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)


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.


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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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