pyriemann.utils.covariance.covariances

pyriemann.utils.covariance.covariances(X, estimator='cov', **kwds)

Estimation of covariance matrices.

Estimates covariance matrices from multi-channel time-series according to a covariance estimator. It supports real and complex-valued data.

Parameters:

Xndarray, shape (n_matrices, n_channels, n_times)

Multi-channel time-series, real or complex-valued.

estimatorstring | callable, default=”cov”

Covariance matrix estimator [est]:

• “corr” for correlation coefficient matrix [corr],

• “cov” for NumPy based covariance matrix [cov],

• “hub” for Huber’s M-estimator based covariance matrix [mest],

• “lwf” for Ledoit-Wolf shrunk covariance matrix [lwf],

• “mcd” for minimum covariance determinant matrix [mcd],

• “oas” for oracle approximating shrunk covariance matrix [oas],

• “sch” for Schaefer-Strimmer shrunk covariance matrix [sch],

• “scm” for sample covariance matrix [scm],

• “stu” for Student-t’s M-estimator based covariance matrix [mest],

• “tyl” for Tyler’s M-estimator based covariance matrix [mest],

• or a callable function.

For regularization, consider “lwf” or “oas”.

For robustness, consider “hub”, “mcd”, “stu” or “tyl”.

For “lwf”, “mcd”, “oas” and “sch” estimators, complex covariance matrices are estimated according to [comp].

**kwdsdict

Any further parameters are passed directly to the covariance estimator.

Returns:

covmatsndarray, shape (n_matrices, n_channels, n_channels)

Covariance matrices.

References

[est]

https://scikit-learn.org/stable/modules/covariance.html

[corr]

https://numpy.org/doc/stable/reference/generated/numpy.corrcoef.html

[cov]

https://numpy.org/doc/stable/reference/generated/numpy.cov.html

[lwf]

https://scikit-learn.org/stable/modules/generated/sklearn.covariance.ledoit_wolf.html

[mcd]

https://scikit-learn.org/stable/modules/generated/sklearn.covariance.MinCovDet.html

[mest] (1,2,3)

pyriemann.utils.covariance.covariance_mest()

[oas]

https://scikit-learn.org/stable/modules/generated/oas-function.html

[sch]

pyriemann.utils.covariance.covariance_sch()

[scm]

pyriemann.utils.covariance.covariance_scm()

[comp]

Enhanced Covariance Matrix Estimators in Adaptive Beamforming R. Abrahamsson, Y. Selen and P. Stoica. 2007 IEEE International Conference on Acoustics, Speech and Signal Processing, Volume 2, 2007.