pol reg.py

# Importing libraries
import numpy as np
import math
import matplotlib.pyplot as plt
# Univariate Polynomial Regression
class PolynomailRegression() :
    def __init__( self, degree, learning_rate, iterations ) :        

        self.degree = degree
        self.learning_rate = learning_rate
        self.iterations = iterations
    # function to transform X
    def transform( self, X ) :
        # initialize X_transform
        X_transform = np.ones( ( self.m, 1 ) )
        j = 0   
        for j in range( self.degree + 1 ) :
            if j != 0 :
                x_pow = np.power( X, j )
                # append x_pow to X_transform
                X_transform = np.append( X_transform, x_pow.reshape( -1, 1 ), axis = 1 )
        return X_transform   
    # function to normalize X_transform
    def normalize( self, X ) :
        X[:, 1:] = ( X[:, 1:] - np.mean( X[:, 1:], axis = 0 ) ) / np.std( X[:, 1:], axis = 0 )
        return X
    # model training
    def fit( self, X, Y ) :
        self.X = X
        self.Y = Y
        self.m, self.n = self.X.shape
        # weight initialization
        self.W = np.zeros( self.degree + 1 )
        # transform X for polynomial  h( x ) = w0 * x^0 + w1 * x^1 + w2 * x^2 + ........+ wn * x^n
        X_transform = self.transform( self.X )
        # normalize X_transform
        X_normalize = self.normalize( X_transform )
        # gradient descent learning
        for i in range( self.iterations ) :
            h = self.predict( self.X )
            error = h - self.Y
            # update weights 
            self.W = self.W - self.learning_rate * ( 1 / self.m ) * np.dot( X_normalize.T, error ) 
        return self
    # predict 
    def predict( self, X ) :
        # transform X for polynomial  h( x ) = w0 * x^0 + w1 * x^1 + w2 * x^2 + ........+ wn * x^n
        X_transform = self.transform( X )
        X_normalize = self.normalize( X_transform )
        return np.dot( X_transform, self.W )       
# Driver code     
def main() :    
    # Create dataset
    X = np.array( [ [1], [2], [3], [4], [5], [6], [7] ] )
    Y = np.array( [ 45000, 50000, 60000, 80000, 110000, 150000, 200000 ] )
    # model training
    model = PolynomailRegression( degree = 2, learning_rate = 0.01, iterations = 500 )
    model.fit( X, Y )
    # Prediction on training set
    Y_pred = model.predict( X )
    # Visualization 
    plt.scatter( X, Y, color = 'blue' )
    plt.plot( X, Y_pred, color = 'orange' )
    plt.title( 'X VERSUS Y' )
    plt.xlabel( 'X' )
    plt.ylabel( ' Y' )
    plt.show()
 
if __name__ == "__main__" : 

     

    main()