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...
| Veröffentlicht in: | IEEE transactions on image processing : a publication of the IEEE Signal Processing Society. - 1992. - 24(2015), 11 vom: 04. Nov., Seite 3729-41 |
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| Weitere Verfasser: | , , , |
| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2015
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| Zugriff auf das übergeordnete Werk: | IEEE transactions on image processing : a publication of the IEEE Signal Processing Society |
| Schlagworte: | Journal Article Research Support, Non-U.S. Gov't |
| Zusammenfassung: | 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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| Beschreibung: | Date Completed 29.04.2016 Date Revised 10.09.2015 published: Print-Electronic Citation Status MEDLINE |
| ISSN: | 1941-0042 |
| DOI: | 10.1109/TIP.2015.2451953 |