Dimensionality reduction based on Distance Preservation to Local Mean (DPLM) for SPD matrices and its application in BCI

TL;DR

This paper introduces DPLM, a nonlinear dimensionality reduction method for SPD matrices that preserves local distances and improves classification in BCI applications, outperforming existing techniques.

Contribution

The paper presents a novel DPLM algorithm that considers SPD geometry, preserves local distances, and enhances classification performance with robustness to outliers.

Findings

DPLM outperforms existing methods in BCI classification tasks.

DPLM is linear in training samples and can incorporate label information.

Combining DPLM with FGMDM classifier achieves state-of-the-art results.

Abstract

In this paper, we propose a nonlinear dimensionality reduction algorithm for the manifold of Symmetric Positive Definite (SPD) matrices that considers the geometry of SPD matrices and provides a low dimensional representation of the manifold with high class discrimination. The proposed algorithm, tries to preserve the local structure of the data by preserving distance to local mean (DPLM) and also provides an implicit projection matrix. DPLM is linear in terms of the number of training samples and may use the label information when they are available in order to performance improvement in classification tasks. We performed several experiments on the multi-class dataset IIa from BCI competition IV. The results show that our approach as dimensionality reduction technique - leads to superior results in comparison with other competitor in the related literature because of its robustness against outliers. The experiments confirm that the combination of DPLM with FGMDM as the classifier leads to the state of the art performance on this dataset.