def test_single_weights_update_reduces_cost_with_zero_delta():
"""Test single weights update reduces cost function with delta = 0."""
random_seed = 0
random_state = check_random_state(random_seed)
n_features = 13
n_components = 7
n_samples = 100
X = random_state.uniform(size=(n_samples, n_features))
K = X.dot(X.T)
C = right_stochastic_matrix((n_components, n_samples),
random_state=random_state)
Z = right_stochastic_matrix((n_samples, n_components),
random_state=random_state)
alpha = np.ones(n_components)
CK = C.dot(K)
CKCt = C.dot(K.dot(C.T))
assert np.allclose(C.sum(axis=1), 1, 1e-12)
assert np.allclose(Z.sum(axis=1), 1, 1e-12)
initial_cost = _kernel_aa_cost(K, Z, C, alpha)
updated_Z = _update_kernel_aa_weights(Z, alpha, CK, CKCt)
final_cost = _kernel_aa_cost(K, updated_Z, C, alpha)
assert final_cost <= initial_cost
assert np.allclose(updated_Z.sum(axis=1), 1, 1e-12)
def test_single_dictionary_update_reduces_cost_with_zero_delta():
"""Test single update step reduces cost function."""
random_seed = 0
random_state = check_random_state(random_seed)
n_features = 10
n_components = 5
n_samples = 400
X = random_state.uniform(size=(n_samples, n_features))
K = X.dot(X.T)
C = right_stochastic_matrix((n_components, n_samples),
random_state=random_state)
Z = right_stochastic_matrix((n_samples, n_components),
random_state=random_state)
alpha = np.ones(n_components)
trace_K = np.trace(K)
KZ = K.dot(Z)
ZtZ = Z.T.dot(Z)
assert np.allclose(C.sum(axis=1), 1, 1e-12)
assert np.allclose(Z.sum(axis=1), 1, 1e-12)
initial_cost = _kernel_aa_cost(K, Z, C, alpha)
updated_C = _update_kernel_aa_dictionary(K, C, alpha, trace_K, KZ, ZtZ)
final_cost = _kernel_aa_cost(K, Z, updated_C, alpha)
assert final_cost <= initial_cost
assert np.allclose(updated_C.sum(axis=1), 1, 1e-12)
def test_repeated_weights_updates_converge_with_nonzero_delta():
"""Test repeated updates converge to a fixed point with delta = 0."""
random_seed = 0
random_state = check_random_state(random_seed)
n_features = 30
n_components = 11
n_samples = 320
max_iterations = 100
tolerance = 1e-6
X = random_state.uniform(size=(n_samples, n_features))
K = X.dot(X.T)
C = right_stochastic_matrix((n_components, n_samples),
random_state=random_state)
Z = right_stochastic_matrix((n_samples, n_components),
random_state=random_state)
assert np.allclose(C.sum(axis=1), 1, tolerance)
assert np.allclose(Z.sum(axis=1), 1, tolerance)
delta = 0.3
alpha = random_state.uniform(low=(1 - delta),
high=(1 + delta),
size=(n_components, ))
initial_cost = _kernel_aa_cost(K, Z, C, alpha)
updated_Z, updated_C, updated_alpha, _, n_iter = _iterate_kernel_aa(
K,
Z,
C,
alpha,
delta=delta,
update_weights=True,
update_dictionary=False,
update_scale_factors=False,
tolerance=tolerance,
max_iterations=max_iterations,
require_monotonic_cost_decrease=True)[:5]
final_cost = _kernel_aa_cost(K, updated_Z, updated_C, updated_alpha)
assert final_cost <= initial_cost
assert n_iter < max_iterations
assert np.allclose(updated_C, C, 1e-12)
assert np.allclose(updated_alpha, alpha, 1e-12)
assert np.allclose(updated_Z.sum(axis=1), 1, 1e-12)
def test_exact_solution_with_zero_delta_is_dictionary_update_fixed_point():
"""Test exact solution is a fixed point of the dictionary update."""
random_seed = 0
random_state = check_random_state(random_seed)
n_features = 10
n_components = 6
n_samples = 100
tolerance = 1e-12
basis = random_state.uniform(size=(n_components, n_features))
Z = right_stochastic_matrix((n_samples, n_components),
random_state=random_state)
archetype_indices = np.zeros(n_components, dtype='i8')
for i in range(n_components):
new_index = False
current_index = 0
while not new_index:
new_index = True
current_index = random_state.randint(low=0, high=n_samples)
for index in archetype_indices:
if current_index == index:
new_index = False
archetype_indices[i] = current_index
C = np.zeros((n_components, n_samples))
component = 0
for index in archetype_indices:
C[component, index] = 1.0
for i in range(n_components):
if i == component:
Z[index, i] = 1.0
else:
Z[index, i] = 0.0
component += 1
X = Z.dot(basis)
basis_projection = C.dot(X)
assert np.allclose(basis_projection, basis, tolerance)
assert np.linalg.norm(X - Z.dot(C.dot(X))) < tolerance
K = X.dot(X.T)
alpha = np.ones(n_components)
initial_cost = _kernel_aa_cost(K, Z, C, alpha)
trace_K = np.trace(K)
KZ = K.dot(Z)
ZtZ = Z.T.dot(Z)
updated_C = _update_kernel_aa_dictionary(K, C, alpha, trace_K, KZ, ZtZ)
final_cost = _kernel_aa_cost(K, Z, updated_C, alpha)
assert abs(final_cost - initial_cost) < tolerance
assert np.allclose(updated_C.sum(axis=1), 1, 1e-12)
assert np.allclose(updated_C, C, tolerance)
