scm_transform: SCMs transformation to use a linear SVM

In LauraMasiero/RiemannR: RiemannR - EEG-based BCI analysis with Riemannian geometry

Description

This function allows to transform the given sample covariance matrices in a matrix usable in a SVM with linear kernel. This is a different way to implement a Riemannian kernel SVM for SCMs classification.

Usage

scm_transform(scm_list, centroid)

Arguments

scm_list	a list of numeric sample covariance matrices.
centroid	a numeric matrix used as reference for the tangent space mapping. See Details below.

Details

The SCMs transformation is achieved with a logaritmic mapping of the matrices, that's to say the matrices are projected from the Riemannian manifold in the tangent euclidean space. The tangent space is computed in a reference point: the centroid. For the formulation details see the References below.

Value

It returns a numeric matrix conatining all the upper triangular parts of the SCM in input, vectorized with the vect operator.

Author(s)

Laura Masiero, email: [e-mail]

References

Barachant, Alexandre, Stéphane Bonnet, Marco Congedo e Christian Jutten, (2013). "Classification of covariance matrices using a Riemannian-based kernel for BCI applications". In: Neurocomputing. issn: 09252312. doi: 10.1016/j.neucom.2012.12.039.

See Also

vect

LauraMasiero/RiemannR documentation built on Sept. 29, 2020, 9:51 p.m.