sklearn.mixture
.GaussianMixture¶

class
sklearn.mixture.
GaussianMixture
(n_components=1, *, covariance_type='full', tol=0.001, reg_covar=1e06, max_iter=100, n_init=1, init_params='kmeans', weights_init=None, means_init=None, precisions_init=None, random_state=None, warm_start=False, verbose=0, verbose_interval=10)[source]¶ Gaussian Mixture.
Representation of a Gaussian mixture model probability distribution. This class allows to estimate the parameters of a Gaussian mixture distribution.
Read more in the User Guide.
New in version 0.18.
 Parameters
 n_componentsint, defaults to 1.
The number of mixture components.
 covariance_type{‘full’ (default), ‘tied’, ‘diag’, ‘spherical’}
String describing the type of covariance parameters to use. Must be one of:
 ‘full’
each component has its own general covariance matrix
 ‘tied’
all components share the same general covariance matrix
 ‘diag’
each component has its own diagonal covariance matrix
 ‘spherical’
each component has its own single variance
 tolfloat, defaults to 1e3.
The convergence threshold. EM iterations will stop when the lower bound average gain is below this threshold.
 reg_covarfloat, defaults to 1e6.
Nonnegative regularization added to the diagonal of covariance. Allows to assure that the covariance matrices are all positive.
 max_iterint, defaults to 100.
The number of EM iterations to perform.
 n_initint, defaults to 1.
The number of initializations to perform. The best results are kept.
 init_params{‘kmeans’, ‘random’}, defaults to ‘kmeans’.
The method used to initialize the weights, the means and the precisions. Must be one of:
'kmeans' : responsibilities are initialized using kmeans. 'random' : responsibilities are initialized randomly.
 weights_initarraylike, shape (n_components, ), optional
The userprovided initial weights, defaults to None. If it None, weights are initialized using the
init_params
method. means_initarraylike, shape (n_components, n_features), optional
The userprovided initial means, defaults to None, If it None, means are initialized using the
init_params
method. precisions_initarraylike, optional.
The userprovided initial precisions (inverse of the covariance matrices), defaults to None. If it None, precisions are initialized using the ‘init_params’ method. The shape depends on ‘covariance_type’:
(n_components,) if 'spherical', (n_features, n_features) if 'tied', (n_components, n_features) if 'diag', (n_components, n_features, n_features) if 'full'
 random_stateint, RandomState instance or None, optional (default=None)
Controls the random seed given to the method chosen to initialize the parameters (see
init_params
). In addition, it controls the generation of random samples from the fitted distribution (see the methodsample
). Pass an int for reproducible output across multiple function calls. See Glossary. warm_startbool, default to False.
If ‘warm_start’ is True, the solution of the last fitting is used as initialization for the next call of fit(). This can speed up convergence when fit is called several times on similar problems. In that case, ‘n_init’ is ignored and only a single initialization occurs upon the first call. See the Glossary.
 verboseint, default to 0.
Enable verbose output. If 1 then it prints the current initialization and each iteration step. If greater than 1 then it prints also the log probability and the time needed for each step.
 verbose_intervalint, default to 10.
Number of iteration done before the next print.
 Attributes
 weights_arraylike, shape (n_components,)
The weights of each mixture components.
 means_arraylike, shape (n_components, n_features)
The mean of each mixture component.
 covariances_arraylike
The covariance of each mixture component. The shape depends on
covariance_type
:(n_components,) if 'spherical', (n_features, n_features) if 'tied', (n_components, n_features) if 'diag', (n_components, n_features, n_features) if 'full'
 precisions_arraylike
The precision matrices for each component in the mixture. A precision matrix is the inverse of a covariance matrix. A covariance matrix is symmetric positive definite so the mixture of Gaussian can be equivalently parameterized by the precision matrices. Storing the precision matrices instead of the covariance matrices makes it more efficient to compute the loglikelihood of new samples at test time. The shape depends on
covariance_type
:(n_components,) if 'spherical', (n_features, n_features) if 'tied', (n_components, n_features) if 'diag', (n_components, n_features, n_features) if 'full'
 precisions_cholesky_arraylike
The cholesky decomposition of the precision matrices of each mixture component. A precision matrix is the inverse of a covariance matrix. A covariance matrix is symmetric positive definite so the mixture of Gaussian can be equivalently parameterized by the precision matrices. Storing the precision matrices instead of the covariance matrices makes it more efficient to compute the loglikelihood of new samples at test time. The shape depends on
covariance_type
:(n_components,) if 'spherical', (n_features, n_features) if 'tied', (n_components, n_features) if 'diag', (n_components, n_features, n_features) if 'full'
 converged_bool
True when convergence was reached in fit(), False otherwise.
 n_iter_int
Number of step used by the best fit of EM to reach the convergence.
 lower_bound_float
Lower bound value on the loglikelihood (of the training data with respect to the model) of the best fit of EM.
See also
BayesianGaussianMixture
Gaussian mixture model fit with a variational inference.
Examples
>>> import numpy as np >>> from sklearn.mixture import GaussianMixture >>> X = np.array([[1, 2], [1, 4], [1, 0], [10, 2], [10, 4], [10, 0]]) >>> gm = GaussianMixture(n_components=2, random_state=0).fit(X) >>> gm.means_ array([[10., 2.], [ 1., 2.]]) >>> gm.predict([[0, 0], [12, 3]]) array([1, 0])
Methods
aic
(self, X)Akaike information criterion for the current model on the input X.
bic
(self, X)Bayesian information criterion for the current model on the input X.
fit
(self, X[, y])Estimate model parameters with the EM algorithm.
fit_predict
(self, X[, y])Estimate model parameters using X and predict the labels for X.
get_params
(self[, deep])Get parameters for this estimator.
predict
(self, X)Predict the labels for the data samples in X using trained model.
predict_proba
(self, X)Predict posterior probability of each component given the data.
sample
(self[, n_samples])Generate random samples from the fitted Gaussian distribution.
score
(self, X[, y])Compute the persample average loglikelihood of the given data X.
score_samples
(self, X)Compute the weighted log probabilities for each sample.
set_params
(self, **params)Set the parameters of this estimator.

