Code-Example-016.1-LogisticRegression-without-lib-BackUP.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic Regression implementation without Scikit-learn\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "from scipy.stats import norm\n",
    "from sklearn.datasets import make_blobs\n",
    "\n",
    "from matplotlib import pyplot\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import matplotlib.cm as cm\n",
    "from random import sample"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generating Some Example Data with 2 Features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_feature = 2 # the number of features\n",
    "n_components = 2 # the number of clusters\n",
    "\n",
    "n=1000 # the number of total samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  2.21895948,  -9.0632939 ],\n",
       "       [ -1.17379771,  -4.92688779],\n",
       "       [  0.79041678, -14.59641646],\n",
       "       ...,\n",
       "       [ -0.78260563, -21.50260563],\n",
       "       [ -3.21323086, -13.90436388],\n",
       "       [ -1.40482172,  -9.1035902 ]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# generate isotropic Gaussian blobs (data from mixture Gaussian distributions)\n",
    "X, y = make_blobs(n_samples=n, # the number of total samples\n",
    "                  centers=n_components, # the number of clusters\n",
    "                  n_features=n_feature, # the number of features\n",
    "                  cluster_std = [5] * n_components, # the std of each cluster\n",
    "                  random_state=2) # 2\n",
    "\n",
    "# X = np.hstack((np.ones((m, 1)), X))\n",
    "\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x = [ 2.21895948 -9.0632939 ] , y = 1\n",
      "x = [-1.17379771 -4.92688779] , y = 0\n",
      "x = [  0.79041678 -14.59641646] , y = 0\n",
      "x = [-0.98141459 -0.14837778] , y = 1\n",
      "x = [ 6.64249161 -1.88234499] , y = 1\n"
     ]
    }
   ],
   "source": [
    "for i in range(5):\n",
    "    print('x =', X[i, ], ', y =', y[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 0, 1, 1, 0, 1, 0, 1, 1])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Just to show you what is inside it. We print the first 10 elements of this numpy array. \n",
    "y[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# scatter plot, data points annotated by different colors\n",
    "df = pd.DataFrame(dict(feature_1=X[:,0], feature_2=X[:,1], label=y))\n",
    "\n",
    "\n",
    "cluster_name = set(y)\n",
    "colors = dict(zip(cluster_name, cm.rainbow(np.linspace(0, 1, len(cluster_name)))))\n",
    "fig, ax = pyplot.subplots()\n",
    "\n",
    "grouped = df.groupby('label')\n",
    "\n",
    "for key, group in grouped:\n",
    "    group.plot(ax=ax, kind='scatter', x='feature_1', y='feature_2', label=key, color=colors[key].reshape(1,-1))\n",
    "    \n",
    "pyplot.title('Original 2D Data from {} Clusters'.format(n_components))\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# Create Test/Train\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=123)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(z):\n",
    "    \"\"\"\n",
    "    To convert continuous value into a range of 0 to 1\n",
    "\n",
    "    I/P\n",
    "    ----------\n",
    "    z : Continuous value\n",
    "\n",
    "    O/P\n",
    "    -------\n",
    "    Value in range between 0 to 1.\n",
    "    \"\"\"\n",
    "    g = 1 / (1 + np.exp(-z))\n",
    "    return g"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cost_function(X, y, weights):\n",
    "    \"\"\"\n",
    "    Compute cost for logistic regression.\n",
    "\n",
    "    I/P\n",
    "    ----------\n",
    "    X : 2D array where each row represent the training example and each column represent the feature ndarray. \n",
    "        Dimension(m x n)\n",
    "        m= number of training examples\n",
    "        n= number of features (including X_0 column of ones)\n",
    "    y : 1D array of labels/target value for each traing example. dimension(1 x m)\n",
    "\n",
    "    weights : 1D array of fitting parameters or weights. Dimension (1 x n)\n",
    "\n",
    "    O/P\n",
    "    -------\n",
    "    cost : The cost of using theta as the parameter for logistic regression to fit the data points in X and y.\n",
