GaussianMixture #

classsklearn.mixture.GaussianMixture(n_components=1,*,covariance_type='full',tol=0.001,reg_covar=1e-06,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 mixturedistribution.

Read more in theUser Guide.

Added in version 0.18.

Parameters:

n_componentsint, default=1

The number of mixture components.

covariance_type{‘full’, ‘tied’, ‘diag’, ‘spherical’}, default=’full’

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.

For an example of usingcovariance_type, refer toGaussian Mixture Model Selection.

tolfloat, default=1e-3

The convergence threshold. EM iterations will stop when thelower bound average gain is below this threshold.

reg_covarfloat, default=1e-6

Non-negative regularization added to the diagonal of covariance.Allows to assure that the covariance matrices are all positive.

max_iterint, default=100

The number of EM iterations to perform.

n_initint, default=1

The number of initializations to perform. The best results are kept.

init_params{‘kmeans’, ‘k-means++’, ‘random’, ‘random_from_data’}, default=’kmeans’

The method used to initialize the weights, the means and theprecisions.String must be one of:

‘kmeans’ : responsibilities are initialized using kmeans.
‘k-means++’ : use the k-means++ method to initialize.
‘random’ : responsibilities are initialized randomly.
‘random_from_data’ : initial means are randomly selected data points.

Changed in version v1.1:init_params now accepts ‘random_from_data’ and ‘k-means++’ asinitialization methods.

weights_initarray-like of shape (n_components, ), default=None

The user-provided initial weights.If it is None, weights are initialized using theinit_params method.

means_initarray-like of shape (n_components, n_features), default=None

The user-provided initial means,If it is None, means are initialized using theinit_params method.

precisions_initarray-like, default=None

The user-provided initial precisions (inverse of the covariancematrices).If it is 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, default=None

Controls the random seed given to the method chosen to initialize theparameters (seeinit_params).In addition, it controls the generation of random samples from thefitted distribution (see the methodsample).Pass an int for reproducible output across multiple function calls.SeeGlossary.

warm_startbool, default=False

If ‘warm_start’ is True, the solution of the last fitting is used asinitialization for the next call of fit(). This can speed upconvergence when fit is called several times on similar problems.In that case, ‘n_init’ is ignored and only a single initializationoccurs upon the first call.Seethe Glossary.

verboseint, default=0

Enable verbose output. If 1 then it prints the currentinitialization and each iteration step. If greater than 1 thenit prints also the log probability and the time neededfor each step.

verbose_intervalint, default=10

Number of iteration done before the next print.

Attributes:

weights_array-like of shape (n_components,)

The weights of each mixture components.

means_array-like of shape (n_components, n_features)

The mean of each mixture component.

covariances_array-like

The covariance of each mixture component.The shape depends oncovariance_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'

For an example of using covariances, refer toGMM covariances.

precisions_array-like

The precision matrices for each component in the mixture. A precisionmatrix is the inverse of a covariance matrix. A covariance matrix issymmetric positive definite so the mixture of Gaussian can beequivalently parameterized by the precision matrices. Storing theprecision matrices instead of the covariance matrices makes it moreefficient to compute the log-likelihood of new samples at test time.The shape depends oncovariance_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_array-like

The cholesky decomposition of the precision matrices of each mixturecomponent. A precision matrix is the inverse of a covariance matrix.A covariance matrix is symmetric positive definite so the mixture ofGaussian can be equivalently parameterized by the precision matrices.Storing the precision matrices instead of the covariance matrices makesit more efficient to compute the log-likelihood of new samples at testtime. The shape depends oncovariance_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 of the best fit of EM was reached, 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 log-likelihood (of the training data withrespect to the model) of the best fit of EM.

lower_bounds_array-like of shape (n_iter_,)

The list of lower bound values on the log-likelihood from eachiteration of the best fit of EM.

n_features_in_int

Number of features seen duringfit.

Added in version 0.24.

feature_names_in_ndarray of shape (n_features_in_,)

Names of features seen duringfit. Defined only whenXhas feature names that are all strings.

Added in version 1.0.

See also

BayesianGaussianMixture: Gaussian mixture model fit with a variational inference.

