sigmoid(hypo)))\n",
    "    second = np.multiply((1 - y), np.log(1 - sigmoid(hypo)))\n",
    "    cost = np.sum(first - second) / X.shape[0]\n",
    "    return cost"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's edit the data, seperating between target variable and our features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "data.insert(0, 'Bias', 1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = data.drop(['Admitted'], axis=1)\n",
    "y =data.drop(['Bias', 'Exam 1', 'Exam 2'], axis=1) \n",
    "theta = np.zeros(X.shape[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6931471805599453"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "costfunction1(theta, X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nice, let's edit this and get the gradients."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient(theta, X, y):\n",
    "    theta = np.matrix(theta)\n",
    "    X = np.matrix(X)\n",
    "    y = np.matrix(y)\n",
    "    #let's calculate gradients\n",
    "    hypo = X * theta.T\n",
    "    e = sigmoid(hypo) - y # calculating just one -avoiding redundancy\n",
    "    parameters = int(theta.ravel().shape[1])# looping through all theta\n",
    "    grads = np.zeros(theta.shape)\n",
    "    for j in range(parameters):\n",
    "            grads[0,j] = (np.sum(np.multiply(e, X[:,j]))) / X.shape[0]\n",
    "    \n",
    "    return grads"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ -0.1       , -12.00921659, -11.26284221]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grads = gradient(theta, X, y)\n",
    "grads"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ok, now we are going to use the optimization function from the scikit-learn module to minimize the cost function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([-25.16131872,   0.20623159,   0.20147149]), 36, 0)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.optimize import minimize\n",
    "import scipy.optimize as opt\n",
    "#result =minimize(costfunction1, theta, args=(X, y), jac=gradient(theta, X, y))\n",
    "result = opt.fmin_tnc(func=costfunction1, x0=theta, fprime=gradient, args=(X, y))\n",
    "result\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.20349770158947425"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "costfunction1(result[0], X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our lowest cost (this is problem with a convex cost function so it has to be the lowest cost). Let's write the function predict."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict(theta, X):\n",
    "    predict = np.sum(sigmoid(X * theta.T))\n",
    "    return predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "prediction is: 0.776290625526598\n"
     ]
    }
   ],
   "source": [
    "testing = np.matrix(np.array([1, 45, 85]))\n",
    "prediction = predict(np.matrix(result[0]), testing)\n",
    "print('prediction is:',(prediction))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ok, so according to the text instructions in 1.2.4 we got the right answer. Let's write the predict function with a threshold of 0.5>=."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict1(theta, X):\n",
    "    X = np.matrix(X)\n",
    "    theta = np.matrix(theta)\n",
    "    predict = sigmoid(X * theta.T)\n",
    "    predict = predict >= 0.5\n",
    "    predict = predict.astype(int)\n",
    "    return predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "prediction = predict1(result[0], X)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ok, now we have our predictions, now let's compare them to the actual results we already have in the \"attended\" column in the original data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "accuracy is:  89.0%\n"
     ]
    }
   ],
   "source": [
    "accuracy = (np.sum(prediction == np.matrix(data['Admitted']).T)) / prediction.shape[0]\n",
    "#np.matrix(data['Admitted']).T.shape, prediction.shape\n",
    "print('accuracy is: ','{:.1%}'.format(accuracy))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ok, we got 89 percent, nice. Let's plot the decision bounday."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "final =result[0]\n",
    "\n",
    "plot_X = np.array([min(X.values[:, 2]-2), max(X.values[:, 2])+2])\n",
    "plot_y = (-1/final[2]) * (final[1] * plot_X + final[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x27c63358e80>]"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x27c632c8550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax1 = fig.add_subplot(111)\n",
    "ax1.scatter(admitted['Exam 1'],admitted['Exam 2'], s=10, c='r', label='Admitted', marker='o')\n",
    "ax1.scatter(not_admitted['Exam 1'],not_admitted['Exam 2'], s=10, c='b', label = 'Not admitted', marker='^')\n",
    "plt.legend(loc='lower left');\n",
    "\n",
    "plt.plot(plot_X, plot_y, 'k-', lw=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that some of the samples are behind the black boundary line, that's why we have 0.89 accuracy, Perhaps a different classifier would be better for this task (SVM with flexible boundaries etc...)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "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>Test 1</th>\n",
       "      <th>Test 2</th>\n",
       "      <th>Accepted</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.051267</td>\n",
       "      <td>0.699560</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.092742</td>\n",
       "      <td>0.684940</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.213710</td>\n",
       "      <td>0.692250</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.375000</td>\n",
       "      <td>0.502190</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.513250</td>\n",
       "      <td>0.465640</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>-0.524770</td>\n",
       "      <td>0.209800</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>-0.398040</td>\n",
       "      <td>0.034357</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>-0.305880</td>\n",
       "      <td>-0.192250</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.016705</td>\n",
       "      <td>-0.404240</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.131910</td>\n",
       "      <td>-0.513890</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.385370</td>\n",
       "      <td>-0.565060</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.529380</td>\n",
       "      <td>-0.521200</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.638820</td>\n",
       "      <td>-0.243420</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.736750</td>\n",
       "      <td>-0.184940</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.546660</td>\n",
       "      <td>0.487570</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0.322000</td>\n",
       "      <td>0.582600</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0.166470</td>\n",
       "      <td>0.538740</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>-0.046659</td>\n",
       "      <td>0.816520</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>-0.173390</td>\n",
       "      <td>0.699560</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>-0.478690</td>\n",
       "      <td>0.633770</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>-0.605410</td>\n",
       "      <td>0.597220</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>-0.628460</td>\n",
       "      <td>0.334060</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>-0.593890</td>\n",
       "      <td>0.005117</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>-0.421080</td>\n",
       "      <td>-0.272660</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>-0.115780</td>\n",
       "      <td>-0.396930</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>0.201040</td>\n",
       "      <td>-0.601610</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0.466010</td>\n",
       "      <td>-0.535820</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>0.673390</td>\n",
       "      <td>-0.535820</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>-0.138820</td>\n",
       "      <td>0.546050</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>-0.294350</td>\n",
       "      <td>0.779970</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>88</th>\n",
       "      <td>-0.403800</td>\n",
       "      <td>0.706870</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>89</th>\n",
       "      <td>-0.380760</td>\n",
       "      <td>0.918860</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90</th>\n",
       "      <td>-0.507490</td>\n",
       "      <td>0.904240</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>91</th>\n",
       "      <td>-0.547810</td>\n",
       "      <td>0.706870</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>92</th>\n",
       "      <td>0.103110</td>\n",
       "      <td>0.779970</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>93</th>\n",
       "      <td>0.057028</td>\n",
       "      <td>0.918860</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94</th>\n",
       "      <td>-0.104260</td>\n",
       "      <td>0.991960</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>-0.081221</td>\n",
       "      <td>1.108900</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>0.287440</td>\n",
       "      <td>1.087000</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>0.396890</td>\n",
       "      <td>0.823830</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>0.638820</td>\n",
       "      <td>0.889620</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>0.823160</td>\n",
       "      <td>0.663010</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100</th>\n",
       "      <td>0.673390</td>\n",
       "      <td>0.641080</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>101</th>\n",
       "      <td>1.070900</td>\n",
       "      <td>0.100150</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>102</th>\n",
       "      <td>-0.046659</td>\n",
       "      <td>-0.579680</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>103</th>\n",
       "      <td>-0.236750</td>\n",
       "      <td>-0.638160</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>104</th>\n",
       "      <td>-0.150350</td>\n",
       "      <td>-0.367690</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>105</th>\n",
       "      <td>-0.490210</td>\n",
       "      <td>-0.301900</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>106</th>\n",
       "      <td>-0.467170</td>\n",
       "      <td>-0.133770</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>107</th>\n",
       "      <td>-0.288590</td>\n",
       "      <td>-0.060673</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>108</th>\n",
       "      <td>-0.611180</td>\n",
       "      <td>-0.067982</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>109</th>\n",
