Simple Logistic Regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 100\n",
    "x_zeros = np.random.multivariate_normal(mean=np.array((-1, -1)), cov=0.1*np.eye(2), size=(N//2,))\n",
    "y_zeros = np.zeros((N//2,),dtype=np.float32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X0 shape : (50, 2), Y0 shape : (50,)\n"
     ]
    }
   ],
   "source": [
    "print(f\"X0 shape : {x_zeros.shape}, Y0 shape : {y_zeros.shape}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_ones = np.random.multivariate_normal(mean=np.array((1, 1)), cov=0.1*np.eye(2), size=(N//2,))\n",
    "y_ones = np.ones((N//2,),dtype=np.float32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X1 shape : (50, 2), Y1 shape : (50,)\n"
     ]
    }
   ],
   "source": [
    "print(f\"X1 shape : {x_ones.shape}, Y1 shape : {y_ones.shape}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "#we are keeping y of x_zeros is zero and y of x_ones one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X shape : (100, 2)\n"
     ]
    }
   ],
   "source": [
    "X = np.concatenate((x_zeros,x_ones))\n",
    "print(f\"X shape : {X.shape}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Y shape : (100, 1)\n"
     ]
    }
   ],
   "source": [
    "Y = np.concatenate((y_zeros,y_ones)).reshape((100,1))\n",
    "print(f\"Y shape : {Y.shape}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x_zeros[:,0],x_zeros[:,1],color=\"blue\")\n",
    "plt.scatter(x_ones[:,0],x_ones[:,1],color=\"red\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "import tensorflow as tf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:From c:\\users\\shambu\\appdata\\local\\programs\\python\\python37\\lib\\site-packages\\tensorflow\\python\\ops\\nn_impl.py:180: add_dispatch_support.<locals>.wrapper (from tensorflow.python.ops.array_ops) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Use tf.where in 2.0, which has the same broadcast rule as np.where\n"
     ]
    }
   ],
   "source": [
    "with tf.name_scope(\"Placeholders\"):\n",
    "    x = tf.placeholder(tf.float32,(100,2))\n",
    "    y = tf.placeholder(tf.float32,(100,1))\n",
    "\n",
    "with tf.name_scope(\"Weights\"):\n",
    "    W = tf.Variable(tf.random_normal((1,2)))\n",
    "    b = tf.Variable(tf.random_normal((1,1)))\n",
    "\n",
    "with tf.name_scope(\"Prediction\"):\n",
    "    Z = tf.transpose(tf.add(tf.matmul(W,tf.transpose(x)), b))\n",
    "\n",
    "with tf.name_scope(\"Loss\"):\n",
    "    L = tf.nn.sigmoid_cross_entropy_with_logits(labels=y, logits=Z)\n",
    "    L = tf.reduce_mean(L)\n",
    "\n",
    "with tf.name_scope(\"Optimizer\"):\n",
    "    train_op = tf.train.AdamOptimizer(0.001).minimize(L)\n",
    "\n",
    "with tf.name_scope(\"Summaries\"):\n",
    "    tf.summary.scalar(\"Loss\",L)\n",
    "    merged = tf.summary.merge_all()\n",
    "\n",
    "train_writer = tf.summary.FileWriter(r'C:\\Users\\Shambu\\Google Drive\\Deep Learning\\Notebooks', tf.get_default_graph())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch : 0, Loss : 1.2854710817337036\n",
      "Epoch : 100, Loss : 1.1379623413085938\n",
      "Epoch : 200, Loss : 1.0025415420532227\n",
      "Epoch : 300, Loss : 0.8803645372390747\n",
      "Epoch : 400, Loss : 0.7719499468803406\n",
      "Epoch : 500, Loss : 0.6771627068519592\n",
      "Epoch : 600, Loss : 0.5952466726303101\n",
      "Epoch : 700, Loss : 0.5249888896942139\n",
      "Epoch : 800, Loss : 0.4649426341056824\n",
      "Epoch : 900, Loss : 0.41362830996513367\n",
      "Epoch : 1000, Loss : 0.3696697950363159\n",
      "Epoch : 1100, Loss : 0.33186134696006775\n",
      "Epoch : 1200, Loss : 0.29918405413627625\n",
      "Epoch : 1300, Loss : 0.2707951068878174\n",
      "Epoch : 1400, Loss : 0.2460036426782608\n",
      "Epoch : 1500, Loss : 0.22424465417861938\n",
      "Epoch : 1600, Loss : 0.2050555944442749\n",
      "Epoch : 1700, Loss : 0.1880565583705902\n",
      "Epoch : 1800, Loss : 0.17293331027030945\n",
      "Epoch : 1900, Loss : 0.15942499041557312\n",
      "Epoch : 2000, Loss : 0.14731375873088837\n"
     ]
    }
   ],
   "source": [
    "with tf.Session() as sess:\n",
    "    sess.run(tf.global_variables_initializer())\n",
    "    for i in range(2001):\n",
    "        feed_dict = {x:X,y:Y}\n",
    "        _, loss = sess.run([train_op, L], feed_dict=feed_dict)\n",
    "        summary = sess.run(merged,feed_dict=feed_dict) \n",
    "        if i%100 is 0: print(f\"Epoch : {i}, Loss : {loss}\")\n",
    "        train_writer.add_summary(summary, i)\n",
    "    w_out = sess.run(W)\n",
    "    logits = sess.run(Z, feed_dict={x:X})\n",
    "    y_hat = sess.run(tf.math.sigmoid(logits))\n",
    "    y_hat[y_hat>=0.5]  = 1\n",
    "    y_hat[y_hat<0.5] = 0\n",
    "    b_out = sess.run(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy of the model : 100.0%\n"
     ]
    }
   ],
   "source": [
    "accuracy =  1- (np.sum(abs(Y - y_hat)))/Y.shape[0]\n",
    "print(f\"Accuracy of the model : {accuracy*100}%\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def decision_points(b,w1,w2):\n",
    "    max_x1 = np.max(X[:,0])\n",
    "    max_x2 = np.max(X[:,1])\n",
    "    x1 = -b/w1 - (max_x2*w2)/w1\n",
    "    x2 = -b/w2 - (max_x1*w1)/w2\n",
    "    return [max_x1,x2],[x1,max_x2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x_zeros[:,0],x_zeros[:,1],color=\"blue\")\n",
    "plt.scatter(x_ones[:,0],x_ones[:,1],color=\"red\")\n",
    "w = np.squeeze(w_out)\n",
    "x,y = decision_points(b_out,w[0],w[1])\n",
    "plt.plot(x,y,color=\"black\")\n",
    "plt.show()"
   ]
  }
 ],
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