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Sparse Coding and Dictionary Learning for Symmetric Positive Definite Matrices: A Kernel Approach

  • Mehrtash T. Harandi
  • Conrad Sanderson
  • Richard Hartley
  • Brian C. Lovell
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7573)

Abstract

Recent advances suggest that a wide range of computer vision problems can be addressed more appropriately by considering non-Euclidean geometry. This paper tackles the problem of sparse coding and dictionary learning in the space of symmetric positive definite matrices, which form a Riemannian manifold. With the aid of the recently introduced Stein kernel (related to a symmetric version of Bregman matrix divergence), we propose to perform sparse coding by embedding Riemannian manifolds into reproducing kernel Hilbert spaces. This leads to a convex and kernel version of the Lasso problem, which can be solved efficiently. We furthermore propose an algorithm for learning a Riemannian dictionary (used for sparse coding), closely tied to the Stein kernel. Experiments on several classification tasks (face recognition, texture classification, person re-identification) show that the proposed sparse coding approach achieves notable improvements in discrimination accuracy, in comparison to state-of-the-art methods such as tensor sparse coding, Riemannian locality preserving projection, and symmetry-driven accumulation of local features.

Keywords

Riemannian Manifold Face Recognition Recognition Accuracy Sparse Representation Sparse Code 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Mehrtash T. Harandi
    • 1
    • 2
  • Conrad Sanderson
    • 1
    • 2
  • Richard Hartley
    • 3
    • 4
  • Brian C. Lovell
    • 1
    • 2
  1. 1.NICTASt LuciaAustralia
  2. 2.School of ITEEUniversity of QueenslandAustralia
  3. 3.NICTACanberraAustralia
  4. 4.Australian National UniversityCanberraAustralia

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