Sparse Coding on Symmetric Positive Definite Manifolds Using Bregman Divergences

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.

• Publication year

  2014

• Venue

  IEEE Transactions on Neural Networks and Learning Systems

• Publication date

  2014-08-29

• Fields of study

  Mathematics, Computer Science, Medicine

• Identifiers
  DOI 10.1109/TNNLS.2014.2387383arXiv 1409.0083PMID 25643414
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

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