def _m_step(self, observation, embedding, quadratic_form, affiliation,
saliency, hermitize, covariance_norm, eigenvalue_floor,
covariance_type, fixed_covariance, weight_constant_axis,
spatial_weight, spectral_weight):
F, T, D = observation.shape
_, _, E = embedding.shape
_, K, _ = affiliation.shape
masked_affiliation = affiliation * saliency[..., None, :]
if -2 in weight_constant_axis:
weight = 1 / K
else:
weight = np.sum(masked_affiliation,
axis=weight_constant_axis,
keepdims=True)
weight /= np.sum(weight, axis=-2, keepdims=True)
weight = np.squeeze(weight, axis=weight_constant_axis)
embedding_ = np.reshape(embedding, (1, F * T, E))
masked_affiliation_ = np.reshape(
np.transpose(masked_affiliation, (1, 0, 2)),
(K, F * T)) # 'fkt->k,ft'
gaussian = GaussianTrainer()._fit(
y=embedding_,
saliency=masked_affiliation_,
covariance_type=covariance_type,
)
if fixed_covariance is not None:
assert fixed_covariance.shape == gaussian.covariance.shape, (
f'{fixed_covariance.shape} != {gaussian.covariance.shape}')
gaussian = gaussian.__class__(mean=gaussian.mean,
covariance=fixed_covariance)
cacg = ComplexAngularCentralGaussianTrainer()._fit(
y=np.swapaxes(observation[..., None, :, :], -1, -2),
saliency=masked_affiliation,
quadratic_form=quadratic_form,
hermitize=hermitize,
covariance_norm=covariance_norm,
eigenvalue_floor=eigenvalue_floor,
)
return GCACGMM(weight=weight,
gaussian=gaussian,
cacg=cacg,
weight_constant_axis=weight_constant_axis,
spatial_weight=spatial_weight,
spectral_weight=spectral_weight)
def test_gaussian(self):
samples = 10000
mean = np.ones((3, ))
covariance = 2 * np.eye(3)
x = np.random.multivariate_normal(mean, covariance, size=(samples, ))
model = GaussianTrainer().fit(x)
assert_allclose(model.mean, mean, atol=0.1)
assert_allclose(model.covariance, covariance, atol=0.1)
def _m_step(self, x, affiliation, saliency, covariance_type):
masked_affiliation = affiliation * saliency[..., None, :]
weight = np.einsum("...kn->...k", masked_affiliation)
weight /= np.einsum("...n->...", saliency)[..., None]
gaussian = GaussianTrainer()._fit(y=x,
saliency=masked_affiliation,
covariance_type=covariance_type)
return GMM(weight=weight, gaussian=gaussian)
def test_spherical_gaussian(self):
samples = 10000
mean = np.ones((3, ))
covariance = 2 * np.eye(3)
x = np.random.multivariate_normal(mean, covariance, size=(samples, ))
model = GaussianTrainer().fit(x, covariance_type="spherical")
assert_allclose(model.mean, mean, atol=0.1)
assert_allclose(model.covariance,
np.mean(np.diag(covariance)),
atol=0.1)
def _m_step(
self,
x,
affiliation,
saliency,
covariance_type,
fixed_covariance,
):
masked_affiliation = affiliation * saliency[..., None, :]
weight = np.einsum("...kn->...k", masked_affiliation)
weight /= np.einsum("...n->...", saliency)[..., None]
gaussian = GaussianTrainer()._fit(y=x[..., None, :, :],
saliency=masked_affiliation,
covariance_type=covariance_type)
if fixed_covariance is not None:
assert fixed_covariance.shape == gaussian.covariance.shape, (
f'{fixed_covariance.shape} != {gaussian.covariance.shape}')
gaussian = gaussian.__class__(mean=gaussian.mean,
covariance=fixed_covariance)
return GMM(weight=weight, gaussian=gaussian)
def _m_step(self, observation, embedding, quadratic_form, affiliation,
saliency, hermitize, trace_norm, eigenvalue_floor,
covariance_type, fixed_covariance, weight_constant_axis,
spatial_weight, spectral_weight):
F, T, D = observation.shape
_, _, E = embedding.shape
_, K, _ = affiliation.shape
assert K == 4, f'This fancy sharing is just tested for K == 4 != {K}.'
masked_affiliation = affiliation * saliency[..., None, :]
if -2 in weight_constant_axis:
weight = 1 / K
else:
weight = np.sum(masked_affiliation,
axis=weight_constant_axis,
keepdims=True)
weight /= np.sum(weight, axis=-2, keepdims=True)
weight = np.squeeze(weight, axis=weight_constant_axis)
embedding_ = np.reshape(embedding, (1, F * T, E))
masked_affiliation_for_gaussian = np.stack(
(masked_affiliation[:, 0, :] + masked_affiliation[:, 1, :],
masked_affiliation[:, 2, :] + masked_affiliation[:, 3, :]),
axis=1)
masked_affiliation_for_gaussian = np.reshape(
np.transpose(masked_affiliation_for_gaussian, (1, 0, 2)),
(2, F * T)) # 'fkt->k,ft'
gaussian = GaussianTrainer()._fit(
y=embedding_,
saliency=masked_affiliation_for_gaussian,
covariance_type=covariance_type,
)
if fixed_covariance is not None:
assert fixed_covariance.shape == gaussian.covariance.shape, (
f'{fixed_covariance.shape} != {gaussian.covariance.shape}')
gaussian = gaussian.__class__(mean=gaussian.mean,
covariance=fixed_covariance)
# There are 4 classes in quadratic_form. Entry 1 and 2 are equal.
assert np.mean(
np.abs(quadratic_form[:, 1, :] - quadratic_form[:, 2, :])) < 1e-4
quadratic_form = quadratic_form[:, [0, 1, 3], :]
masked_affiliation_for_cacg = np.stack(
(masked_affiliation[:, 0, :], masked_affiliation[:, 1, :] +
masked_affiliation[:, 2, :], masked_affiliation[:, 3, :]),
axis=1)
cacg = ComplexAngularCentralGaussianTrainer()._fit(
y=observation[..., None, :, :],
saliency=masked_affiliation_for_cacg,
quadratic_form=quadratic_form,
hermitize=hermitize,
trace_norm=trace_norm,
eigenvalue_floor=eigenvalue_floor,
)
# Expand again
gaussian = gaussian.__class__(mean=np.stack(
(gaussian.mean[0, :], gaussian.mean[0, :], gaussian.mean[1, :],
gaussian.mean[1, :])),
covariance=np.stack((
gaussian.covariance[0],
gaussian.covariance[0],
gaussian.covariance[1],
gaussian.covariance[1],
)))
# print('gaussian.mean.shape', gaussian.mean.shape)
# print('gaussian.covariance.shape', gaussian.covariance.shape)
# Expand again
cacg = ComplexAngularCentralGaussian.from_covariance(
covariance=np.stack((cacg.covariance[:, 0, :, :],
cacg.covariance[:, 1, :, :],
cacg.covariance[:, 1, :, :],
cacg.covariance[:, 2, :, :]),
axis=1))
# print('cacg.covariance.shape', cacg.covariance.shape)
return GCACGMM(weight=weight,
gaussian=gaussian,
cacg=cacg,
weight_constant_axis=weight_constant_axis,
spatial_weight=spatial_weight,
spectral_weight=spectral_weight)