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 :ref:`User Guide <gmm>`.
.. versionadded:: 0.18
Parameters ---------- n_components : int, 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
tol : float, defaults to 1e-3. The convergence threshold. EM iterations will stop when the lower bound average gain is below this threshold.
reg_covar : float, defaults to 1e-6. Non-negative regularization added to the diagonal of covariance. Allows to assure that the covariance matrices are all positive.
max_iter : int, defaults to 100. The number of EM iterations to perform.
n_init : int, 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_init : array-like, shape (n_components, ), optional The user-provided initial weights, defaults to None. If it None, weights are initialized using the `init_params` method.
means_init : array-like, shape (n_components, n_features), optional The user-provided initial means, defaults to None, If it None, means are initialized using the `init_params` method.
precisions_init : array-like, optional. The user-provided 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_state : int, RandomState instance or None, optional (default=None) If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by `np.random`.
warm_start : bool, 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 :term:`the Glossary <warm_start>`.
verbose : int, 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_interval : int, default to 10. Number of iteration done before the next print.
Attributes ---------- weights_ : array-like, shape (n_components,) The weights of each mixture components.
means_ : array-like, 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.
See Also -------- BayesianGaussianMixture : Gaussian mixture model fit with a variational inference.