def verify_cubic_features1D():
X = np.array([[np.sqrt(3)], [0]])
X_cube = np.sort(cubic_features(X))
X_correct = np.array([[1., np.sqrt(9), np.sqrt(27), np.sqrt(27)], [0., 0., 0., 1.]])
if np.all(np.absolute(X_cube - X_correct) < 1.0e-6):
print("Verifying cubic features of 1 dimension: Passed")
else:
print("Verifying cubic features of 1 dimension: Failed")
def verify_cubic_features2D2():
X = np.array([[np.sqrt(3), 0], [0, np.sqrt(3)]])
X_cube = np.sort(cubic_features(X))
X_correct = np.array([[0., 0., 0., 0., 0., 0., 1., 3., 5.19615242, 5.19615242],
[0., 0., 0., 0., 0., 0., 1., 3., 5.19615242, 5.19615242]])
if np.all(np.absolute(X_cube - X_correct) < 1.0e-6):
print("Verifying cubic features of 2 dimensions asymmetric vectors: Passed")
else:
print("Verifying cubic features of 2 dimensions asymmetric vectors: Failed")
def verify_cubic_features2D():
X = np.array([[np.sqrt(3), np.sqrt(3)], [0, 0]])
X_cube = np.sort(cubic_features(X))
X_correct = np.array([[1., 3., 3., 5.19615242, 5.19615242, 5.19615242, 5.19615242, 7.34846923, 9., 9.],
[0., 0., 0., 0., 0., 0., 0., 0., 0., 1.]])
if np.all(np.absolute(X_cube - X_correct) < 1.0e-6):
print("Verifying cubic features of 2 dimensions: Passed")
else:
print("Verifying cubic features of 2 dimensions: Failed")
secondimage_reconstructed = reconstruct_PC(train_pca[1, ], pcs, n_components,
train_x)
plot_images(secondimage_reconstructed)
plot_images(train_x[1, ])
## Cubic Kernel ##
# TODO: Find the 10-dimensional PCA representation of the training and test set
n_components = 10
pcs10 = principal_components(train_x)
train_pca10 = project_onto_PC(train_x, pcs10, n_components)
test_pca10 = project_onto_PC(test_x, pcs10, n_components)
# TODO: First fill out cubicFeatures() function in features.py as the below code requires it.
train_cube = cubic_features(train_pca10)
test_cube = cubic_features(test_pca10)
# train_cube (and test_cube) is a representation of our training (and test) data
# after applying the cubic kernel feature mapping to the 10-dimensional PCA representations.
# TODO: Train your softmax regression model using (train_cube, train_y)
# and evaluate its accuracy on (test_cube, test_y).
temp_parameter = 1
theta, cost_function_history = softmax_regression(train_cube,
train_y,
temp_parameter,
alpha=0.3,
lambda_factor=1.0e-4,
k=10,
num_iterations=150)
plot_cost_function_over_time(cost_function_history)
