def check_project_onto_PC():
ex_name = "Project onto PC"
X = np.array([
[0, 1, 2, 3],
[1, 2, 3, 4],
[2, 3, 4, 5],
])
pcs = features.principal_components(X)
# exp_res = np.array([
# [-2, 0, 0],
# [0, 0, 0],
# [2, 0, 0]
# ])
exp_res = np.array([[2, 0, 0], [0, 0, 0], [-2, 0, 0]])
n_components = 3
if check_array(ex_name, features.project_onto_PC, exp_res, X, pcs,
n_components):
return
X = np.array([
[1, 2, 3],
[2, 4, 6],
[3, 6, 9],
[4, 8, 12],
])
pcs = features.principal_components(X)
exp_res = np.array([
[5.61248608, 0],
[1.87082869, 0],
[-1.87082869, 0],
[-5.61248608, 0],
])
n_components = 2
if check_array(ex_name, features.project_onto_PC, exp_res, X, pcs,
n_components):
return
log(green("PASS"), ex_name, "")
def check_project_onto_PC():
ex_name = "Project onto PC"
X = np.array([
[0, 1, 2, 3],
[1, 2, 3, 4],
[2, 3, 4, 5],
])
pcs = features.principal_components(X)
exp_res = np.array([[-2, 0, 0], [0, 0, 0], [2, 0, 0]])
n_components = 3
if check_array(ex_name, features.project_onto_PC, exp_res, X, pcs,
n_components):
return
log(green("PASS"), ex_name, "")
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],
])
x_centered, feature_means = features.center_data(X)
pcs = features.principal_components(x_centered)
exp_res = np.array([
[5.61248608, 0],
[1.87082869, 0],
[-1.87082869, 0],
[-5.61248608, 0],
])
n_components = 2
if check_array(ex_name, features.project_onto_PC, exp_res, X, pcs,
n_components, feature_means):
return
log(green("PASS"), ex_name, "")
# raise NotImplementedError
# TODO: Run run_softmax_on_MNIST_mod3(), report the error rate
print('Mod3 softmax test_error=', run_softmax_on_MNIST_mod3(temp_parameter=1))
#######################################################################
# 7. Classification Using Manually Crafted Features
#######################################################################
## Dimensionality reduction via PCA ##
# TODO: First fill out the PCA functions in features.py as the below code depends on them.
n_components = 18
pcs = principal_components(train_x)
train_pca = project_onto_PC(train_x, pcs, n_components)
test_pca = project_onto_PC(test_x, pcs, n_components)
# train_pca (and test_pca) is a representation of our training (and test) data
# after projecting each example onto the first 18 principal components.
# TODO: Train your softmax regression model using (train_pca, train_y)
# and evaluate its accuracy on (test_pca, test_y).
temp_parameter = 1
theta, cost_function_history = softmax_regression(train_pca,
train_y,
temp_parameter,
alpha=0.3,
lambda_factor=1.0e-4,
k=10,
num_iterations=150)
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, :])))