    "    \"\"\"\n",
    "    m, n = X.shape\n",
    "    x_dot_weights = X.dot(weights)\n",
    "\n",
    "    cost = 1.0 / m * (-y.T.dot(np.log(sigmoid(x_dot_weights))) - (1 - y).T.dot(np.log(1 - sigmoid(x_dot_weights))))\n",
    "\n",
    "    return cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient(X, y, weights):\n",
    "    \"\"\"\n",
    "    Compute gradient for logistic regression.\n",
    "\n",
    "    I/P\n",
    "    ----------\n",
    "    X : 2D array where each row represent the training example and each column represent the feature ndarray. \n",
    "    Dimension(m x n)\n",
    "        m = number of training examples\n",
    "        n = number of features (including X_0 column of ones)\n",
    "    y : 1D array of labels/target value for each traing example. dimension(1 x m)\n",
    "\n",
    "    weights : 1D array of fitting parameters or weights. Dimension (1 x n)\n",
    "\n",
    "    O/P\n",
    "    -------\n",
    "    grad: (numpy array)The gradient of the cost with respect to the parameters theta\n",
    "    \"\"\"\n",
    "    m, n = X.shape\n",
    "    x_dot_weights = X.dot(weights)\n",
    "\n",
    "    grad = (1.0 / m )* (sigmoid(x_dot_weights) - y).T.dot(X)\n",
    "\n",
    "    return grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6931471805599452\n",
      "[-0.67306356 -2.04334234]\n"
     ]
    }
   ],
   "source": [
    "weights = np.zeros(n_feature)\n",
    "\n",
    "\n",
    "cost = cost_function(X_train, y_train, weights)\n",
    "grad = gradient(X_train, y_train, weights)\n",
    "\n",
    "print(cost)\n",
    "print(grad)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost is:  0.6931471805599452\n",
      "Cost is:  0.6511134846383863\n",
      "Cost is:  0.6229190405104336\n",
      "Cost is:  0.6036035082550789\n",
      "Cost is:  0.5900191803151973\n",
      "Cost is:  0.5802123005192353\n",
      "Cost is:  0.5729596806860497\n",
      "Cost is:  0.5674791245365729\n",
      "Cost is:  0.5632577662507976\n",
      "Cost is:  0.5599508128988057\n",
      "Cost is:  0.5573209544439478\n",
      "Cost is:  0.5552013119692717\n",
      "Cost is:  0.5534722323572873\n",
      "Cost is:  0.5520464066691345\n",
      "Cost is:  0.5508591097625558\n",
      "Cost is:  0.5498616639131213\n",
      "Cost is:  0.5490169768875469\n",
      "Cost is:  0.5482964423386212\n",
      "Cost is:  0.5476777519263867\n",
      "Cost is:  0.5471433283213929\n",
      "Cost is:  0.5466791878435846\n",
      "Cost is:  0.5462741047978773\n",
      "Cost is:  0.5459189905440345\n",
      "Cost is:  0.5456064273138438\n",
      "Cost is:  0.5453303148290213\n",
      "Cost is:  0.5450856000165373\n",
      "Cost is:  0.5448680685411954\n",
      "Cost is:  0.5446741827442848\n",
      "Cost is:  0.5445009547150678\n",
      "Cost is:  0.5443458461715964\n",
      "Cost is:  0.5442066889517527\n",
      "Cost is:  0.5440816214600913\n",
      "Cost is:  0.5439690375493144\n",
      "Cost is:  0.5438675451535706\n",
      "Cost is:  0.5437759326158412\n",
      "Cost is:  0.5436931411211442\n",
      "Cost is:  0.543618242002312\n",
      "Cost is:  0.5435504179553223\n",
      "Cost is:  0.5434889474080857\n",
      "Cost is:  0.5434331914459675\n",
      "Cost is:  0.5433825828207332\n",
      "Cost is:  0.5433366166656732\n",
      "Cost is:  0.5432948426148073\n",
      "Cost is:  0.5432568580831242\n",
      "Cost is:  0.5432223025114468\n",
      "Cost is:  0.5431908524164782\n",
      "Cost is:  0.5431622171160342\n",
      "Cost is:  0.5431361350230083\n",
      "Cost is:  0.5431123704205175\n",
      "Cost is:  0.5430907106459192\n",
      "Cost is:  0.5430709636237131\n",
      "Cost is:  0.5430529556973652\n",
      "Cost is:  0.5430365297182582\n",
      "Cost is:  0.5430215433566582\n",
      "Cost is:  0.5430078676050905\n",
      "Cost is:  0.5429953854490447\n",
      "Cost is:  0.5429839906836915\n",
      "Cost is:  0.5429735868584079\n",
      "Cost is:  0.542964086333523\n",
      "Cost is:  0.5429554094358684\n",
      "Cost is:  0.5429474837015622\n",
      "Cost is:  0.5429402431959985\n",
      "Cost is:  0.5429336279023322\n",
      "Cost is:  0.5429275831708595\n",
      "Cost is:  0.5429220592226568\n",
      "Cost is:  0.5429170107016453\n",
