Logistic_Regression_Vorpal.py

logistic-regression_vorpal.py

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+import csv 
+import numpy as np 
+import matplotlib.pyplot as plt 
+
+
+def loadCSV(filename): 
+	''' 
+	function to load dataset 
+	'''
+	with open(filename,"r") as csvfile: 
+		lines = csv.reader(csvfile) 
+		dataset = list(lines) 
+		for i in range(len(dataset)): 
+			dataset[i] = [float(x) for x in dataset[i]]	 
+	return np.array(dataset) 
+
+
+def normalize(X): 
+	''' 
+	function to normalize feature matrix, X 
+	'''
+	mins = np.min(X, axis = 0) 
+	maxs = np.max(X, axis = 0) 
+	rng = maxs - mins 
+	norm_X = 1 - ((maxs - X)/rng) 
+	return norm_X 
+
+
+def logistic_func(beta, X): 
+	''' 
+	logistic(sigmoid) function 
+	'''
+	return 1.0/(1 + np.exp(-np.dot(X, beta.T))) 
+
+
+def log_gradient(beta, X, y): 
+	''' 
+	logistic gradient function 
+	'''
+	first_calc = logistic_func(beta, X) - y.reshape(X.shape[0], -1) 
+	final_calc = np.dot(first_calc.T, X) 
+	return final_calc 
+
+
+def cost_func(beta, X, y): 
+	''' 
+	cost function, J 
+	'''
+	log_func_v = logistic_func(beta, X) 
+	y = np.squeeze(y) 
+	step1 = y * np.log(log_func_v) 
+	step2 = (1 - y) * np.log(1 - log_func_v) 
+	final = -step1 - step2 
+	return np.mean(final) 
+
+
+def grad_desc(X, y, beta, lr=.01, converge_change=.001): 
+	''' 
+	gradient descent function 
+	'''
+	cost = cost_func(beta, X, y) 
+	change_cost = 1
+	num_iter = 1
+
+	while(change_cost > converge_change): 
+		old_cost = cost 
+		beta = beta - (lr * log_gradient(beta, X, y)) 
+		cost = cost_func(beta, X, y) 
+		change_cost = old_cost - cost 
+		num_iter += 1
+
+	return beta, num_iter 
+
+
+def pred_values(beta, X): 
+	''' 
+	function to predict labels 
+	'''
+	pred_prob = logistic_func(beta, X) 
+	pred_value = np.where(pred_prob >= .5, 1, 0) 
+	return np.squeeze(pred_value) 
+
+
+def plot_reg(X, y, beta): 
+	''' 
+	function to plot decision boundary 
+	'''
+	# labelled observations 
+	x_0 = X[np.where(y == 0.0)] 
+	x_1 = X[np.where(y == 1.0)] 
+
+	# plotting points with diff color for diff label 
+	plt.scatter([x_0[:, 1]], [x_0[:, 2]], c='b', label='y = 0') 
+	plt.scatter([x_1[:, 1]], [x_1[:, 2]], c='r', label='y = 1') 
+
+	# plotting decision boundary 
+	x1 = np.arange(0, 1, 0.1) 
+	x2 = -(beta[0,0] + beta[0,1]*x1)/beta[0,2] 
+	plt.plot(x1, x2, c='k', label='reg line') 
+
+	plt.xlabel('x1') 
+	plt.ylabel('x2') 
+	plt.legend() 
+	plt.show() 
+
+
+
+if __name__ == "__main__": 
+	# load the dataset 
+	dataset = loadCSV('dataset1.csv') 
+
+	# normalizing feature matrix 
+	X = normalize(dataset[:, :-1]) 
+
+	# stacking columns wth all ones in feature matrix 
+	X = np.hstack((np.matrix(np.ones(X.shape[0])).T, X)) 
+
+	# response vector 
+	y = dataset[:, -1] 
+
+	# initial beta values 
+	beta = np.matrix(np.zeros(X.shape[1])) 
+
+	# beta values after running gradient descent 
+	beta, num_iter = grad_desc(X, y, beta) 
+
+	# estimated beta values and number of iterations 
+	print("Estimated regression coefficients:", beta) 
+	print("No. of iterations:", num_iter) 
+
+	# predicted labels 
+	y_pred = pred_values(beta, X) 
+
+	# number of correctly predicted labels 
+	print("Correctly predicted labels:", np.sum(y == y_pred)) 
+
+	# plotting regression line 
+	plot_reg(X, y, beta)