{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 277,
   "metadata": {},
   "outputs": [],
   "source": [
    "# imports\n",
    "import numpy as np\n",
    "import scipy as sc\n",
    "import numpy.linalg as LA\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.utils import shuffle\n",
    "\n",
    "# this allows plots to appear directly in the notebook\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generating Data: Two Classes are generated from two different Gaussian Clusters "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 278,
   "metadata": {},
   "outputs": [],
   "source": [
    "# generating data\n",
    "d = 2  # dimension \n",
    "m = 100 # number of training samples \n",
    "c = 2.7 # parameter controlling seperation between the clusters\n",
    "mu1 = c*np.array([1,1])\n",
    "mu2 = -mu1 \n",
    "sigma_squared_1 = 1.5\n",
    "sigma_squared_2 = sigma_squared_1 \n",
    "\n",
    "X_train_1 = np.random.multivariate_normal(mu1,sigma_squared_1*np.identity(d),int(m/2)) \n",
    "X_train_2 = np.random.multivariate_normal(mu2,sigma_squared_2*np.identity(d),int(m/2)) \n",
    "X_train = np.concatenate((X_train_1,X_train_2),axis=0)\n",
    "\n",
    "Y_train_1 = np.ones((int(m/2),1))\n",
    "Y_train_2 = 0*np.ones((int(m/2),1))\n",
    "Y_train = np.concatenate((Y_train_1,Y_train_2),axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 279,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train = np.column_stack((np.ones((X_train.shape[0],1)),X_train)) # adding 1 as X0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 280,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0xa1603dac8>"
      ]
     },
     "execution_count": 280,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa160e45c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X_train_1[:,0],X_train_1[:,1], color='b',marker='o')\n",
    "plt.scatter(X_train_2[:,0],X_train_2[:,1], color='r',marker='o')\n",
    "plt.title('Two Gaussian clusters with different labels')\n",
    "plt.xlabel('x1')\n",
    "plt.ylabel('x2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 281,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(x):\n",
    "    return 1 / (1 + np.exp(-x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 282,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cross_entropy(y,y_est):\n",
    "    return -y*np.log(y_est)-(1-y)*np.log(1-y_est)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 283,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_cost(X,Y,theta):\n",
    "    m = X.shape[0] \n",
    "    loss= 0 \n",
    "    for i in range(m):\n",
    "        loss += cross_entropy(Y[i],sigmoid(np.dot(X[i,:],theta)))  \n",
    "    return loss "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gradient Descent "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 284,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_step_log_reg(theta_current, X, Y, learning_rate):\n",
    "\n",
    "    m = X.shape[0]\n",
    "    \n",
    "    grad = np.zeros_like(theta_current)\n",
    "    \n",
    "    for i in range(m):\n",
    "        grad += (sigmoid(np.dot(X[i,:],theta_current))-Y[i])*X[i,:]\n",
    "        \n",
    "        \n",
    "    theta_current += -learning_rate*grad \n",
    "    return theta_current"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 285,
   "metadata": {},
   "outputs": [],
   "source": [
    "# initializations\n",
    "theta = np.random.randn(3)\n",
    "learning_rate = 1e-5\n",
    "num_iterations = 6000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 286,
   "metadata": {},
   "outputs": [],
   "source": [
    "# shuffle the data set \n",
    "X_train, Y_train = shuffle(X_train, Y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 287,
   "metadata": {},
   "outputs": [],
   "source": [
    "# gradient descent\n",
    "cost_vec = []\n",
    "for t in range(num_iterations):\n",
    "    theta = gradient_step_log_reg(theta, X_train, Y_train, learning_rate)\n",
    "    if t%50==0:\n",
    "        cost_vec.append(compute_cost(X_train, Y_train, theta))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot cost vs iteration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 288,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0xa162c7fd0>"
      ]
     },
     "execution_count": 288,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa160b6f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "iterations = np.linspace(0,num_iterations, num=len(cost_vec))\n",
    "plt.plot(iterations,cost_vec)\n",
    "plt.xlabel('iterations')\n",
    "plt.ylabel('cost')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 289,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.50290993,  1.00720295,  0.79526924])"
      ]
     },
     "execution_count": 289,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualize the final seperating line "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 290,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0xa162ad4a8>"
      ]
     },
     "execution_count": 290,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa163552b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X_train_1[:,0],X_train_1[:,1], color='b',marker='o')\n",
    "plt.scatter(X_train_2[:,0],X_train_2[:,1], color='r',marker='o')\n",
    "plt.title('Logistic regression line seperating the two classes')\n",
    "plt.plot([-4,4], (np.array([-4,4])*-theta[1]-theta[0])/theta[2],'r')\n",
    "plt.xlabel('x1')\n",
    "plt.ylabel('x2')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.15"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}