8000 Modification of the GaussianMixture class. · scikit-learn/scikit-learn@5b4b151 · GitHub
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Modification of the GaussianMixture class.
Remove the useless computation of the covariance matrix. Prepare the integration of the BayesianGaussianMixture class.
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‎sklearn/mixture/gaussian_mixture.py

Lines changed: 102 additions & 84 deletions
Original file line numberDiff line numberDiff line change
@@ -137,14 +137,9 @@ def _check_precisions(precisions, covariance_type, n_components, n_features):
137137

138138
###############################################################################
139139
# Gaussian mixture parameters estimators (used by the M-Step)
140-
ESTIMATE_PRECISION_ERROR_MESSAGE = ("The algorithm has diverged because of "
141-
"too few samples per components. Try to "
142-
"decrease the number of components, "
143-
"or increase reg_covar.")
144140

145-
146-
def _estimate_gaussian_precisions_cholesky_full(resp, X, nk, means, reg_covar):
147-
"""Estimate the full precision matrices.
141+
def _estimate_gaussian_covariances_full(resp, X, nk, means, reg_covar):
142+
"""Estimate the full covariance matrices.
148143
149144
Parameters
150145
----------
@@ -160,27 +155,20 @@ def _estimate_gaussian_precisions_cholesky_full(resp, X, nk, means, reg_covar):
160155
161156
Returns
162157
-------
163-
precisions_chol : array, shape (n_components, n_features, n_features)
164-
The cholesky decomposition of the precision matrix.
158+
covariances : array, shape (n_components, n_features, n_features)
159+
The covariance matrix of the current components.
165160
"""
166161
n_components, n_features = means.shape
167-
precisions_chol = np.empty((n_components, n_features, n_features))
162+
covariances = np.empty((n_components, n_features, n_features))
168163
for k in range(n_components):
169164
diff = X - means[k]
170-
covariance = np.dot(resp[:, k] * diff.T, diff) / nk[k]
171-
covariance.flat[::n_features + 1] += reg_covar
172-
try:
173-
cov_chol = linalg.cholesky(covariance, lower=True)
174-
except linalg.LinAlgError:
175-
raise ValueError(ESTIMATE_PRECISION_ERROR_MESSAGE)
176-
precisions_chol[k] = linalg.solve_triangular(cov_chol,
177-
np.eye(n_features),
178-
lower=True).T
179-
return precisions_chol
165+
covariances[k] = np.dot(resp[:, k] * diff.T, diff) / nk[k]
166+
covariances[k].flat[::n_features + 1] += reg_covar
167+
return covariances
180168

181169

182-
def _estimate_gaussian_precisions_cholesky_tied(resp, X, nk, means, reg_covar):
183-
"""Estimate the tied precision matrix.
170+
def _estimate_gaussian_covariances_tied(resp, X, nk, means, reg_covar):
171+
"""Estimate the tied covariance matrix.
184172
185173
Parameters
186174
----------
@@ -196,26 +184,20 @@ def _estimate_gaussian_precisions_cholesky_tied(resp, X, nk, means, reg_covar):
196184
197185
Returns
198186
-------
199-
precisions_chol : array, shape (n_features, n_features)
200-
The cholesky decomposition of the precision matrix.
187+
covariance : array, shape (n_features, n_features)
188+
The tied covariance matrix of the components.
201189
"""
202-
n_samples, n_features = X.shape
190+
n_samples, _ = X.shape
203191
avg_X2 = np.dot(X.T, X)
204192
avg_means2 = np.dot(nk * means.T, means)
205-
covariances = avg_X2 - avg_means2
206-
covariances /= n_samples
207-
covariances.flat[::len(covariances) + 1] += reg_covar
208-
try:
209-
cov_chol = linalg.cholesky(covariances, lower=True)
210-
except linalg.LinAlgError:
211-
raise ValueError(ESTIMATE_PRECISION_ERROR_MESSAGE)
212-
precisions_chol = linalg.solve_triangular(cov_chol, np.eye(n_features),
213-
lower=True).T
214-
return precisions_chol
193+
covariance = avg_X2 - avg_means2
194+
covariance /= n_samples
195+
covariance.flat[::len(covariance) + 1] += reg_covar
196+
return covariance
215197

