def test_cacgmm(self):
samples = 10000
weight = np.array([0.3, 0.7])
covariance = np.array([
[[10, 1 + 1j, 1 + 1j], [1 - 1j, 5, 1], [1 - 1j, 1, 2]],
[[2, 0, 0], [0, 3, 0], [0, 0, 2]],
])
covariance /= np.trace(covariance, axis1=-2, axis2=-1)[..., None, None]
x = sample_cacgmm(samples, weight, covariance)
model = CACGMMTrainer().fit(
x,
num_classes=2,
covariance_norm='trace',
)
# Permutation invariant testing
best_permutation = solve_permutation(model.cacg.covariance[:, :, :],
covariance)
assert_allclose(model.cacg.covariance[best_permutation, :],
covariance,
atol=0.1)
model.weight = model.weight[best_permutation, ]
assert model.weight[0] < model.weight[1], model.weight
assert_allclose(model.weight, weight[:, None], atol=0.15)
def test_sample_cacgmm():
np.random.seed(0)
samples = 10000
weight = np.array([0.3, 0.7])
num_classes = weight.shape[0]
labels = np.random.choice(
range(num_classes), size=(samples,), p=weight
)
covariance = np.array(
[
[[10, 1 + 1j, 1 + 1j], [1 - 1j, 5, 1], [1 - 1j, 1, 2]],
[[2, 0, 0], [0, 3, 0], [0, 0, 2]],
]
)
covariance /= np.trace(covariance, axis1=-2, axis2=-1)[..., None, None]
dimension = covariance.shape[-1]
x_ref = np.zeros((samples, dimension), dtype=np.complex128)
for l in range(num_classes):
cacg = ComplexAngularCentralGaussian.from_covariance(
covariance=covariance[l, :, :]
)
x_ref[labels == l, :] = cacg.sample(size=(np.sum(labels == l),))
np.random.seed(0)
x = sample_cacgmm(samples, weight, covariance)
np.testing.assert_equal(x, x_ref)
def test_cacgmm_independent_dimension(self):
samples = 10000
weight = np.array([0.3, 0.7])
covariance = np.array(
[
[[10, 1 + 1j, 1 + 1j], [1 - 1j, 5, 1], [1 - 1j, 1, 2]],
[[2, 0, 0], [0, 3, 0], [0, 0, 2]],
]
)
covariance /= np.trace(covariance, axis1=-2, axis2=-1)[..., None, None]
x = sample_cacgmm(samples, weight, covariance)
model = CACGMMTrainer().fit(
x[None, ...],
num_classes=2,
covariance_norm='trace',
)
# Permutation invariant testing
best_permutation = solve_permutation(model.cacg.covariance[0, :, :, :], covariance)
assert_allclose(
np.squeeze(model.weight, axis=(0, -1))[best_permutation,],
weight,
atol=0.15
)
assert_allclose(
model.cacg.covariance[0, best_permutation, :], covariance, atol=0.1
)
model = CACGMMTrainer().fit(
np.array([x, x]),
num_classes=2,
covariance_norm='trace',
)
for f in range(model.weight.shape[0]):
# Permutation invariant testing
best_permutation = solve_permutation(model.cacg.covariance[f, :, :, :], covariance)
assert_allclose(
np.squeeze(model.weight, axis=-1)[f, best_permutation,],
weight,
atol=0.15,
)
assert_allclose(
model.cacg.covariance[f, best_permutation, :],
covariance,
atol=0.1,
)
def test_cacgmm_sad_init(self):
samples = 10000
weight = np.array([0.3, 0.7])
num_classes, = weight.shape
covariance = np.array([
[[10, 1 + 1j, 1 + 1j], [1 - 1j, 5, 1], [1 - 1j, 1, 2]],
[[2, 0, 0], [0, 3, 0], [0, 0, 2]],
])
covariance /= np.trace(covariance, axis1=-2, axis2=-1)[..., None, None]
x, labels = sample_cacgmm(samples,
weight,
covariance,
return_label=True)
affiliations = labels_to_one_hot(labels, num_classes, axis=-2)
# test initialization
model = CACGMMTrainer().fit(
x,
initialization=affiliations,
covariance_norm='trace',
)
# test initialization with independent
model = CACGMMTrainer().fit(
np.array([x]),
initialization=np.array([affiliations]),
covariance_norm='trace',
)
# test initialization with independent and broadcasted initialization
model = CACGMMTrainer().fit(
np.array([x, x, x]),
initialization=np.array([affiliations]),
covariance_norm='trace',
)
# test initialization with independent
model = CACGMMTrainer().fit(
np.array([x, x]),
initialization=np.array([affiliations, affiliations]),
covariance_norm='trace',
)