Publication Type

Journal Article

Version

publishedVersion

Publication Date

10-2018

Abstract

Symmetric positive definite (SPD) matrices have been employed for data representation in many visual recognition tasks. The success is mainly attributed to learning discriminative SPD matrices encoding the Riemannian geometry of the underlying SPD manifolds. In this paper, we propose a geometry-aware SPD similarity learning (SPDSL) framework to learn discriminative SPD features by directly pursuing a manifold-manifold transformation matrix of full column rank. Specifically, by exploiting the Riemannian geometry of the manifolds of fixed-rank positive semidefinite (PSD) matrices, we present a new solution to reduce optimization over the space of column full-rank transformation matrices to optimization on the PSD manifold, which has a well-established Riemannian structure. Under this solution, we exploit a new supervised SPDSL technique to learn the manifold-manifold transformation by regressing the similarities of selected SPD data pairs to their ground-truth similarities on the target SPD manifold. To optimize the proposed objective function, we further derive an optimization algorithm on the PSD manifold. Evaluations on three visual classification tasks show the advantages of the proposed approach over the existing SPD-based discriminant learning methods.

Keywords

Discriminative SPD matrices;Riemannian geometry;SPD manifold;geometry-aware SPD similarity learning;PSD manifold

Discipline

Databases and Information Systems | Graphics and Human Computer Interfaces

Research Areas

Data Science and Engineering

Publication

IEEE Transactions on Circuits and Systems for Video Technology

Volume

28

Issue

10

First Page

2513

Last Page

2523

ISSN

1051-8215

Identifier

10.1109/TCSVT.2017.2729660

Publisher

Institute of Electrical and Electronics Engineers

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