def test_B_grad(self, random_rank4_parafac2_tensor):
X = random_rank4_parafac2_tensor.construct_tensor()
A = random_rank4_parafac2_tensor.A
blueprint_B = random_rank4_parafac2_tensor.blueprint_B
C = random_rank4_parafac2_tensor.C
ktensor = KruskalTensor([A, blueprint_B, C])
projected_X = ktensor.construct_tensor()
wrong_decomposition = Parafac2Tensor.random_init(
sizes=random_rank4_parafac2_tensor.shape,
rank=random_rank4_parafac2_tensor.rank
)
sub_problem = Parafac2RLS()
sub_problem.update_decomposition(
X, wrong_decomposition, projected_X, should_update_projections=False
)
new_B = wrong_decomposition.blueprint_B
def loss(x):
B = x.reshape(wrong_decomposition.blueprint_B.shape)
factor_matrices = [wrong_decomposition.A, B, wrong_decomposition.C]
estimated = np.einsum('ir, jr, kr -> ijk', *factor_matrices)
return np.linalg.norm(estimated - projected_X)**2
deriv = approx_fprime(new_B.ravel(), loss, epsilon=np.sqrt(np.finfo(float).eps))
assert np.allclose(deriv, 0, atol=1e-4, rtol=1e-4)
def test_minimum(self, random_rank4_ktensor, **kwargs):
# Check if loss increases after pertubation
X = random_rank4_ktensor.construct_tensor()
wrong_decomposition = KruskalTensor.random_init(
random_rank4_ktensor.shape,
rank=random_rank4_ktensor.rank
)
for mode in range(3):
sub_problem = self.SubProblem(mode=mode, **kwargs)
sub_problem.update_decomposition(X, wrong_decomposition)
factor_matrix = wrong_decomposition.factor_matrices[mode]
fm_norm = np.linalg.norm(factor_matrix)
for noise in range(1, 11):
noise /= 100
factor_matrix_perturbed = self.perturb_factor_matrix(factor_matrix, noise)
def loss(x):
factor_matrices = [
fm for fm in wrong_decomposition.factor_matrices
]
factor_matrices[mode] = x
estimated = np.einsum('ir, jr, kr -> ijk', *factor_matrices)
return np.linalg.norm(estimated - X)**2
assert loss(factor_matrix) <= loss(factor_matrix_perturbed)
def check_gradient(self, decomposition, **kwargs):
X = decomposition.construct_tensor()
wrong_decomposition = KruskalTensor.random_init(
decomposition.shape,
rank=decomposition.rank,
random_method='uniform'
)
num_modes = len(decomposition.factor_matrices)
letters = [chr(ord('i') + mode) for mode in range(num_modes)]
einsum_pattern = ''.join(f'{l}r, ' for l in letters)[:-2] + ' -> ' + ''.join(letters)
for mode in range(num_modes):
print('kwargs', kwargs)
rls = self.SubProblem(mode=mode, **kwargs)
rls.update_decomposition(X, wrong_decomposition)
def loss(x):
factor_matrices = [
fm for fm in wrong_decomposition.factor_matrices
]
factor_matrices[mode] = x.reshape(factor_matrices[mode].shape)
estimated = np.einsum(einsum_pattern, *factor_matrices)
return np.linalg.norm(estimated - X)**2
raveled_fm = wrong_decomposition.factor_matrices[mode].ravel()
deriv = approx_fprime(
raveled_fm,
loss,
epsilon=np.sqrt(np.finfo(float).eps)
)
np.testing.assert_allclose(0, deriv/loss(raveled_fm), atol=1e-3, rtol=1e-3)
def test_projected_X(self, random_rank4_parafac2_tensor):
X = random_rank4_parafac2_tensor.construct_slices()
A = random_rank4_parafac2_tensor.A
blueprint_B = random_rank4_parafac2_tensor.blueprint_B
C = random_rank4_parafac2_tensor.C
ktensor = KruskalTensor([A, blueprint_B, C])
projected_X = ktensor.construct_tensor()
wrong_decomposition = Parafac2Tensor.random_init(
sizes=random_rank4_parafac2_tensor.shape,
rank=random_rank4_parafac2_tensor.rank
)
sub_problem = Parafac2RLS()
sub_problem.update_decomposition(
X, wrong_decomposition, projected_X, should_update_projections=True
)
for projection in wrong_decomposition.projection_matrices:
assert np.allclose(projection.T@projection, np.identity(projection.shape[1]))
def random_nonnegative_rank4_ktensor(self):
return KruskalTensor.random_init([30, 40, 50], 4, random_method='uniform')
def random_rank4_ktensor(self):
return KruskalTensor.random_init([30, 40, 50], rank=4)