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Low rank representation on Riemannian manifold of symmetric positive definite matrices

Fu, Y., Gao, J., Hong, X. and Tien, D. (2015) Low rank representation on Riemannian manifold of symmetric positive definite matrices. In: Proceedings of the 2015 SIAM International Conference on Data Mining. SIAM, pp. 316-324. ISBN 9781611974010

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To link to this item DOI: 10.1137/1.9781611974010.36

Abstract/Summary

Sparse coding aims to find a more compact representation based on a set of dictionary atoms. A well-known technique looking at 2D sparsity is the low rank representation (LRR). However, in many computer vision applications, data often originate from a manifold, which is equipped with some Riemannian geometry. In this case, the existing LRR becomes inappropriate for modeling and incorporating the intrinsic geometry of the manifold that is potentially important and critical to applications. In this paper, we generalize the LRR over the Euclidean space to the LRR model over a specific Rimannian manifold—the manifold of symmetric positive matrices (SPD). Experiments on several computer vision datasets showcase its noise robustness and superior performance on classification and segmentation compared with state-of-the-art approaches.

Item Type:Book or Report Section
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Computer Science
ID Code:45599
Uncontrolled Keywords:Riemannian manifold, Symmetric Positive Definite, LRR, Feature Extraction
Publisher:SIAM

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