aic
(self, X)[source]¶ Akaike information criterion for the current model on the input X.
 Parameters
 Xarray of shape (n_samples, n_dimensions)
 Returns
 aicfloat
The lower the better.

bic
(self, X)[source]¶ Bayesian information criterion for the current model on the input X.
 Parameters
 Xarray of shape (n_samples, n_dimensions)
 Returns
 bicfloat
The lower the better.

fit
(self, X, y=None)[source]¶ Estimate model parameters with the EM algorithm.
The method fits the model
n_init
times and sets the parameters with which the model has the largest likelihood or lower bound. Within each trial, the method iterates between Estep and Mstep formax_iter
times until the change of likelihood or lower bound is less thantol
, otherwise, aConvergenceWarning
is raised. Ifwarm_start
isTrue
, thenn_init
is ignored and a single initialization is performed upon the first call. Upon consecutive calls, training starts where it left off. Parameters
 Xarraylike, shape (n_samples, n_features)
List of n_featuresdimensional data points. Each row corresponds to a single data point.
 Returns
 self

fit_predict
(self, X, y=None)[source]¶ Estimate model parameters using X and predict the labels for X.
The method fits the model n_init times and sets the parameters with which the model has the largest likelihood or lower bound. Within each trial, the method iterates between Estep and Mstep for
max_iter
times until the change of likelihood or lower bound is less thantol
, otherwise, aConvergenceWarning
is raised. After fitting, it predicts the most probable label for the input data points.New in version 0.20.
 Parameters
 Xarraylike, shape (n_samples, n_features)
List of n_featuresdimensional data points. Each row corresponds to a single data point.
 Returns
 labelsarray, shape (n_samples,)
Component labels.

get_params
(self, deep=True)[source]¶ Get parameters for this estimator.
 Parameters
 deepbool, default=True
If True, will return the parameters for this estimator and contained subobjects that are estimators.
 Returns
 paramsmapping of string to any
Parameter names mapped to their values.

predict
(self, X)[source]¶ Predict the labels for the data samples in X using trained model.
 Parameters
 Xarraylike, shape (n_samples, n_features)
List of n_featuresdimensional data points. Each row corresponds to a single data point.
 Returns
 labelsarray, shape (n_samples,)
Component labels.

predict_proba
(self, X)[source]¶ Predict posterior probability of each component given the data.
 Parameters
 Xarraylike, shape (n_samples, n_features)
List of n_featuresdimensional data points. Each row corresponds to a single data point.
 Returns
 resparray, shape (n_samples, n_components)
Returns the probability each Gaussian (state) in the model given each sample.

sample
(self, n_samples=1)[source]¶ Generate random samples from the fitted Gaussian distribution.
 Parameters
 n_samplesint, optional
Number of samples to generate. Defaults to 1.
 Returns
 Xarray, shape (n_samples, n_features)
Randomly generated sample
 yarray, shape (nsamples,)
Component labels

score
(self, X, y=None)[source]¶ Compute the persample average loglikelihood of the given data X.
 Parameters
 Xarraylike, shape (n_samples, n_dimensions)
List of n_featuresdimensional data points. Each row corresponds to a single data point.
 Returns
 log_likelihoodfloat
Log likelihood of the Gaussian mixture given X.

score_samples
(self, X)[source]¶ Compute the weighted log probabilities for each sample.
 Parameters
 Xarraylike, shape (n_samples, n_features)
List of n_featuresdimensional data points. Each row corresponds to a single data point.
 Returns
 log_probarray, shape (n_samples,)
Log probabilities of each data point in X.

set_params
(self, **params)[source]¶ Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as pipelines). The latter have parameters of the form
<component>__<parameter>
so that it’s possible to update each component of a nested object. Parameters
 **paramsdict
Estimator parameters.
 Returns
 selfobject
Estimator instance.