# sklearn.mixture.GaussianMixture¶

class sklearn.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 mixture distribution.

Read more in the User Guide.

New 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

tolfloat, default=1e-3

The convergence threshold. EM iterations will stop when the lower 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’, ‘random’}, default=’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_initarray-like of shape (n_components, ), default=None

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

precisions_initarray-like, default=None

The user-provided initial precisions (inverse of the covariance matrices). 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 the parameters (see init_params). In addition, it controls the generation of random samples from the fitted distribution (see the method sample). Pass an int for reproducible output across multiple function calls. See Glossary.

warm_startbool, default=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=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=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 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_array-like

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 log-likelihood 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_array-like

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 log-likelihood 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 log-likelihood (of the training data with respect to the model) of the best fit of EM.

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

 Akaike information criterion for the current model on the input X. Bayesian information criterion for the current model on the input X. fit(X[, y]) Estimate model parameters with the EM algorithm. fit_predict(X[, y]) Estimate model parameters using X and predict the labels for X. get_params([deep]) Get parameters for this estimator. Predict the labels for the data samples in X using trained model. Predict posterior probability of each component given the data. sample([n_samples]) Generate random samples from the fitted Gaussian distribution. score(X[, y]) Compute the per-sample average log-likelihood of the given data X. Compute the weighted log probabilities for each sample. set_params(**params) Set the parameters of this estimator.
aic(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(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(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 E-step and M-step for max_iter times until the change of likelihood or lower bound is less than tol, otherwise, a ConvergenceWarning is raised. If warm_start is True, then n_init is ignored and a single initialization is performed upon the first call. Upon consecutive calls, training starts where it left off.

Parameters
Xarray-like of shape (n_samples, n_features)

List of n_features-dimensional data points. Each row corresponds to a single data point.

Returns
self
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 with which the model has the largest likelihood or lower bound. Within each trial, the method iterates between E-step and M-step for max_iter times until the change of likelihood or lower bound is less than tol, otherwise, a ConvergenceWarning is raised. After fitting, it predicts the most probable label for the input data points.

New in version 0.20.

Parameters
Xarray-like of shape (n_samples, n_features)

List of n_features-dimensional data points. Each row corresponds to a single data point.

Returns
labelsarray, shape (n_samples,)

Component labels.

get_params(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
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 row corresponds to a single data point.

Returns
labelsarray, shape (n_samples,)

Component labels.

predict_proba(X)[source]

Predict posterior probability of each component given the data.

Parameters
Xarray-like of shape (n_samples, n_features)

List of n_features-dimensional 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(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 row corresponds to a single data point.

Returns
log_likelihoodfloat

Log likelihood of the Gaussian mixture given X.

score_samples(X)[source]

Compute the weighted log probabilities for each sample.

Parameters
Xarray-like of shape (n_samples, n_features)

List of n_features-dimensional 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(**params)[source]

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). 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
selfestimator instance

Estimator instance.