       "      <td>-0.663020</td>\n",
       "      <td>-0.214180</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>110</th>\n",
       "      <td>-0.599650</td>\n",
       "      <td>-0.418860</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>111</th>\n",
       "      <td>-0.726380</td>\n",
       "      <td>-0.082602</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>112</th>\n",
       "      <td>-0.830070</td>\n",
       "      <td>0.312130</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>113</th>\n",
       "      <td>-0.720620</td>\n",
       "      <td>0.538740</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>114</th>\n",
       "      <td>-0.593890</td>\n",
       "      <td>0.494880</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>115</th>\n",
       "      <td>-0.484450</td>\n",
       "      <td>0.999270</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>116</th>\n",
       "      <td>-0.006336</td>\n",
       "      <td>0.999270</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>117</th>\n",
       "      <td>0.632650</td>\n",
       "      <td>-0.030612</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>118 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       Test 1    Test 2  Accepted\n",
       "0    0.051267  0.699560         1\n",
       "1   -0.092742  0.684940         1\n",
       "2   -0.213710  0.692250         1\n",
       "3   -0.375000  0.502190         1\n",
       "4   -0.513250  0.465640         1\n",
       "5   -0.524770  0.209800         1\n",
       "6   -0.398040  0.034357         1\n",
       "7   -0.305880 -0.192250         1\n",
       "8    0.016705 -0.404240         1\n",
       "9    0.131910 -0.513890         1\n",
       "10   0.385370 -0.565060         1\n",
       "11   0.529380 -0.521200         1\n",
       "12   0.638820 -0.243420         1\n",
       "13   0.736750 -0.184940         1\n",
       "14   0.546660  0.487570         1\n",
       "15   0.322000  0.582600         1\n",
       "16   0.166470  0.538740         1\n",
       "17  -0.046659  0.816520         1\n",
       "18  -0.173390  0.699560         1\n",
       "19  -0.478690  0.633770         1\n",
       "20  -0.605410  0.597220         1\n",
       "21  -0.628460  0.334060         1\n",
       "22  -0.593890  0.005117         1\n",
       "23  -0.421080 -0.272660         1\n",
       "24  -0.115780 -0.396930         1\n",
       "25   0.201040 -0.601610         1\n",
       "26   0.466010 -0.535820         1\n",
       "27   0.673390 -0.535820         1\n",
       "28  -0.138820  0.546050         1\n",
       "29  -0.294350  0.779970         1\n",
       "..        ...       ...       ...\n",
       "88  -0.403800  0.706870         0\n",
       "89  -0.380760  0.918860         0\n",
       "90  -0.507490  0.904240         0\n",
       "91  -0.547810  0.706870         0\n",
       "92   0.103110  0.779970         0\n",
       "93   0.057028  0.918860         0\n",
       "94  -0.104260  0.991960         0\n",
       "95  -0.081221  1.108900         0\n",
       "96   0.287440  1.087000         0\n",
       "97   0.396890  0.823830         0\n",
       "98   0.638820  0.889620         0\n",
       "99   0.823160  0.663010         0\n",
       "100  0.673390  0.641080         0\n",
       "101  1.070900  0.100150         0\n",
       "102 -0.046659 -0.579680         0\n",
       "103 -0.236750 -0.638160         0\n",
       "104 -0.150350 -0.367690         0\n",
       "105 -0.490210 -0.301900         0\n",
       "106 -0.467170 -0.133770         0\n",
       "107 -0.288590 -0.060673         0\n",
       "108 -0.611180 -0.067982         0\n",
       "109 -0.663020 -0.214180         0\n",
       "110 -0.599650 -0.418860         0\n",
       "111 -0.726380 -0.082602         0\n",
       "112 -0.830070  0.312130         0\n",
       "113 -0.720620  0.538740         0\n",
       "114 -0.593890  0.494880         0\n",
       "115 -0.484450  0.999270         0\n",
       "116 -0.006336  0.999270         0\n",
       "117  0.632650 -0.030612         0\n",
       "\n",
       "[118 rows x 3 columns]"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path = os.getcwd() + '/\\Exercise2\\ex2\\ex2data2.txt'\n",
    "data2 = pd.read_csv(path, header=None, names=['Test 1', 'Test 2', 'Accepted'])\n",
    "data2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's visualize the data like figure 3 in the pdf file."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "passed = pd.DataFrame(data2.loc[data2['Accepted'].isin([1])])\n",
    "failed = pd.DataFrame(data2.loc[data2['Accepted'].isin([0])])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Microchips accptence and failure dataset')"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x27c65076860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax1 = fig.add_subplot(111)\n",
    "ax1.scatter(passed['Test 1'],passed['Test 2'], s=10, c='r', label='Passed', marker='o')\n",
    "ax1.scatter(failed['Test 1'],failed['Test 2'], s=10, c='b', label = 'Failed', marker='^')\n",
    "plt.legend(loc='upper right');\n",
    "plt.title('Microchips accptence and failure dataset')"
   ]
  },
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    "Ok, no linear boundary is possible in this case. Let's create polynomial features in order to fit the boundary better then the simple logistic regression which is basically a straight line."
   ]
  }
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