216198

217-
def _estimate_gaussian_precisions_cholesky_diag(resp, X, nk, means, reg_covar):
218-
"""Estimate the diagonal precision matrices.
199+
def _estimate_gaussian_covariances_diag(resp, X, nk, means, reg_covar):
200+
"""Estimate the diagonal covariance vectors.
219201
220202
Parameters
221203
----------
@@ -231,21 +213,17 @@ def _estimate_gaussian_precisions_cholesky_diag(resp, X, nk, means, reg_covar):
231213
232214
Returns
233215
-------
234-
precisions_chol : array, shape (n_components, n_features)
235-
The cholesky decomposition of the precision matrix.
216+
covariances : array, shape (n_components, n_features)
217+
The covariance vector of the current components.
236< F438 code>218
"""
237219
avg_X2 = np.dot(resp.T, X * X) / nk[:, np.newaxis]
238220
avg_means2 = means ** 2
239221
avg_X_means = means * np.dot(resp.T, X) / nk[:, np.newaxis]
240-
covariances = avg_X2 - 2 * avg_X_means + avg_means2 + reg_covar
241-
if np.any(np.less_equal(covariances, 0.0)):
242-
raise ValueError(ESTIMATE_PRECISION_ERROR_MESSAGE)
243-
return 1. / np.sqrt(covariances)
222+
return avg_X2 - 2 * avg_X_means + avg_means2 + reg_covar
244223

245224

246-
def _estimate_gaussian_precisions_cholesky_spherical(resp, X, nk, means,
247-
reg_covar):
248-
"""Estimate the spherical precision matrices.
225+
def _estimate_gaussian_covariances_spherical(resp, X, nk, means, reg_covar):
226+
"""Estimate the spherical variance values.
249227
250228
Parameters
251229
----------
@@ -261,16 +239,11 @@ def _estimate_gaussian_precisions_cholesky_spherical(resp, X, nk, means,
261239
262240
Returns
263241
-------
264-
precisions_chol : array, shape (n_components,)
265-
The cholesky decomposition of the precision matrix.
242+
variances : array, shape (n_components,)
243+
The variance values of each components.
266244
"""
267-
avg_X2 = np.dot(resp.T, X * X) / nk[:, np.newaxis]
268-
avg_means2 = means ** 2
269-
avg_X_means = means * np.dot(resp.T, X) / nk[:, np.newaxis]
270-
covariances = (avg_X2 - 2 * avg_X_means + avg_means2 + reg_covar).mean(1)
271-
if np.any(np.less_equal(covariances, 0.0)):
272-
raise ValueError(ESTIMATE_PRECISION_ERROR_MESSAGE)
273-
return 1. / np.sqrt(covariances)
245+
return _estimate_gaussian_covariances_diag(resp, X, nk,
246+
means, reg_covar).mean(1)
274247