      "Cost is:  0.5429123962699641\n",
      "Cost is:  0.5429081782421266\n",
      "Cost is:  0.5429043222539708\n",
      "Cost is:  0.542900796962862\n",
      "Cost is:  0.5428975737760049\n",
      "Cost is:  0.5428946266040695\n",
      "Cost is:  0.5428919316376376\n",
      "Cost is:  0.5428894671442425\n",
      "Cost is:  0.5428872132840112\n",
      "Cost is:  0.5428851519421238\n",
      "Cost is:  0.5428832665764897\n",
      "Cost is:  0.5428815420792007\n",
      "Cost is:  0.5428799646504698\n",
      "Cost is:  0.5428785216838873\n",
      "Cost is:  0.5428772016619454\n",
      "Cost is:  0.5428759940608845\n",
      "Cost is:  0.5428748892640024\n",
      "Cost is:  0.542873878482655\n",
      "Cost is:  0.5428729536842463\n",
      "Cost is:  0.5428721075265764\n",
      "Cost is:  0.542871333297972\n",
      "Cost is:  0.5428706248626766\n",
      "Cost is:  0.5428699766110342\n",
      "Cost is:  0.5428693834140316\n",
      "Cost is:  0.5428688405818162\n",
      "Cost is:  0.5428683438258308\n",
      "Cost is:  0.5428678892242494\n",
      "Cost is:  0.5428674731904173\n",
      "Cost is:  0.5428670924440339\n",
      "Cost is:  0.5428667439848355\n",
      "Cost is:  0.5428664250685578\n",
      "Cost is:  0.5428661331849773\n",
      "Cost is:  0.5428658660378528\n",
      "Cost is:  0.5428656215265973\n"
     ]
    }
   ],
   "source": [
    "# Now we optimize it using Gradient Descent. \n",
    "num_iterations = 100\n",
    "learnin_rate = 0.01\n",
    "\n",
    "cost_list = []\n",
    "\n",
    "for i in range(0, num_iterations):\n",
    "    \n",
    "    cost = cost_function(X_train, y_train, weights)\n",
    "    print(\"Cost is: \", cost)\n",
    "    cost_list.append(cost)\n",
    "    \n",
    "    grad = gradient(X_train, y_train, weights)\n",
    "    \n",
    "    weights = weights - learnin_rate * grad    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.arange(num_iterations), cost_list)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict(weights, X):\n",
    "    \"\"\"\n",
    "    Predict the class between 0 and 1 using learned logistic regression parameters weights.\n",
    "    Using threshold value 0.5 to convert probability value to class value \n",
    "\n",
    "    I/P\n",
    "    ----------\n",
    "    X : 2D array where each row represent the training example and each column represent the feature ndarray. \n",
    "        Dimension(m x n)\n",
    "        m= number of training examples\n",
    "        n= number of features (including X_0 column of ones)\n",
    "\n",
    "    theta : 1D array of fitting parameters or weights. Dimension (1 x n)\n",
    "\n",
    "    O/P\n",
    "    -------\n",
    "    Class type based on threshold\n",
    "    \"\"\"\n",
    "    p = sigmoid(X.dot(weights)) >= 0.5\n",
    "    return p.astype(int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0,\n",
       "       1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0,\n",
       "       0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0,\n",
       "       0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1,\n",
       "       0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,\n",
       "       0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1,\n",
       "       0, 0])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predictions = predict(weights, X_test)\n",
    "predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0,\n",
       "       1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0,\n",
       "       0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1,\n",
       "       1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0,\n",
       "       1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1,\n",
       "       1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0,\n",
       "       0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1,\n",
       "       1, 1])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy is:  0.7\n"
     ]
    }
   ],
   "source": [
    "# Correct Predictions are the cases that are equal. \n",
    "\n",
    "correct = np.sum(predictions == y_test)\n",
    "\n",
    "\n",
    "print(\"Accuracy is: \", correct/y_test.size)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}