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

Source: [Riemannian joint dimensionality reduction and dictionary learning on symmetric positive definite manifold](<https://www.sota2.com/research/paper/68fa65541e209131cea09b5c>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T21:24:52.728Z

Authors: Hiroyuki Kasai, Bamdev Mishra

Published: 2019-02-11T23:49:03.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1902.04186>)

[PDF](<https://arxiv.org/pdf/1902.04186.pdf>)