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

TL;DR

This paper introduces a novel Riemannian joint approach for dimensionality reduction and dictionary learning on SPD manifolds, improving image classification performance by unifying these processes within a Riemannian optimization framework.

Contribution

It proposes the first joint Riemannian framework for simultaneous dimensionality reduction and dictionary learning on SPD manifolds for classification.

Findings

Outperforms existing algorithms in image classification tasks

Demonstrates the effectiveness of joint learning on SPD manifolds

Utilizes Riemannian optimization for improved convergence and results

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.