Sparse coding and dictionary learning for symmetric positive definite matrices: a kernel approach

  • Authors:

  • Mehrtash T. Harandi;Conrad Sanderson;Richard Hartley;Brian C. Lovell

  • Affiliations:

  • NICTA, St Lucia, QLD, Australia,School of ITEE, University of Queensland, QLD, Australia;NICTA, St Lucia, QLD, Australia,School of ITEE, University of Queensland, QLD, Australia;NICTA, Canberra, ACT, Australia,Australian National University, Canberra, ACT, Australia;NICTA, St Lucia, QLD, Australia,School of ITEE, University of Queensland, QLD, Australia

  • Venue:
  • ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part II
  • Year:
  • 2012

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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.