Sparse Coding on Symmetric Positive Definite Manifolds Using Bregman Divergences

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Harandi, Mehrtash T
Hartley, Richard
Lovell, Brian
Sanderson, Conrad
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2016
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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.

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IEEE Transactions on Neural Networks and Learning Systems

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27

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6

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© 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

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Artificial intelligence

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Harandi, MT; Hartley, R; Lovell, B; Sanderson, C, Sparse Coding on Symmetric Positive Definite Manifolds Using Bregman Divergences, IEEE Transactions on Neural Networks and Learning Systems, 2016, 27 (6), pp. 1294-1306

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