def test_gaussian_mixture_aic_bic():
# Test the aic and bic criteria
rng = np.random.RandomState(0)
n_samples, n_features, n_components = 50, 3, 2
X = rng.randn(n_samples, n_features)
# standard gaussian entropy
sgh = 0.5 * (fast_logdet(np.cov(X.T, bias=1)) + n_features *
(1 + np.log(2 * np.pi)))
for cv_type in COVARIANCE_TYPE:
g = GaussianMixture(n_components=n_components,
covariance_type=cv_type,
random_state=rng,
max_iter=200)
g.fit(X)
aic = 2 * n_samples * sgh + 2 * g._n_parameters()
bic = (2 * n_samples * sgh + np.log(n_samples) * g._n_parameters())
bound = n_features / np.sqrt(n_samples)
assert (g.aic(X) - aic) / n_samples < bound
assert (g.bic(X) - bic) / n_samples < bound
def test_gaussian_mixture_n_parameters():
# Test that the right number of parameters is estimated
rng = np.random.RandomState(0)
n_samples, n_features, n_components = 50, 5, 2
X = rng.randn(n_samples, n_features)
n_params = {'spherical': 13, 'diag': 21, 'tied': 26, 'full': 41}
for cv_type in COVARIANCE_TYPE:
g = GaussianMixture(n_components=n_components,
covariance_type=cv_type,
random_state=rng).fit(X)
assert g._n_parameters() == n_params[cv_type]
def cluster(data, aff, link, cov, k, c_true=None):
"""
Cluster according to specified method
input:
data - nxk numpy matrix of data
c_true - n array of true cluster membership
aff - affinity, element of ['euclidean','manhattan','cosine'] or none for EM
from scratch
link - linkage, element of ['ward','complete','average','single'], or none for
EM from scratch
cov - covariance, element of ['full','tied','diag','spherical']
k - # of clusters
output:
c_hat - n array of clustering results
means - kxd array of means of mixture components
bic - Bayes Information Criterion for this clustering
ari - Adjusted Rand Index to comparing clustering result to true clustering
reg - regularization parameter that was used in the clustering results
(0 or 1e-6)
"""
iter_num = 100
if aff == "none" or link == "none":
try: # no regularization
reg = 0
gmm = GaussianMixture(
n_components=k,
covariance_type=cov,
reg_covar=reg,
max_iter=iter_num,
verbose=0,
verbose_interval=1,
)
c_hat = gmm.fit_predict(data)
bic = processBIC(data, gmm.weights_, gmm.means_, gmm.covariances_, cov)
if any([sum(c_hat == i) <= 1 for i in range(k)]) or bic == -np.inf:
raise ValueError
# if there was a numerical error during EM,or while calculating BIC,
# or if the clustering found a class with only one element
except: # regularize
reg = 1e-6
gmm = GaussianMixture(
n_components=k,
covariance_type=cov,
reg_covar=reg,
max_iter=iter_num,
verbose=0,
verbose_interval=1,
)
c_hat = gmm.fit_predict(data)
bic = processBIC(data, gmm.weights_, gmm.means_, gmm.covariances_, cov)
else:
one_hot = agglomerate(data, aff, link, k)
weights, means, precisions = initialize_params(data, one_hot, cov)
try:
reg = 0
gmm = GaussianMixture(
n_components=k,
covariance_type=cov,
weights_init=weights,
means_init=means,
precisions_init=precisions,
max_iter=iter_num,
reg_covar=reg,
verbose=0,
verbose_interval=1,
)
c_hat = gmm.fit_predict(data)
bic = processBIC(data, gmm.weights_, gmm.means_, gmm.covariances_, cov)
if any([sum(c_hat == i) <= 1 for i in range(k)]) or bic == -np.inf:
raise ValueError
# if there was a numerical error, or if initial clustering produced a
# mixture component with only one element
except:
reg = 1e-6
gmm = GaussianMixture(
n_components=k,
covariance_type=cov,
weights_init=weights,
means_init=means,
precisions_init=precisions,
max_iter=iter_num,
reg_covar=reg,
verbose=0,
verbose_interval=1,
)
c_hat = gmm.fit_predict(data)
bic = processBIC(data, gmm.weights_, gmm.means_, gmm.covariances_, cov)
if c_true is not None:
ari = adjusted_rand_score(c_true, c_hat)
else:
ari = None
means = gmm.means_
return c_hat, means, bic, ari, reg, gmm._n_parameters()
