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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| Vydané v: | IEEE transactions on image processing Ročník 24; číslo 11; s. 3729 - 3741 |
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| Hlavní autori: | , , , , |
| Médium: | Journal Article |
| Jazyk: | English |
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United States
IEEE
01.11.2015
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| ISSN: | 1057-7149, 1941-0042 |
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| 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. |
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| AbstractList | 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. |
| Author | Yunde Jia Peihua Li Jian Zhang Junsong Yuan Yuwei Wu |
| Author_xml | – sequence: 1 givenname: Yuwei surname: Wu fullname: Wu, Yuwei – sequence: 2 givenname: Yunde surname: Jia fullname: Jia, Yunde – sequence: 3 givenname: Peihua surname: Li fullname: Li, Peihua – sequence: 4 givenname: Jian surname: Zhang fullname: Zhang, Jian – sequence: 5 givenname: Junsong surname: Yuan fullname: Yuan, Junsong |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/26151938$$D View this record in MEDLINE/PubMed |
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| Keywords | Kernel sparse coding image classification visual tracking face recognition region covariance descriptor symmetric positive definite matrices Riemannian manifold |
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| Snippet | The symmetric positive-definite (SPD) matrix, as a connected Riemannian manifold, has become increasingly popular for encoding image information. Most existing... |
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| SubjectTerms | 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 |
| Title | Manifold Kernel Sparse Representation of Symmetric Positive-Definite Matrices and Its Applications |
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