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

Hiroyuki Kasai; Bamdev Mishra

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arXiv · 1902.04186

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

Hiroyuki Kasai·Bamdev Mishra

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Abstract

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

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BibTeX RIS

Hiroyuki Kasai, Bamdev Mishra. 2019-02-11. Riemannian joint dimensionality reduction and dictionary learning on symmetric positive definite manifold. https://arxiv.org/abs/1902.04186

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