8.18.1. sklearn.mixture.GMM

class sklearn.mixture.GMM(n_components=1, covariance_type='diag', random_state=None, thresh=0.01, min_covar=0.001)

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.

Parameters :

n_components : int, optional

Number of mixture components. Defaults to 1.

covariance_type : string (read-only), optional

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

rng : numpy.random object, optional

Must support the full numpy random number generator API.

min_covar : float, optional

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

thresh : float, optional

Convergence threshold.

See also

DPGMM

Ininite 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=None, min_covar=0.001, n_components=2,
        random_state=None, thresh=0.01)
>>> 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=None, min_covar=0.001, n_components=2,
        random_state=None, thresh=0.01)
>>> np.round(g.weights_, 2)
array([ 0.5,  0.5])

Attributes

covariance_type	string	String describing the type of covariance parameters used by the GMM. Must be one of ‘spherical’, ‘tied’, ‘diag’, ‘full’.
weights_	array, shape (n_components,)	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,) 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.

Methods

aic(X)	Akaike information criterion for the current model fit
bic(X)	Bayesian information criterion for the current model fit
decode(*args, **kwargs)	DEPRECATED: will be removed in v0.12;
eval(X)	Evaluate the model on data
fit(X[, n_iter, n_init, thresh, params, ...])	Estimate model parameters with the expectation-maximization algorithm.
get_params([deep])	Get parameters for the estimator
predict(X)	Predict label for data.
predict_proba(X)	Predict posterior probability of data under each Gaussian
rvs(*args, **kwargs)	DEPRECATED: will be removed in v0.12;
sample([n_samples, random_state])	Generate random samples from the model.
score(X)	Compute the log probability under the model.
set_params(**params)	Set the parameters of the estimator.

__init__(n_components=1, covariance_type='diag', random_state=None, thresh=0.01, min_covar=0.001)

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) :

decode(*args, **kwargs)

DEPRECATED: will be removed in v0.12; use the score or predict method instead, depending on the question

Find most likely mixture components for each point in X.

DEPRECATED IN VERSION 0.10; WILL BE REMOVED IN VERSION 0.12 use the score or predict method instead, depending on the question.

Parameters :

X : array_like, shape (n, n_features)

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

Returns :

logprobs : array_like, shape (n_samples,)

Log probability of each point in obs under the model.

components : array_like, shape (n_samples,)

Index of the most likelihod mixture components for each observation

eval(X)

Evaluate the model on data

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

fit(X, n_iter=100, n_init=1, thresh=0.01, params='wmc', init_params='wmc')

Estimate model parameters with the expectation-maximization algorithm.

A initialization step is performed before entering the em algorithm. If you want to avoid this step, set the keyword argument init_params to the empty string ‘’. Likewise, if you would like just to do an initialization, call this method with 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.

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’.

get_params(deep=True)

Get parameters for the estimator

Parameters :

deep: boolean, optional :

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

predict(X)

Predict label for data.

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

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.

rvs(*args, **kwargs)

DEPRECATED: will be removed in v0.12; use the score or predict method instead, depending on the question

Generate random samples from the model.

DEPRECATED IN VERSION 0.11; WILL BE REMOVED IN VERSION 0.12 use sample instead

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)

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

set_params(**params)

Set the parameters of the 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 :