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

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 sp...

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Bibliographic Details
Published in:IEEE transactions on image processing Vol. 24; no. 11; pp. 3729 - 3741
Main Authors: Wu, Yuwei, Jia, Yunde, Li, Peihua, Zhang, Jian, Yuan, Junsong
Format: Journal Article
Language:English
Published: United States IEEE 01.11.2015
Subjects:
Algorithms
Biometric Identification
Covariance matrices
Databases, Factual
Dictionaries
Face recognition
Geometry
Humans
Image classification
Image Processing, Computer-Assisted - methods
Kernel
Kernel sparse coding
Machine Learning
Manifolds
Measurement
Region covariance descriptor
Riemannian manifold
Sparse matrices
Symmetric Positive Definite Matrices
Visual tracking
Kernel sparse coding
image classification
visual tracking
face recognition
region covariance descriptor
symmetric positive definite matrices
Riemannian manifold
ISSN:1057-7149, 1941-0042
Online Access:Get full text
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Summary: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.
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ISSN:1057-7149
1941-0042
DOI:10.1109/TIP.2015.2451953