  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.
