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Dictionary leaning (DL) and dimensionality reduction (DR) are powerful toolsto analyze high-dimensional noisy signals. This paper presents a proposal of anovel Riemannian joint dimensionality reduction and dictionary learning(R-JDRDL) on symmetric positive definite (SPD) manifolds for classificationtasks. The joint learning considers the interaction between dimensionalityreduction and dictionary learning procedures by connecting them into a unifiedframework. We exploit a Riemannian optimization framework for solving DL and DRproblems jointly. Finally, we demonstrate that the proposed R-JDRDL outperformsexisting state-of-the-arts algorithms when used for image classification tasks.

Riemannian joint dimensionality reduction and dictionary learning on symmetric positive definite manifold