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

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