def normalize_observation(observation):
observation = _unit_norm(
observation,
axis=-1,
eps=np.finfo(observation.dtype).tiny,
eps_style='where',
)
return np.ascontiguousarray(np.swapaxes(observation, -2, -1))
def _m_step(
self,
x,
quadratic_form,
affiliation,
saliency,
dirichlet_prior_concentration,
hermitize,
covariance_norm,
eigenvalue_floor,
weight_constant_axis,
):
if saliency is None:
masked_affiliation = affiliation
if dirichlet_prior_concentration == 1:
weight = np.mean(affiliation,
axis=weight_constant_axis,
keepdims=True)
elif np.isposinf(dirichlet_prior_concentration):
*independent, K, T = affiliation.shape[-2:]
weight = np.broadcast_to(1 / K, [*independent, K, 1])
else:
assert dirichlet_prior_concentration >= 1, dirichlet_prior_concentration
assert weight_constant_axis == (-1, ), (
'ToDo: implement weight_constant_axis ({}) for '
'dirichlet_prior_concentration ({}).').format(
weight_constant_axis, dirichlet_prior_concentration)
# affiliation: ..., K, T
tmp = np.sum(affiliation,
axis=weight_constant_axis,
keepdims=True)
K, T = affiliation.shape[-2:]
weight = (tmp + (dirichlet_prior_concentration - 1)) / (
T + (dirichlet_prior_concentration - 1) * K)
else:
assert dirichlet_prior_concentration == 1, dirichlet_prior_concentration
masked_affiliation = affiliation * saliency[..., None, :]
weight = _unit_norm(
np.sum(masked_affiliation,
axis=weight_constant_axis,
keepdims=True),
ord=1,
axis=-1,
eps=1e-10,
eps_style='where',
)
cacg = ComplexAngularCentralGaussianTrainer()._fit(
y=x[..., None, :, :],
saliency=masked_affiliation,
quadratic_form=quadratic_form,
hermitize=hermitize,
covariance_norm=covariance_norm,
eigenvalue_floor=eigenvalue_floor,
)
return CACGMM(weight=weight, cacg=cacg)
def _estimate_mixture_weight_with_dirichlet_prior_concentration(
affiliation,
saliency=None,
weight_constant_axis=-1,
dirichlet_prior_concentration=1,
):
"""
This function is a starting point for those that want to use a Dirichlet
prior with a plug-in rule (i.e. MAP estimate instead of MMSE estimate).
"""
affiliation = np.asarray(affiliation)
if isinstance(weight_constant_axis, int) and \
weight_constant_axis % affiliation.ndim - affiliation.ndim == -2:
K = affiliation.shape[-2]
return np.full([K, 1], 1 / K)
if saliency is None:
if dirichlet_prior_concentration == 1:
weight = np.mean(affiliation,
axis=weight_constant_axis,
keepdims=True)
elif np.isposinf(dirichlet_prior_concentration):
*independent, K, T = affiliation.shape[-2:]
weight = np.broadcast_to(1 / K, [*independent, K, 1])
else:
assert dirichlet_prior_concentration >= 1, dirichlet_prior_concentration # noqa
assert weight_constant_axis == (-1, ), (
'ToDo: implement weight_constant_axis ({}) for '
'dirichlet_prior_concentration ({}).').format(
weight_constant_axis, dirichlet_prior_concentration)
# affiliation: ..., K, T
tmp = np.sum(affiliation, axis=weight_constant_axis, keepdims=True)
K, T = affiliation.shape[-2:]
weight = (tmp + (dirichlet_prior_concentration - 1)) / (
T + (dirichlet_prior_concentration - 1) * K)
else:
assert dirichlet_prior_concentration == 1, dirichlet_prior_concentration # noqa
masked_affiliation = affiliation * saliency[..., None, :]
weight = _unit_norm(
np.sum(masked_affiliation,
axis=weight_constant_axis,
keepdims=True),
ord=1,
axis=-1,
eps=1e-10,
eps_style='where',
)
return weight
def _m_step(
self,
x,
quadratic_form,
affiliation,
saliency,
dirichlet_prior_concentration,
