pyriemann.utils.covariance.covariance_sch¶
- pyriemann.utils.covariance.covariance_sch(X)¶
Schaefer-Strimmer shrunk covariance estimator.
Shrinkage covariance estimator [1]:
\[C = (1 - \gamma) C_\text{scm} + \gamma T\]where \(T\) is the diagonal target matrix:
\[T[i,j] = \{ C_\text{scm}[i,i] \ \text{if} i = j, 0 \text{otherwise} \}\]Note that the optimal \(\gamma\) is estimated by the authors’ method.
- Parameters
- Xndarray, shape (n_channels, n_times)
Multi-channel time-series.
- Returns
- covndarray, shape (n_channels, n_channels)
Schaefer-Strimmer shrunk covariance matrix.
Notes
New in version 0.3.
References
- 1
A shrinkage approach to large-scale covariance estimation and implications for functional genomics J. Schafer, and K. Strimmer. Statistical Applications in Genetics and Molecular Biology, Volume 4, Issue 1, 2005.