pyriemann.clustering.GaussianMixture

class pyriemann.clustering.GaussianMixture(n_components=1, metric='riemann', weights_init=None, means_init=None, tol=1e-05, maxiter=100, random_state=None, verbose=False)

Gaussian mixture model.

Representation of a Gaussian mixture model (GMM) probability distribution for SPD matrices by expectation-maximization (EM) algorithm [1].

Parameters:

n_componentsinteger, default=1

Number of mixture components.

metricstring | dict, default=”riemann”

Metric used for mean update (for the list of supported metrics, see pyriemann.geometry.mean.gmean()) and for tangent space map (see pyriemann.geometry.tangent_space.tangent_space()). The metric can be a dict with two keys, “mean” and “map” in order to pass different metrics.

weights_initNone | ndarray, shape (n_components,), defaut=None

Initial weights. If None, it uses equal weights.

means_initNone | ndarray, shape (n_components,), defaut=None

Initial means of Gaussians. If None, it randomly selects training matrices.

tolfloat, default=1e-5

Tolerance to stop the EM algorithm.

maxiterint, default=100

Maximum number of iterations of EM algorithm.

random_stateNone | integer | np.RandomState, default=None

The generator used to initialize the Gaussian models. If an integer is given, it fixes the seed. Defaults to the global numpy random number generator.

verbosebool, default=False

Verbose flag.

Attributes:

weights_ndarray, shape (n_components,)

Weight of each mixture component.

means_ndarray, shape (n_components, n_channels, n_channels)

Mean of each mixture component.

covariances_ndarray, shape (n_components, n_ts, n_ts)

Covariance of each mixture component.

Notes

Added in version 0.11.

References

[1]

Gaussian mixture regression on symmetric positive definite matrices manifolds: Application to wrist motion estimation with sEMG N. Jacquier & S. Calinon. IEEE IROS, 2017

__init__(n_components=1, metric='riemann', weights_init=None, means_init=None, tol=1e-05, maxiter=100, random_state=None, verbose=False)

Init.

fit(X, y=None)

Fit the mixture with EM.

Parameters:

Xndarray, shape (n_matrices, n_channels, n_channels)

Set of SPD matrices.

yNone

Not used, here for compatibility with sklearn API.

Returns:

selfGaussianMixture instance

The GaussianMixture instance.

fit_predict(X, y=None)

Fit and predict in a single function.

Parameters:

Xndarray, shape (n_matrices, n_channels, n_channels)

Set of SPD matrices.

yNone

Not used, here for compatibility with sklearn API.

Returns:

predndarray of int, shape (n_matrices,)

Prediction for each matrix according to the closest cluster.

get_metadata_routing()

Get metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Returns:

routingMetadataRequest

A MetadataRequest encapsulating routing information.

get_params(deep=True)

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)

Get the predictions.

Parameters:

Xndarray, shape (n_matrices, n_channels, n_channels)

Set of SPD matrices.

Returns:

predndarray of int, shape (n_matrices,)

Predictions for each matrix.

predict_proba(X)

Predict probabilities.

Parameters:

Xndarray, shape (n_matrices, n_channels, n_channels)

Set of SPD matrices.

Returns:

probndarray, shape (n_matrices, n_components)

Probabilities for each component.

sample(n_matrices=1)

Generate random matrices from the fitted Gaussian distribution.

Warning: GMM is calibrated using the Gaussian model [1], while this sampling uses the wrapped Gaussian model [2].

Parameters:

n_matricesint, default=1

Number of matrices to generate.

Returns:

Xarray, shape (n_matrices, n_channels, n_channels)

Randomly generated matrices.

yarray, shape (n_matrices,)

Component labels.

References

[1]

Intrinsic statistics on Riemannian manifolds: Basic tools for geometric measurements X. Pennec. Journal of Mathematical Imaging and Vision, 2006

[2]

Wrapped gaussian on the manifold of symmetric positive definite matrices T. de Surrel, F. Lotte, S. Chevallier, and F. Yger. ICML, 2025

score(X, y=None)

Compute the average log-likelihood of the given matrices.

Parameters:

Xndarray, shape (n_matrices, n_channels, n_channels)

Set of SPD matrices.

yNone

Not used, here for compatibility with sklearn API.

Returns:

scorefloat

Log-likelihood of matrices under the Gaussian mixture model.

set_params(**params)

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.

Examples using pyriemann.clustering.GaussianMixture

Clustering algorithm comparison

Clustering algorithm comparison