Neighborhood Preserved Sparse Representation for Robust Classification on Symmetric Positive Definite Matrices

TL;DR

This paper introduces a novel kernel sparse representation classification method tailored for symmetric positive definite matrices, leveraging Riemannian geometry to improve classification accuracy in computer vision tasks.

Contribution

It proposes a neighborhood preserved kernel SRC method on SPD manifolds using Log-Euclidean kernels, addressing the limitation of existing SRC methods to Euclidean vector data.

Findings

Achieves better classification accuracy than state-of-the-art methods

Effectively characterizes local Riemannian geometry of SPD data

Demonstrates robustness on multiple benchmark databases

Abstract

Due to its promising classification performance, sparse representation based classification(SRC) algorithm has attracted great attention in the past few years. However, the existing SRC type methods apply only to vector data in Euclidean space. As such, there is still no satisfactory approach to conduct classification task for symmetric positive definite (SPD) matrices which is very useful in computer vision. To address this problem, in this paper, a neighborhood preserved kernel SRC method is proposed on SPD manifolds. Specifically, by embedding the SPD matrices into a Reproducing Kernel Hilbert Space (RKHS), the proposed method can perform classification on SPD manifolds through an appropriate Log-Euclidean kernel. Through exploiting the geodesic distance between SPD matrices, our method can effectively characterize the intrinsic local Riemannian geometry within data so as to well unravel the underlying sub-manifold structure. Despite its simplicity, experimental results on several famous database demonstrate that the proposed method achieves better classification results than the state-of-the-art approaches.