def fit(self,
data,
max_iter=DEFAULT_MAX_ITER,
lr_mean=DEFAULT_LR,
conv_factor_mean=DEFAULT_CONV_FACTOR):
"""Fit a Gaussian mixture model (GMM) given the data.
Alternates between Expectation and Maximization steps
for some number of iterations.
Parameters
----------
data : array-like, shape=[n_samples, n_features]
Training data, where n_samples is the number of samples
and n_features is the number of features.
max_iter : int
Optional, default: 100.
Maximum number of iterations.
lr_mean : float
Optional, default: 5e-2.
Learning rate for the mean.
conv_factor_mean : float
Optional, default: 5e-3.
Convergence factor for the mean.
Returns
-------
self : object
Return the components of the computed
Gaussian mixture model: means, variances and mixture_coefficients.
"""
self._dimension = data.shape[-1]
if self.initialisation_method == 'kmeans':
kmeans = RiemannianKMeans(metric=self.metric,
n_clusters=self.n_gaussians,
init='random',
mean_method='frechet-poincare-ball')
centroids = kmeans.fit(X=data, max_iter=100)
labels = kmeans.predict(X=data)
self.means = centroids
self.variances = gs.zeros(self.n_gaussians)
labeled_data = gs.vstack([labels, gs.transpose(data)])
labeled_data = gs.transpose(labeled_data)
for label, centroid in enumerate(centroids):
label_mask = gs.where(labeled_data[:, 0] == label)
grouped_by_label = labeled_data[label_mask][:, 1:]
v = variance(grouped_by_label, centroid, self.metric)
if grouped_by_label.shape[0] == 1:
v += MIN_VAR_INIT
self.variances[label] = v
else:
self.means = (gs.random.rand(self.n_gaussians, self._dimension) -
0.5) / self._dimension
self.variances = gs.random.rand(self.n_gaussians) / 10 + 0.8
self.mixture_coefficients = \
gs.ones(self.n_gaussians) / self.n_gaussians
posterior_probabilities = gs.ones((data.shape[0], self.means.shape[0]))
self.variances_range,\
self.normalization_factor_var, \
self.phi_inv_var =\
self.metric.normalization_factor_init(
gs.arange(
ZETA_LOWER_BOUND, ZETA_UPPER_BOUND, ZETA_STEP))
for epoch in range(max_iter):
old_posterior_probabilities = posterior_probabilities
posterior_probabilities = self._expectation(data)
condition = gs.mean(
gs.abs(old_posterior_probabilities - posterior_probabilities))
if (condition < EM_CONV_RATE and epoch > MINIMUM_EPOCHS):
logging.info('EM converged in %s iterations', epoch)
return self.means, self.variances, self.mixture_coefficients
self._maximization(data,
posterior_probabilities,
lr_means=lr_mean,
conv_factor_mean=conv_factor_mean)
logging.info('WARNING: EM did not converge \n'
'Please increase MINIMUM_EPOCHS.')
return self.means, self.variances, self.mixture_coefficients
def fit(self, data):
"""Fit a Gaussian mixture model (GMM) given the data.
Alternates between Expectation and Maximization steps
for some number of iterations.
Parameters
----------
data : array-like, shape=[n_samples, n_features]
Training data, where n_samples is the number of samples
and n_features is the number of features.
Returns
-------
self : object
Return the components of the computed
Gaussian mixture model: means, variances and mixture_coefficients.
"""
self._dimension = data.shape[-1]
if self.initialisation_method == "kmeans":
kmeans = RiemannianKMeans(
metric=self.metric,
n_clusters=self.n_gaussians,
init="random",
init_step_size=self.init_step_size,
mean_method="batch",
)
centroids = kmeans.fit(X=data)
labels = kmeans.predict(X=data)
self.means = centroids
self.variances = gs.zeros(self.n_gaussians)
labeled_data = gs.vstack([labels, gs.transpose(data)])
labeled_data = gs.transpose(labeled_data)
for label, centroid in enumerate(centroids):
label_mask = gs.where(labeled_data[:, 0] == label)
grouped_by_label = labeled_data[label_mask][:, 1:]
v = variance(grouped_by_label, centroid, self.metric)
if grouped_by_label.shape[0] == 1:
v += MIN_VAR_INIT
self.variances[label] = v
else:
self.means = (gs.random.rand(self.n_gaussians, self._dimension) -
0.5) / self._dimension
self.variances = gs.random.rand(self.n_gaussians) / 10 + 0.8
self.mixture_coefficients = gs.ones(
self.n_gaussians) / self.n_gaussians
posterior_probabilities = gs.ones((data.shape[0], self.means.shape[0]))
(
self.variances_range,
self.normalization_factor_var,
self.phi_inv_var,
) = self.normalization_factor_init(
gs.arange(ZETA_LOWER_BOUND, ZETA_UPPER_BOUND, ZETA_STEP))
for epoch in range(self.max_iter):
old_posterior_probabilities = posterior_probabilities
posterior_probabilities = self._expectation(data)
condition = gs.mean(
gs.abs(old_posterior_probabilities - posterior_probabilities))
if condition < EM_CONV_RATE and epoch > MINIMUM_EPOCHS:
logging.info("EM converged in %s iterations", epoch)
return self.means, self.variances, self.mixture_coefficients
self._maximization(data, posterior_probabilities)
logging.info("WARNING: EM did not converge \n"
"Please increase MINIMUM_EPOCHS.")
return self.means, self.variances, self.mixture_coefficients
