# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1902.04186