def test_single_dictionary_update_reduces_cost_function_with_nonzero_lambda():
"""Test single dictionary update reduces regularized cost function."""
random_seed = 0
random_state = check_random_state(random_seed)
n_features = 11
n_components = 6
n_samples = 230
lambda_W = 3.2
X = random_state.uniform(size=(n_samples, n_features))
W = random_state.uniform(size=(n_features, n_components))
Z = right_stochastic_matrix((n_samples, n_components),
random_state=random_state)
assert np.allclose(Z.sum(axis=1), 1, 1e-14)
prefactor = (4.0 / (n_features * n_components * (n_components - 1)))
GW = prefactor * (n_components * np.eye(n_components) - 1)
ZtZ = Z.T.dot(Z)
initial_cost = _gpnh_cost(X, Z, W, lambda_W=lambda_W)
updated_W = _update_gpnh_dictionary(X, Z, ZtZ, GW, lambda_W=lambda_W)
final_cost = _gpnh_cost(X, Z, updated_W, lambda_W=lambda_W)
assert final_cost <= initial_cost
def test_exact_solution_is_weights_update_fixed_point_with_nonzero_lambda():
"""Test exact solution is a fixed point of regularized weights update step."""
random_seed = 0
random_state = check_random_state(random_seed)
n_features = 24
n_components = 8
n_samples = 200
lambda_W = 3.8
tolerance = 1e-6
W = random_state.uniform(size=(n_features, n_components))
Z = right_stochastic_matrix((n_samples, n_components),
random_state=random_state)
assert np.allclose(Z.sum(axis=1), 1, tolerance)
X = Z.dot(W.T)
initial_cost = _gpnh_cost(X, Z, W, lambda_W=lambda_W)
updated_Z = _update_gpnh_weights(X, Z, W)
final_cost = _gpnh_cost(X, updated_Z, W, lambda_W=lambda_W)
assert np.allclose(Z, updated_Z, tolerance)
assert abs(final_cost - initial_cost) < tolerance
def test_single_weights_updates_reduces_cost_function_with_nonzero_lambda():
"""Test single weights update reduces cost function."""
random_seed = 0
random_state = check_random_state(random_seed)
n_features = 43
n_components = 10
n_samples = 320
lambda_W = 4.2
X = random_state.uniform(size=(n_samples, n_features))
W = random_state.uniform(size=(n_features, n_components))
Z = right_stochastic_matrix((n_samples, n_components),
random_state=random_state)
assert np.allclose(Z.sum(axis=1), 1, 1e-14)
initial_cost = _gpnh_cost(X, Z, W, lambda_W=lambda_W)
updated_Z = _update_gpnh_weights(X, Z, W)
final_cost = _gpnh_cost(X, updated_Z, W, lambda_W=lambda_W)
assert final_cost <= initial_cost
def test_cost_returns_zero_for_perfect_reconstruction_no_regularization():
"""Test cost is zero for perfect factorization."""
random_seed = 0
random_state = check_random_state(random_seed)
n_features = 5
n_components = 3
n_samples = 30
tolerance = 1e-14
lambda_W = 0
W = random_state.uniform(size=(n_features, n_components))
Z = right_stochastic_matrix((n_samples, n_components),
random_state=random_state)
assert np.allclose(Z.sum(axis=1), 1, tolerance)
X = Z.dot(W.T)
cost = _gpnh_cost(X, Z, W, lambda_W=lambda_W)
expected_cost = 0
assert abs(cost - expected_cost) < 1e-14
def test_repeated_dictionary_updates_converge_with_nonzero_lambda():
"""Test repeated updates converge to fixed point for regularized problem."""
random_seed = 0
random_state = check_random_state(random_seed)
n_features = 27
n_components = 13
n_samples = 500
max_iterations = 100
tolerance = 1e-6
lambda_W = 1.5
X = random_state.uniform(size=(n_samples, n_features))
W = random_state.uniform(size=(n_features, n_components))
Z = right_stochastic_matrix((n_samples, n_components),
random_state=random_state)
assert np.allclose(Z.sum(axis=1), 1, 1e-12)
initial_cost = _gpnh_cost(X, Z, W, lambda_W=lambda_W)
updated_Z, updated_W, _, n_iter, _, _ = _iterate_gpnh_convex_coding(
X,
Z,
W,
lambda_W=lambda_W,
update_weights=False,
update_dictionary=True,
tolerance=tolerance,
max_iterations=max_iterations,
require_monotonic_cost_decrease=True,
verbose=True)
final_cost = _gpnh_cost(X, updated_Z, updated_W, lambda_W=lambda_W)
assert final_cost <= initial_cost
assert n_iter < max_iterations
def test_exact_solution_is_dictionary_update_fixed_point():
"""Test exact solution is a fixed point of dictionary update step."""
random_seed = 0
random_state = check_random_state(random_seed)
n_features = 10
n_components = 6
n_samples = 40
lambda_W = 0
tolerance = 1e-6
W = random_state.uniform(size=(n_features, n_components))
Z = right_stochastic_matrix((n_samples, n_components),
random_state=random_state)
assert np.allclose(Z.sum(axis=1), 1, tolerance)
X = Z.dot(W.T)
prefactor = (4.0 / (n_features * n_components * (n_components - 1)))
GW = prefactor * (n_components * np.eye(n_components) - 1)
ZtZ = Z.T.dot(Z)
initial_cost = _gpnh_cost(X, Z, W, lambda_W=lambda_W)
updated_W = _update_gpnh_dictionary(X, Z, ZtZ, GW, lambda_W=lambda_W)
final_cost = _gpnh_cost(X, Z, updated_W, lambda_W=lambda_W)
assert np.allclose(updated_W, W, tolerance)
assert abs(final_cost - initial_cost) < tolerance