Sparse coding on symmetric positive definite manifolds using Bregman divergences

Harandi, Mehrtash T., Hartley, Richard, Lovell. Brian and Sanderson, Conrad (2016) Sparse coding on symmetric positive definite manifolds using Bregman divergences. IEEE Transactions on Neural Networks and Learning Systems, 27 6: 1294-1306. doi:10.1109/TNNLS.2014.2387383

Author Harandi, Mehrtash T.
Hartley, Richard
Lovell. Brian
Sanderson, Conrad
Title Sparse coding on symmetric positive definite manifolds using Bregman divergences
Journal name IEEE Transactions on Neural Networks and Learning Systems   Check publisher's open access policy
ISSN 2162-2388
Publication date 2016-05-16
Year available 2015
Sub-type Article (original research)
DOI 10.1109/TNNLS.2014.2387383
Open Access Status Not Open Access
Volume 27
Issue 6
Start page 1294
End page 1306
Total pages 13
Place of publication Piscataway, NJ, United States
Publisher Institute of Electrical and Electronics Engineers
Language eng
Abstract 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.
Keyword Bregman's divergences
Dictionary learning
Kernel methods
Riemannian's geometry
Sparse coding
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: HERDC Pre-Audit
School of Information Technology and Electrical Engineering Publications
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Citation counts: TR Web of Science Citation Count  Cited 5 times in Thomson Reuters Web of Science Article | Citations
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Created: Wed, 22 Jun 2016, 01:55:36 EST by Conrad Sanderson on behalf of School of Information Technol and Elec Engineering