def test_pca(A, p):
pca = PCA(A, p)
Ap, G = pca.get_reduced()
A_re = pca.reconstruction(Ap)
error = frobeniu_norm_error(A, A_re)
print('PCA-Reconstruction error for {k} components is'.format(k=p), error)
return G
def test_ae(A, p):
model = AE(d_hidden_rep=p)
model.train(A, A, 128, 300)
A_re = model.reconstruction(A)
final_w = model.get_params()
error = frobeniu_norm_error(A, A_re)
print(
'AE-Reconstruction error for {k}-dimensional hidden representation is'.
format(k=p), error)
return final_w
def test_pca(A, p):
pca = PCA(A, p)
Ap, G = pca.get_reduced()
A_re = pca.reconstruction(Ap)
# mean centering A
A = torch.tensor(A)
ones_matrix = torch.ones((A.shape[1], 1), dtype=torch.double)
A_mean = torch.div(torch.mm(A, ones_matrix), A.shape[1])
A_centered = (A - torch.mm(A_mean, torch.transpose(ones_matrix, 0, 1)))
error = frobeniu_norm_error(A_centered, A_re)
print('PCA-Reconstruction error for {k} components is'.format(k=p), error)
return G
n = A.shape[1]
A_norm = (A - ((1 / n) * A @ np.ones((n, 1))) @ np.ones((1, n)))
ps = [32, 64, 128]
# PCA VS AE (shared weights)
for p in ps:
G = test_pca(A_norm, p)
final_w = test_ae(A, p)
#compare G and final_w
# G:256x64
R = G.T @ W
p = 64
G = test_pca(A_norm, p)
W = test_ae(A_norm, p)
R = G.T @ W
u, s, v = np.linalg.svd(R, full_matrices=True)
Rp = u @ np.eye(u.shape[0], v.shape[0]) @ v
Gp = G @ Rp
print("Gp-W", frobeniu_norm_error(Gp, W))
print('R-Rp', frobeniu_norm_error(R, Rp))
A_re = Gp @ Gp.T @ A_norm
print("Gp reconstruction error:", frobeniu_norm_error(A_norm, A_re))
#AE (shared) vs AE(non-shared)
for p in ps:
final_w = test_ae(A, p)
#multilayer AE
### END YOUR CODE
'AE-Reconstruction error for {k}-dimensional hidden representation is'.
format(k=p), error)
return final_w
if __name__ == '__main__':
dataloc = "./data/USPS.mat"
A = load_data(dataloc)
A = A.T
## Normalize A
A = A / A.max()
### YOUR CODE HERE
# Note: You are free to modify your code here for debugging and justifying your ideas for 5(f)
ps = [32, 64, 128]
for p in ps:
G = test_pca(p)
final_w = test_ae(p)
####### For question 5(f) ########
matrix_transform_G = np.dot(G, G.T)
matrix_transform_W = np.dot(final_w, final_w.T)
matrix_error = frobeniu_norm_error(matrix_transform_G,
matrix_transform_W)
print('Error before transformation of G and W for {} components is {}'.
format(p, frobeniu_norm_error(G, final_w)))
print('Error after transformations of G and W for {} components is {}'.
format(p, matrix_error))
### END YOUR CODE