Sparse coding on symmetric positive definite manifolds using Bregman divergences

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

Research output: Contribution to journalArticleResearchpeer-review

54 Citations (Scopus)


This paper introduces sparse coding and dictionary learning for symmetric positive definite (SPD) matrices, which are often used in machine learning, computer vision, and related areas. Unlike traditional sparse coding schemes that work in vector spaces, in this paper, we discuss how SPD matrices can be described by sparse combination of dictionary atoms, where the atoms are also SPD matrices. We propose to seek sparse coding by embedding the space of SPD matrices into the Hilbert spaces through two types of the Bregman matrix divergences. This not only leads to an efficient way of performing sparse coding but also an online and iterative scheme for dictionary learning. We apply the proposed methods to several computer vision tasks where images are represented by region covariance matrices. Our proposed algorithms outperform state-of-the-art methods on a wide range of classification tasks, including face recognition, action recognition, material classification, and texture categorization.

Original languageEnglish
Article number7024121
Pages (from-to)1294-1306
Number of pages13
JournalIEEE Transactions on Neural Networks and Learning Systems
Issue number6
Publication statusPublished - 1 Jun 2016
Externally publishedYes


  • Bregman's divergences
  • dictionary learning
  • kernel methods
  • Riemannian's geometry
  • sparse coding.

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