275248

276249
def _estimate_gaussian_parameters(X, resp, reg_covar, covariance_type):
@@ -292,29 +265,77 @@ def _estimate_gaussian_parameters(X, resp, reg_covar, covariance_type):
292265
293266
Returns
294267
-------
295-
nk : array, shape (n_components,)
268+
nk : array-like, shape (n_components,)
296269
The numbers of data samples in the current components.
297270
298-
means : array, shape (n_components, n_features)
271+
means : array-like, shape (n_components, n_features)
299272
The centers of the current components.
300273
301-
precisions_cholesky : array
302-
The cholesky decomposition of sample precisions of the current
303-
components. The shape depends of the covariance_type.
274+
covariances : array-like
275+
The covariance matrix of the current components.
276+
The shape depends of the covariance_type.
304277
"""
305278
nk = resp.sum(axis=0) + 10 * np.finfo(resp.dtype).eps
306279
means = np.dot(resp.T, X) / nk[:, np.newaxis]
307-
precs_chol = {"full": _estimate_gaussian_precisions_cholesky_full,
308-
"tied": _estimate_gaussian_precisions_cholesky_tied,
309-
"diag": _estimate_gaussian_precisions_cholesky_diag,
310-
"spherical": _estimate_gaussian_precisions_cholesky_spherical
311-
}[covariance_type](resp, X, nk, means, reg_covar)
312-
return nk, means, precs_chol
280+
covariances = {"full": _estimate_gaussian_covariances_full,
281+
"tied": _estimate_gaussian_covariances_tied,
282+
"diag": _estimate_gaussian_covariances_diag,
283+
"spherical": _estimate_gaussian_covariances_spherical
284+
}[covariance_type](resp, X, nk, means, reg_covar)
285+
return nk, means, covariances
286+
287+
288+
def _compute_precision_cholesky(covariances, covariance_type):
289+
"""Compute the Cholesky decomposition of the precisions.
290+
291+
Parameters
292+
----------
293+
covariances : array-like
294+
The covariance matrix of the current components.
295+
The shape depends of the covariance_type.
296+
297+
covariance_type : {'full', 'tied', 'diag', 'spherical'}
298+
The type of precision matrices.
299+
300+
Returns
301+
-------
302+
precisions_cholesky : array-like
303+
The cholesky decomposition of sample precisions of the current
304+
components. The shape depends of the covariance_type.
305+
"""
306+
estimate_precision_error_message = (
307+
"The algorithm has diverged because of too few samples per "
308+
"components. Try to decrease the number of components, "
309+
"or increase reg_covar.")
310+
311+
if covariance_type in 'full':
312+
n_components, n_features, _ = covariances.shape
313+
precisions_chol = np.empty((n_components, n_features, n_features))
314+
for k, covariance in enumerate(covariances):
315+
try:
316+
cov_chol = linalg.cholesky(covariance, lower=True)
317+
except linalg.LinAlgError:
318+
raise ValueError(estimate_precision_error_message)
319+
precisions_chol[k] = linalg.solve_triangular(cov_chol,
320+
np.eye(n_features),
321+
lower=True).T
322+
elif covariance_type is 'tied':
323+
_, n_features = covariances.shape
324+
try:
325+
cov_chol = linalg.cholesky(covariances, lower=True)
326+
except linalg.LinAlgError:
327+
raise ValueError(estimate_precision_error_message)
328+
precisions_chol = linalg.solve_triangular(cov_chol, np.eye(n_features),
329+
lower=True).T
330+
else:
331+
if np.any(np.less_equal(covariances, 0.0)):
332+
raise ValueError(estimate_precision_error_message)
333+
precisions_chol = 1. / np.sqrt(covariances)
334+
return precisions_chol
313335

