sklearn.mixture.GMM

class sklearn.mixture.GMM(n_components=1, covariance_type='diag', random_state=None, tol=0.001, min_covar=0.001, n_iter=100, n_init=1, params='wmc', init_params='wmc', verbose=0)

Gaussian Mixture Model

Representation of a Gaussian mixture model probability distribution. This class allows for easy evaluation of, sampling from, and maximum-likelihood estimation of the parameters of a GMM distribution.

Initializes parameters such that every mixture component has zero mean and identity covariance.

Read more in the User Guide.

Parameters:

n_components : int, optional

Number of mixture components. Defaults to 1.

covariance_type : string, optional

String describing the type of covariance parameters to use. Must be one of ‘spherical’, ‘tied’, ‘diag’, ‘full’. Defaults to ‘diag’.

random_state: RandomState or an int seed (None by default) :

A random number generator instance

min_covar : float, optional

Floor on the diagonal of the covariance matrix to prevent overfitting. Defaults to 1e-3.

tol : float, optional

Convergence threshold. EM iterations will stop when average gain in log-likelihood is below this threshold. Defaults to 1e-3.

n_iter : int, optional

Number of EM iterations to perform.

n_init : int, optional

Number of initializations to perform. the best results is kept

params : string, optional

Controls which parameters are updated in the training process. Can contain any combination of ‘w’ for weights, ‘m’ for means, and ‘c’ for covars. Defaults to ‘wmc’.

init_params : string, optional

Controls which parameters are updated in the initialization process. Can contain any combination of ‘w’ for weights, ‘m’ for means, and ‘c’ for covars. Defaults to ‘wmc’.

verbose : int, default: 0

Enable verbose output. If 1 then it always prints the current initialization and iteration step. If greater than 1 then it prints additionally the change and time needed for each step.

Attributes:

weights_ : array, shape (n_components,)

This attribute stores the mixing weights for each mixture component.

means_ : array, shape (n_components, n_features)

Mean parameters for each mixture component.

covars_ : array

Covariance parameters for each mixture component. The shape depends on covariance_type:

(n_components, n_features)             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.

See also

DPGMM

Infinite gaussian mixture model, using the dirichlet process, fit with a variational algorithm

VBGMM

Finite gaussian mixture model fit with a variational algorithm, better for situations where there might be too little data to get a good estimate of the covariance matrix.

Examples

>>> import numpy as np
>>> from sklearn import mixture
>>> np.random.seed(1)
>>> g = mixture.GMM(n_components=2)
>>> # Generate random observations with two modes centered on 0
>>> # and 10 to use for training.
>>> obs = np.concatenate((np.random.randn(100, 1),
...                       10 + np.random.randn(300, 1)))
>>> g.fit(obs) 
GMM(covariance_type='diag', init_params='wmc', min_covar=0.001,
        n_components=2, n_init=1, n_iter=100, params='wmc',
        random_state=None, tol=0.001, verbose=0)
>>> np.round(g.weights_, 2)
array([ 0.75,  0.25])
>>> np.round(g.means_, 2)
array([[ 10.05],
       [  0.06]])
>>> np.round(g.covars_, 2) 
array([[[ 1.02]],
       [[ 0.96]]])
>>> g.predict([[0], [2], [9], [10]]) 
array([1, 1, 0, 0]...)
>>> np.round(g.score([[0], [2], [9], [10]]), 2)
array([-2.19, -4.58, -1.75, -1.21])
>>> # Refit the model on new data (initial parameters remain the
>>> # same), this time with an even split between the two modes.
>>> g.fit(20 * [[0]] +  20 * [[10]]) 
GMM(covariance_type='diag', init_params='wmc', min_covar=0.001,
        n_components=2, n_init=1, n_iter=100, params='wmc',
        random_state=None, tol=0.001, verbose=0)
>>> np.round(g.weights_, 2)
array([ 0.5,  0.5])

Methods

aic(X)	Akaike information criterion for the current model fit
bic(X)	Bayesian information criterion for the current model fit
fit(X[, y])	Estimate model parameters with the EM algorithm.
fit_predict(X[, y])	Fit and then predict labels for data.
get_params([deep])	Get parameters for this estimator.
predict(X)	Predict label for data.
predict_proba(X)	Predict posterior probability of data under each Gaussian in the model.
sample([n_samples, random_state])	Generate random samples from the model.
score(X[, y])	Compute the log probability under the model.
score_samples(X)	Return the per-sample likelihood of the data under the model.
set_params(**params)	Set the parameters of this estimator.

__init__(n_components=1, covariance_type='diag', random_state=None, tol=0.001, min_covar=0.001, n_iter=100, n_init=1, params='wmc', init_params='wmc', verbose=0)

aic(X)

Akaike information criterion for the current model fit and the proposed data

Parameters:X : array of shape(n_samples, n_dimensions) Returns:aic: float (the lower the better) :

bic(X)

Bayesian information criterion for the current model fit and the proposed data

Parameters:X : array of shape(n_samples, n_dimensions) Returns:bic: float (the lower the better) :

fit(X, y=None)

Estimate model parameters with the EM algorithm.

A initialization step is performed before entering the expectation-maximization (EM) algorithm. If you want to avoid this step, set the keyword argument init_params to the empty string ‘’ when creating the GMM object. Likewise, if you would like just to do an initialization, set n_iter=0.

Parameters:

X : array_like, shape (n, n_features)

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

Returns:

self :

fit_predict(X, y=None)

Fit and then predict labels for data.

Warning: due to the final maximization step in the EM algorithm, with low iterations the prediction may not be 100% accurate

New in version 0.17: fit_predict method in Gaussian Mixture Model.

Parameters:X : array-like, shape = [n_samples, n_features] Returns:C : array, shape = (n_samples,) component memberships

get_params(deep=True)

Get parameters for this estimator.

Parameters:

deep: boolean, optional :

If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns:

params : mapping of string to any

Parameter names mapped to their values.

predict(X)

Predict label for data.

Parameters:X : array-like, shape = [n_samples, n_features] Returns:C : array, shape = (n_samples,) component memberships

predict_proba(X)

Predict posterior probability of data under each Gaussian in the model.

Parameters:

X : array-like, shape = [n_samples, n_features]

Returns:

responsibilities : array-like, shape = (n_samples, n_components)

Returns the probability of the sample for each Gaussian (state) in the model.

sample(n_samples=1, random_state=None)

Generate random samples from the model.

Parameters:

n_samples : int, optional

Number of samples to generate. Defaults to 1.

Returns:

X : array_like, shape (n_samples, n_features)

List of samples

score(X, y=None)

Compute the log probability under the model.

Parameters:

X : array_like, shape (n_samples, n_features)

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

Returns:

logprob : array_like, shape (n_samples,)

Log probabilities of each data point in X

score_samples(X)

Return the per-sample likelihood of the data under the model.

Compute the log probability of X under the model and return the posterior distribution (responsibilities) of each mixture component for each element of X.

Parameters:

X: array_like, shape (n_samples, n_features) :

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

Returns:

logprob : array_like, shape (n_samples,)

Log probabilities of each data point in X.

responsibilities : array_like, shape (n_samples, n_components)

Posterior probabilities of each mixture component for each observation

set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). The former have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Returns:self :

Examples using sklearn.mixture.GMM

Density Estimation for a mixture of Gaussians

Gaussian Mixture Model Ellipsoids

Gaussian Mixture Model Sine Curve

Gaussian Mixture Model Selection

GMM classification