def check_project_onto_PC():
ex_name = "Project onto PC"
X = np.array([
[1, 2, 3],
[2, 4, 6],
[3, 6, 9],
[4, 8, 12],
])
pcs = features.principal_components(features.center_data(X)[0])
exp_res = np.array([
[5.61248608, 0],
[1.87082869, 0],
[-1.87082869, 0],
[-5.61248608, 0],
])
n_components = 2
feature_means = features.center_data(X)[1]
if check_array(ex_name, features.project_onto_PC, exp_res, X, pcs,
n_components, feature_means):
return
log(green("PASS"), ex_name, "")
temp_parameter)
print('(t = {}) \t\t{:.3}'.format(temp_parameter, test_error_mod3))
print('\nsoftmax mod3 \t\ttest_error:')
for temp_parameter in temp_parameters:
theta = run_softmax("mod3", train_x, update_y(train_y), temp_parameter, 3)
test_error = compute_test_error(test_x, update_y(test_y), theta,
temp_parameter)
print('(t = {}) \t\t{:.3}'.format(temp_parameter, test_error))
#######################################################################
# 8. Dimensionality Reduction Using PCA
#######################################################################
n_components = 18
train_x_c, mean = center_data(train_x)
pcs = principal_components(train_x_c)
train_pca = project_onto_PC(train_x_c, pcs, n_components)
test_pca = project_onto_PC(test_x - mean, pcs, n_components)
# Scatterplot of the first 100 MNIST images, as represented in the space
# spanned by the first 2 principal components found above.
# plot_PC(train_x[range(100), ], pcs, train_y[range(100)])
# First and second MNIST images as reconstructed solely from their 18-dimensional
# principal component representation, compared with the originals.
firstimage_reconstructed = reconstruct_PC(train_pca[0, ], pcs, n_components,
train_x)
secondimage_reconstructed = reconstruct_PC(train_pca[1, :], pcs, n_components,
train_x)
# plot_images(np.vstack((firstimage_reconstructed, secondimage_reconstructed, train_x[0, :], train_x[1, :])))