hermitize,
covariance_norm,
eigenvalue_floor,
):
if saliency is None:
masked_affiliation = affiliation
if dirichlet_prior_concentration == 1:
weight = np.mean(affiliation, axis=-1)
elif np.isposinf(dirichlet_prior_concentration):
K, T = affiliation.shape[-2:]
weight = np.broadcast_to(1 / K, affiliation.shape[:-1])
else:
assert dirichlet_prior_concentration >= 1, dirichlet_prior_concentration
# affiliation: ..., K, T
tmp = np.sum(affiliation, axis=-1)
K, T = affiliation.shape[-2:]
weight = (tmp + (dirichlet_prior_concentration - 1)) / (
T + (dirichlet_prior_concentration - 1) * K)
else:
assert dirichlet_prior_concentration == 1, dirichlet_prior_concentration
masked_affiliation = affiliation * saliency[..., None, :]
weight = _unit_norm(
np.sum(masked_affiliation, axis=-1),
ord=1,
axis=-1,
eps=1e-10,
eps_style='where',
)
cacg = ComplexAngularCentralGaussianTrainer()._fit(
y=x[..., None, :, :],
saliency=masked_affiliation,
quadratic_form=quadratic_form,
hermitize=hermitize,
covariance_norm=covariance_norm,
eigenvalue_floor=eigenvalue_floor,
)
return CACGMM(weight=weight, cacg=cacg)
def normalize_observation(observation):
"""
Attention: swap D and N dim
The dimensions are swapped, because some calculations (e.g. covariance) do
a reduction over the sample (time) dimension. Having the time dimension on
the last axis improves the execution time.
Args:
observation: (..., N, D)
Returns:
normalized observation (..., D, N)
"""
observation = _unit_norm(
observation,
axis=-1,
eps=np.finfo(observation.dtype).tiny,
eps_style='where',
)
return np.ascontiguousarray(np.swapaxes(observation, -2, -1))
def estimate_mixture_weight(
affiliation,
saliency=None,
weight_constant_axis=-1,
):
"""
Estimates the mixture weight of a mixture model.
The simplest version (without saliency and prior):
return np.mean(affiliation, axis=weight_constant_axis, keepdims=True)
Args:
affiliation: Shape: (..., K, T)
saliency: Shape: (..., K, T)
weight_constant_axis: int
Returns:
mixture weight with the same shape as affiliation, except for the
weight_constant_axis that is a singleton:
e.g. for weight_constant_axis == -1: (..., K, 1)
When the weight_constant_axis is -2 or the positive counterpart,
then the returned shape is always (K, 1) and the value if 1/K.
>>> affiliation = [[0.4, 1, 0.4], [0.6, 0, 0.6]]
>>> estimate_mixture_weight(affiliation)
array([[0.6],
[0.4]])
>>> estimate_mixture_weight(affiliation, weight_constant_axis=-2)
array([[0.5],
[0.5]])
>>> estimate_mixture_weight([affiliation, affiliation])
array([[[0.6],
[0.4]],
<BLANKLINE>
[[0.6],
[0.4]]])
>>> estimate_mixture_weight([affiliation, affiliation], weight_constant_axis=-2)
array([[0.5],
[0.5]])
>>> estimate_mixture_weight([affiliation, affiliation], weight_constant_axis=-3)
array([[[0.4, 1. , 0.4],
[0.6, 0. , 0.6]]])
"""
affiliation = np.asarray(affiliation)
if isinstance(weight_constant_axis, int) and \
weight_constant_axis % affiliation.ndim - affiliation.ndim == -2:
K = affiliation.shape[-2]
return np.full([K, 1], 1 / K)
elif isinstance(weight_constant_axis, list):
weight_constant_axis = tuple(weight_constant_axis)
if saliency is None:
weight = np.mean(affiliation, axis=weight_constant_axis, keepdims=True)
else:
masked_affiliation = affiliation * saliency[..., None, :]
weight = _unit_norm(
np.sum(masked_affiliation,
axis=weight_constant_axis,
keepdims=True),
ord=1,
axis=-2,
eps=1e-10,
eps_style='where',
)
return weight