314336

315337
###############################################################################
316338
# Gaussian mixture probability estimators
317-
318339
def _estimate_log_gaussian_prob_full(X, means, precisions_chol):
319340
"""Estimate the log Gaussian probability for 'full' precision.
320341
@@ -497,21 +518,21 @@ class GaussianMixture(BaseMixture):
497518
498519
Attributes
499520
----------
500-
weights_ : array, shape (n_components,)
521+
weights_ : array-like, shape (n_components,)
501522
The weights of each mixture components.
502523
503-
means_ : array, shape (n_components, n_features)
524+
means_ : array-like, shape (n_components, n_features)
504525
The mean of each mixture component.
505526
506-
covariances_ : array
527+
covariances_ : array-like
507528
The covariance of each mixture component.
508529
The shape depends on `covariance_type`::
509530
(n_components,) if 'spherical',
510531
(n_features, n_features) if 'tied',
511532
(n_components, n_features) if 'diag',
512533
(n_components, n_features, n_features) if 'full'
513534
514-
precisions_ : array
535+
precisions_ : array-like
515536
The precision matrices for each component in the mixture. A precision
516537
matrix is the inverse of a covariance matrix. A covariance matrix is
517538
symmetric positive definite so the mixture of Gaussian can be
@@ -524,7 +545,7 @@ class GaussianMixture(BaseMixture):
524545
(n_components, n_features) if 'diag',
525546
(n_components, n_features, n_features) if 'full'
526547
527-
precisions_cholesky_ : array
548+
precisions_cholesky_ : array-like
528549
The cholesky decomposition of the precision matrices of each mixture
529550
component. A precision matrix is the inverse of a covariance matrix.
530551
A covariance matrix is symmetric positive definite so the mixture of
@@ -594,7 +615,7 @@ def _initialize(self, X, resp):
594615
"""
595616
n_samples, _ = X.shape
596617

597-
weights, means, precisions_cholesky = _estimate_gaussian_parameters(
618+
weights, means, covariances = _estimate_gaussian_parameters(
598619
X, resp, self.reg_covar, self.covariance_type)
599620
weights /= n_samples
600621

@@ -603,7 +624,9 @@ def _initialize(self, X, resp):
603624
self.means_ = means if self.means_init is None else self.means_init
604625

605626
if self.precisions_init is None:
606-
self.precisions_cholesky_ = precisions_cholesky
627+
self.covariances_ = covariances
628+
self.precisions_cholesky_ = _compute_precision_cholesky(
629+
covariances, self.covariance_type)
607630
elif self.covariance_type is 'full':
608631
self.precisions_cholesky_ = np.array(
609632
[linalg.cholesky(prec_init, lower=True)
@@ -619,10 +642,13 @@ def _e_step(self, X):
619642
return np.mean(log_prob_norm), np.exp(log_resp)
620643

621644
def _m_step(self, X, resp):
622-
self.weights_, self.means_, self.precisions_cholesky_ = (
645+
n_samples, _ = X.shape
646+
self.weights_, self.means_, self.covariances_ = (
623647
_estimate_gaussian_parameters(X, resp, self.reg_covar,
624648
self.covariance_type))
625-
self.weights_ /= X.shape[0]
649+
self.weights_ /= n_samples
650+
self.precisions_cholesky_ = _compute_precision_cholesky(
651+
self.covariances_, self.covariance_type)
626652

627653
def _estimate_log_prob(self, X):
628654
return {"full": _estimate_log_gaussian_prob_full,
@@ -649,22 +675,14 @@ def _set_parameters(self, params):
649675

650676
if self.covariance_type is 'full':
651677
self.precisions_ = np.empty(self.precisions_cholesky_.shape)
652-
self.covariances_ = np.empty(self.precisions_cholesky_.shape)
653678
for k, prec_chol in enumerate(self.precisions_cholesky_):
654679
self.precisions_[k] = np.dot(prec_chol, prec_chol.T)
655-
cov_chol = linalg.solve_triangular(prec_chol,
656-
np.eye(n_features))
657-
self.covariances_[k] = np.dot(cov_chol.T, cov_chol)
658680

659681
elif self.covariance_type is 'tied':
660682
self.precisions_ = np.dot(self.precisions_cholesky_,
661683
self.precisions_cholesky_.T)
662-
cov_chol = linalg.solve_triangular(self.precisions_cholesky_,
663-
np.eye(n_features))
664-
self.covariances_ = np.dot(cov_chol.T, cov_chol)
665684
else:
666685
self.precisions_ = self.precisions_cholesky_ ** 2
667-
self.covariances_ = 1. / self.precisions_
668686

669687
def _n_parameters(self):
670688
"""Return the number of free parameters in the model."""

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