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

Mehrtash T. Harandi, Conrad Sanderson, Richard Hartley, Brian C. Lovell

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111 Citations (Scopus)

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.

Original languageEnglish
Title of host publicationComputer Vision, ECCV 2012 - 12th European Conference on Computer Vision, Proceedings
Pages216-229
Number of pages14
EditionPART 2
DOIs
Publication statusPublished - 30 Oct 2012
Externally publishedYes
EventEuropean Conference on Computer Vision 2012 - Florence, Italy
Duration: 7 Oct 201213 Oct 2012
Conference number: 12th
https://link.springer.com/book/10.1007/978-3-642-33718-5 (Proceedings)

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 2
Volume7573 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

ConferenceEuropean Conference on Computer Vision 2012
Abbreviated titleECCV 2012
CountryItaly
CityFlorence
Period7/10/1213/10/12
Internet address

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