Heart disease.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# we followed the code in:\n",
    "#https://towardsdatascience.com/a-complete-logistic-regression-algorithm-from-scratch-in-python-step-by-step-ce33eae7d703\n",
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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>age</th>\n",
       "      <th>sex</th>\n",
       "      <th>cp</th>\n",
       "      <th>trtbps</th>\n",
       "      <th>chol</th>\n",
       "      <th>fbs</th>\n",
       "      <th>restecg</th>\n",
       "      <th>thalachh</th>\n",
       "      <th>exng</th>\n",
       "      <th>oldpeak</th>\n",
       "      <th>slp</th>\n",
       "      <th>caa</th>\n",
       "      <th>thall</th>\n",
       "      <th>output</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>63</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>145</td>\n",
       "      <td>233</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>150</td>\n",
       "      <td>0</td>\n",
       "      <td>2.3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>37</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>130</td>\n",
       "      <td>250</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>187</td>\n",
       "      <td>0</td>\n",
       "      <td>3.5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>41</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>130</td>\n",
       "      <td>204</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>172</td>\n",
       "      <td>0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>56</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>120</td>\n",
       "      <td>236</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>178</td>\n",
       "      <td>0</td>\n",
       "      <td>0.8</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>57</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>120</td>\n",
       "      <td>354</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>163</td>\n",
       "      <td>1</td>\n",
       "      <td>0.6</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   age  sex  cp  trtbps  chol  fbs  restecg  thalachh  exng  oldpeak  slp  \\\n",
       "0   63    1   3     145   233    1        0       150     0      2.3    0   \n",
       "1   37    1   2     130   250    0        1       187     0      3.5    0   \n",
       "2   41    0   1     130   204    0        0       172     0      1.4    2   \n",
       "3   56    1   1     120   236    0        1       178     0      0.8    2   \n",
       "4   57    0   0     120   354    0        1       163     1      0.6    2   \n",
       "\n",
       "   caa  thall  output  \n",
       "0    0      1       1  \n",
       "1    0      2       1  \n",
       "2    0      2       1  \n",
       "3    0      2       1  \n",
       "4    0      2       1  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# We used the Heart.csv dataset provided by Kaggle\n",
    "df = pd.read_csv('Heart.csv')\n",
    "df.head()\n",
    "# The output column denotes if the person has a Heart Disease or not 1-NO 0-YES\n",
    "# Esta al revez en toward data science, usan 1 yes 0 no"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# sigmoid function\n",
    "def hypothesis(X, theta):\n",
    "    z = np.dot(theta, X.T)\n",
    "    return 1/(1+np.exp(-(z))) - 0.0000001 # the final small value is to make sure the log is never 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# cost function\n",
    "def cost(X, y, theta):\n",
    "    y1 = hypothesis(X, theta)\n",
    "    return -(1/len(X)) * np.sum(y*np.log(y1) + (1-y)*np.log(1-y1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Gradient Descent\n",
    "def gradient_descent(X, y, theta, alpha, epochs):\n",
    "    m =len(X)\n",
    "    J = [cost(X, y, theta)] \n",
    "    for i in range(0, epochs):\n",
    "        h = hypothesis(X, theta)\n",
    "        for i in range(0, len(X.columns)):\n",
    "            theta[i] -= (alpha/m) * np.sum((h-y)*X.iloc[:, i])\n",
    "        J.append(cost(X, y, theta))\n",
    "    return J, theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Prediction\n",
    "def predict(X, y, theta, alpha, epochs):\n",
    "    J, th = gradient_descent(X, y, theta, alpha, epochs) \n",
    "    h = hypothesis(X, theta)\n",
    "    for i in range(len(h)):\n",
    "        h[i]=1 if h[i]>=0.5 else 0\n",
    "    y = list(y)\n",
    "    acc = np.sum([y[i] == h[i] for i in range(len(y))])/len(y)\n",
    "    return J, acc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# we introduce one extra column for the bias\n",
    "df = pd.concat([pd.Series(1, index = df.index, name = '00'), df], axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define input and output\n",
    "X = df.drop(columns=[\"thall\"])\n",
    "y= df[\"output\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-7-0bea681e0129>:4: RuntimeWarning: invalid value encountered in log\n",
      "  return -(1/len(X)) * np.sum(y*np.log(y1) + (1-y)*np.log(1-y1))\n"
     ]
    }
   ],
   "source": [
    "# Get Accuracy\n",
    "theta = [0.5]*len(X.columns)\n",
    "J, acc = predict(X, y, theta, 0.0001, 25000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.801980198019802"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "acc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.figure(figsize = (12, 8))\n",
    "plt.scatter(range(0, len(J)), J)\n",
    "plt.title(\"Cost as a function of # of iterations\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  },
  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autoclose": false,
   "autocomplete": true,
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
   },
   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  },
  "nbTranslate": {
   "displayLangs": [
    "*"
   ],
   "hotkey": "alt-t",
   "langInMainMenu": true,
   "sourceLang": "en",
   "targetLang": "fr",
   "useGoogleTranslate": true
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}