Title of Paper:Manifold Kernel Sparse Representation of Symmetric Positive-Definite Matrices and Its Applications

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First Author:Wu, Yuwei

Correspondence Author:Jia, YD (reprint author), Beijing Inst Technol, Sch Comp Sci, Beijing Lab Intelligent Informat Technol, Beijing 100081, Peoples R China.

Co-author:Jia, Yunde,Li, Peihua,Zhang, Jian,Yuan, Junsong

Date of Publication:2015-11-01

Journal:IEEE TRANSACTIONS ON IMAGE PROCESSING

Included Journals:SCIE、EI、Scopus

Volume:24

Issue:11

Page Number:3729-3741

ISSN No.:1057-7149

Key Words:Kernel sparse coding; Riemannian manifold; region covariance descriptor; symmetric positive definite matrices; visual tracking; image classification; face recognition

Abstract:The symmetric positive-definite (SPD) matrix, as a connected Riemannian manifold, has become increasingly popular for encoding image information. Most existing sparse models are still primarily developed in the Euclidean space. They do not consider the non-linear geometrical structure of the data space, and thus are not directly applicable to the Riemannian manifold. In this paper, we propose a novel sparse representation method of SPD matrices in the data-dependent manifold kernel space. The graph Laplacian is incorporated into the kernel space to better reflect the underlying geometry of SPD matrices. Under the proposed framework, we design two different positive definite kernel functions that can be readily transformed to the corresponding manifold kernels. The sparse representation obtained has more discriminating power. Extensive experimental results demonstrate good performance of manifold kernel sparse codes in image classification, face recognition, and visual tracking.