机器学习-理解Logistic Regression

import csvimport numpy as npimport 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)

from sklearn import datasets, linear_model, metrics # load the digit datasetdigits = datasets.load_digits() # defining feature matrix(X) and response vector(y)X = digits.datay = digits.target # splitting X and y into training and testing setsfrom sklearn.model_selection import train_test_splitX_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.4, random_state=1) # create logistic regression objectreg = linear_model.LogisticRegression() # train the model using the training setsreg.fit(X_train, y_train) # making predictions on the testing sety_pred = reg.predict(X_test) # comparing actual response values (y_test) with predicted response values (y_pred)print("Logistic Regression model accuracy(in %):", metrics.accuracy_score(y_test, y_pred)*100)