Univariate_Polynomial_Regression.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyNGtCPb2wnm2ZLuTymzKMNJ",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/sfansaria/Machine-Learning/blob/main/Univariate_Polynomial_Regression.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "S9peBa4nOv5U",
        "outputId": "8cca41e7-df68-4ec2-ee5e-4ee94849a35f"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "\n",
        "#import libraries\n",
        "\n",
        "import numpy as np\n",
        "import math\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "#Univariate Polynomial Regression\n",
        "\n",
        "class PolynomialRegression():\n",
        "    def __init__(self,degree, learning_rate, iterations):\n",
        "        self.degree = degree\n",
        "        self.learning_rate = learning_rate\n",
        "        self.iterations = iterations\n",
        "\n",
        "    #Function to transform X\n",
        "    def transform(self, X):\n",
        "        #initialize X_transform\n",
        "        X_transform = np.ones((self.m, 1))\n",
        "\n",
        "        j = 0\n",
        "        for j in range(self.degree+1):\n",
        "          if j != 0:\n",
        "            x_pow = np.power(X, j)\n",
        "            #append x_pow to X_transform\n",
        "            X_transform = np.append(X_transform, x_pow.reshape(-1,1),axis=1)\n",
        "\n",
        "        return X_transform\n",
        "\n",
        "      #Function to normalize X_transform\n",
        "    def normalize(self, X):\n",
        "        X[:, 1:] = (X[:, 1:]-np.mean(X[:, 1:],axis=0))/np.std(X[:, 1:],axis=0)\n",
        "\n",
        "        return X\n",
        "\n",
        "    #Model training\n",
        "    def fit(self, X, Y):\n",
        "        self.X = X\n",
        "        self.Y = Y\n",
        "        self.m, self.n = self.X.shape\n",
        "\n",
        "        #weight initialization\n",
        "        self.W = np.zeros(self.degree+1)\n",
        "\n",
        "        #transform X for polynomial h(x) = w0* x^0+w1*x^1+w2*x^2+......+wn*x^n\n",
        "        X_transform = self.transform(self.X)\n",
        "\n",
        "        #normalize X_transform\n",
        "        X_normalize = self.normalize(X_transform)\n",
        "\n",
        "        #gradient descent learning\n",
        "        for i in range(self.iterations):\n",
        "            h = self.predict(self.X)\n",
        "            error = h - self.Y\n",
        "\n",
        "            #update weights\n",
        "            self.W = self.W - self.learning_rate*(1/self.m)*np.dot(X_normalize.T, error)\n",
        "        return self\n",
        "    #predict\n",
        "\n",
        "    def predict(self, X):\n",
        "       #transform X for polynomial h(x) = w0* x^0+w1*x^1+w2*x^2+......+wn*x^n\n",
        "        X_transform = self.transform(X)\n",
        "\n",
        "        X_normalize = self.normalize(X_transform)\n",
        "\n",
        "        return np.dot(X_transform, self.W)\n",
        "\n",
        "def main():\n",
        "  #create a dataset\n",
        "  X = np.array( [ [1], [2], [3], [4], [5], [6], [7] ] )\n",
        "\n",
        "  Y = np.array( [ 45000, 50000, 60000, 80000, 110000, 150000, 200000 ] )\n",
        "\n",
        "  #X = np.array([ [1], [2], [3], [4], [5], [6], [7] ])\n",
        "  #Y = np.array([ 45000, 50000, 60000, 80000, 110000, 150000, 200000 ])\n",
        "\n",
        "  #model training\n",
        "  model = PolynomialRegression(degree=2, learning_rate=0.01,iterations=500)\n",
        "  model.fit(X, Y)\n",
        "\n",
        "  #Prediction on training set\n",
        "  Y_pred = model.predict(X)\n",
        "\n",
        "  #Visualization\n",
        "  plt.scatter(X, Y, color='red')\n",
        "  plt.plot(X, Y_pred, color='black')\n",
        "  plt.title('X vs Y')\n",
        "  plt.xlabel('X')\n",
        "  plt.ylabel('Y')\n",
        "  plt.show()\n",
        "\n",
        "if __name__==\"__main__\":\n",
        "   main()\n",
        "\n",
        "\n",
        "\n"
      ]
    }
  ]
}