Examples

>>>importnumpyasnp>>>fromsklearn.mixtureimportGaussianMixture>>>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])

For a comparison of Gaussian Mixture with other clustering algorithms, seeComparing different clustering algorithms on toy datasets

aic(X)[source]#

Akaike information criterion for the current model on the input X.

You can refer to thismathematical section for moredetails regarding the formulation of the AIC used.

Parameters:

Xarray of shape (n_samples, n_dimensions): The input samples.

Returns:

aicfloat: The lower the better.

bic(X)[source]#

Bayesian information criterion for the current model on the input X.

You can refer to thismathematical section for moredetails regarding the formulation of the BIC used.

For an example of GMM selection usingbic information criterion,refer toGaussian Mixture Model Selection.

Parameters:

Xarray of shape (n_samples, n_dimensions): The input samples.

Returns:

bicfloat: The lower the better.

fit(X,y=None)[source]#

Estimate model parameters with the EM algorithm.

The method fits the modeln_init times and sets the parameters withwhich the model has the largest likelihood or lower bound. Within eachtrial, the method iterates between E-step and M-step formax_itertimes until the change of likelihood or lower bound is less thantol, otherwise, aConvergenceWarning is raised.Ifwarm_start isTrue, thenn_init is ignored and a singleinitialization is performed upon the first call. Upon consecutivecalls, training starts where it left off.

Parameters:

Xarray-like of shape (n_samples, n_features): List of n_features-dimensional data points. Each rowcorresponds to a single data point.
yIgnored: Not used, present for API consistency by convention.

Returns:

selfobject: The fitted mixture.

fit_predict(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 withwhich the model has the largest likelihood or lower bound. Within eachtrial, the method iterates between E-step and M-step formax_itertimes until the change of likelihood or lower bound is less thantol, otherwise, aConvergenceWarning israised. After fitting, it predicts the most probable label for theinput data points.

Added in version 0.20.

Parameters:

Xarray-like of shape (n_samples, n_features): List of n_features-dimensional data points. Each rowcorresponds to a single data point.
yIgnored: Not used, present for API consistency by convention.

Returns:

labelsarray, shape (n_samples,): Component labels.

get_metadata_routing()[source]#

Get metadata routing of this object.

Please checkUser Guide on how the routingmechanism works.

Returns:

routingMetadataRequest: AMetadataRequest encapsulatingrouting information.

get_params(deep=True)[source]#

Get parameters for this estimator.

Parameters:

deepbool, default=True: If True, will return the parameters for this estimator andcontained subobjects that are estimators.

Returns:

paramsdict: Parameter names mapped to their values.

predict(X)[source]#

Predict the labels for the data samples in X using trained model.

Parameters:

Xarray-like of shape (n_samples, n_features): List of n_features-dimensional data points. Each rowcorresponds to a single data point.

Returns:

labelsarray, shape (n_samples,): Component labels.

predict_proba(X)[source]#

Evaluate the components’ density for each sample.

Parameters:

Xarray-like of shape (n_samples, n_features): List of n_features-dimensional data points. Each rowcorresponds to a single data point.

Returns:

resparray, shape (n_samples, n_components): Density of each Gaussian component for each sample in X.

sample(n_samples=1)[source]#

Generate random samples from the fitted Gaussian distribution.

Parameters:

n_samplesint, default=1: Number of samples to generate.

Returns:

Xarray, shape (n_samples, n_features): Randomly generated sample.
yarray, shape (nsamples,): Component labels.

score(X,y=None)[source]#

Compute the per-sample average log-likelihood of the given data X.

Parameters:

Xarray-like of shape (n_samples, n_dimensions): List of n_features-dimensional data points. Each rowcorresponds to a single data point.
yIgnored: Not used, present for API consistency by convention.

Returns:

log_likelihoodfloat: Log-likelihood ofX under the Gaussian mixture model.

score_samples(X)[source]#

Compute the log-likelihood of each sample.

Parameters:

Xarray-like of shape (n_samples, n_features): List of n_features-dimensional data points. Each rowcorresponds to a single data point.

Returns:

log_probarray, shape (n_samples,): Log-likelihood of each sample inX under the current model.

set_params(**params)[source]#

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects(such asPipeline). The latter haveparameters of the form<component>__<parameter> so that it’spossible to update each component of a nested object.

Parameters: