DocumentCode :
113160
Title :
Manifold Kernel Sparse Representation of Symmetric Positive-Definite Matrices and Its Applications
Author :
Yuwei Wu ; Yunde Jia ; Peihua Li ; Jian Zhang ; Junsong Yuan
Author_Institution :
Beijing Lab. of Intell. Inf. Technol., Beijing Inst. of Technol., Beijing, China
Volume :
24
Issue :
11
fYear :
2015
fDate :
Nov. 2015
Firstpage :
3729
Lastpage :
3741
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.
Keywords :
graph theory; image representation; matrix algebra; Riemannian manifold; SPD matrix; data dependent manifold kernel space; encoding image information; face recognition; graph Laplacian; image classification; manifold Kernel sparse representation; manifold kernel sparse codes; nonlinear geometrical structure; sparse representation; symmetric positive-definite matrices; visual tracking; Covariance matrices; Dictionaries; Geometry; Kernel; Manifolds; Measurement; Sparse matrices; Face recognition; Image classification; Kernel sparse coding; Region covariance descriptor; Riemannian manifold; Symmetric Positive Definite Matrices; Visual tracking; face recognition; image classification; region covariance descriptor; symmetric positive definite matrices; visual tracking;
fLanguage :
English
Journal_Title :
Image Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1057-7149
Type :
jour
DOI :
10.1109/TIP.2015.2451953
Filename :
7145428
Link To Document :
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