import matplotlib.pyplot as plt
import numpy as np
from numpy.linalg import pinv
from common_functions import load_data, J_liner_regression, add_zero_feature, gradient_descent, matrix_args, feature_normalize
if __name__ == '__main__':
X, y = load_data('ex1data2.txt')
mu, sigma, X = feature_normalize(X)
X = add_zero_feature(X)
iterations = 400
alphas = [0.01, 0.1]
f, axarr = plt.subplots(len(alphas), sharex=True)
plt.xlabel('Number of Iterations')
plt.ylabel('Cost J')
for i, alpha in enumerate(alphas):
theta = np.zeros((X.shape[1], 1))
theta, J_history = gradient_descent(J_liner_regression, X, y, iterations, theta, alpha)
axarr[i].set_title('Alpha = {}'.format(alpha))
axarr[i].plot(range(len(J_history)), J_history)
plt.show()
# % Estimate the price of a 1650 sq-ft, 3 br house
# % ====================== YOUR CODE HERE ======================
# % Recall that the first column of X is all-ones. Thus, it does
# % not need to be normalized.
x = np.ones((1, X.shape[1]))
ax = fig.add_subplot(10, 10, i + 1, xticks=[], yticks=[])
ax.imshow(x.reshape(32, 32).T, cmap=plt.cm.Greys_r, interpolation='nearest')
plt.show()
if __name__ == '__main__':
data = sio.loadmat('ex7data1.mat')
X = data['X']
x1, x2 = X.T
plt.plot(x1, x2, 'bo')
plt.show()
mu, sigma, X_norm = feature_normalize(X)
U, S = pca(X_norm)
print('Top eigenvector: ');
print(' U[:,0] = %s' % U[:, 0])
print('(you should expect to see -0.707107 -0.707107)')
K = 1
Z = project_data(X_norm, U, K)
print('Projection of the first example: %s' % Z[0])
print('(this value should be about 1.49631261)')
X_rec = recover_data(Z, U, K)
print('Approximation of the first example: %s' % X_rec[0])
print('(this value should be about -1.05805279 -1.05805279)')
lambda_coef = 0
error_train, error_val = learning_curve(X_extended, y, add_zero_feature(Xval), yval, lambda_coef)
plt.plot(range(1, m + 1), error_train, label="Train")
plt.plot(range(1, m + 1), error_val, c="r", label="Cross validation")
plt.legend()
plt.title("Learning curve for linear regression (pow of polynomial = 1)")
plt.xlabel("Number of training examples)")
plt.ylabel("Error")
plt.axis([0, 13, 0, 150])
plt.show()
p = 8
mu, sigma, X_poly = feature_normalize(poly_features(X, p))
X_poly = add_zero_feature(X_poly)
prepare_X = lambda X: add_zero_feature((poly_features(X, p) - m) / sigma)
X_poly_test = prepare_X(Xtest)
X_poly_val = prepare_X(Xval)
lambda_coef = 1
theta = train_linear_regression(X_poly, y, lambda_coef)
x = np.arange(np.min(X) - 15, np.max(X) + 25, 0.05)[:, np.newaxis]
x_poly = prepare_X(x)
plt.plot(x, np.dot(x_poly, theta))
plot_data()
import matplotlib.pyplot as plt
import numpy as np
from numpy.linalg import pinv
from common_functions import load_data, J_liner_regression, add_zero_feature, gradient_descent, matrix_args, feature_normalize
if __name__ == '__main__':
X, y = load_data('ex1data2.txt')
mu, sigma, X = feature_normalize(X)
X = add_zero_feature(X)
iterations = 400
alphas = [0.01, 0.1]
f, axarr = plt.subplots(len(alphas), sharex=True)
plt.xlabel('Number of Iterations')
plt.ylabel('Cost J')
for i, alpha in enumerate(alphas):
theta = np.zeros((X.shape[1], 1))
theta, J_history = gradient_descent(J_liner_regression, X, y,
iterations, theta, alpha)
axarr[i].set_title('Alpha = {}'.format(alpha))
axarr[i].plot(range(len(J_history)), J_history)
plt.show()
# % Estimate the price of a 1650 sq-ft, 3 br house
# % ====================== YOUR CODE HERE ======================
# % Recall that the first column of X is all-ones. Thus, it does
# % not need to be normalized.
lambda_coef = 0
error_train, error_val = learning_curve(X_extended, y, add_zero_feature(Xval), yval, lambda_coef)
plt.plot(range(1, m+1), error_train, label='Train')
plt.plot(range(1, m+1), error_val, c='r', label='Cross validation')
plt.legend()
plt.title('Learning curve for linear regression (pow of polynomial = 1)')
plt.xlabel('Number of training examples)')
plt.ylabel('Error')
plt.axis([0, 13, 0, 150])
plt.show()
p = 8
mu, sigma, X_poly = feature_normalize(poly_features(X, p))
X_poly = add_zero_feature(X_poly)
prepare_X = lambda X: add_zero_feature((poly_features(X, p)-m)/sigma)
X_poly_test = prepare_X(Xtest)
X_poly_val = prepare_X(Xval)
lambda_coef = 1
theta = train_linear_regression(X_poly, y, lambda_coef)
x = np.arange(np.min(X) - 15, np.max(X) + 25, 0.05)[:, np.newaxis]
x_poly = prepare_X(x)
plt.plot(x, np.dot(x_poly, theta))
plot_data()
cmap=plt.cm.Greys_r,
interpolation='nearest')
plt.show()
if __name__ == '__main__':
data = sio.loadmat('ex7data1.mat')
X = data['X']
x1, x2 = X.T
plt.plot(x1, x2, 'bo')
plt.show()
mu, sigma, X_norm = feature_normalize(X)
U, S = pca(X_norm)
print('Top eigenvector: ')
print(' U[:,0] = %s' % U[:, 0])
print('(you should expect to see -0.707107 -0.707107)')
K = 1
Z = project_data(X_norm, U, K)
print('Projection of the first example: %s' % Z[0])
print('(this value should be about 1.49631261)')
X_rec = recover_data(Z, U, K)
print('Approximation of the first example: %s' % X_rec[0])
print('(this value should be about -1.05805279 -1.05805279)')