Publication Type

Conference Proceeding Article

Version

publishedVersion

Publication Date

2-2017

Abstract

Symmetric Positive Definite (SPD) matrix learning methods have become popular in many image and video processing tasks, thanks to their ability to learn appropriate statistical representations while respecting Riemannian geometry of underlying SPD manifolds. In this paper we build a Riemannian network architecture to open up a new direction of SPD matrix non-linear learning in a deep model. In particular, we devise bilinear mapping layers to transform input SPD matrices to more desirable SPD matrices, exploit eigenvalue rectification layers to apply a non-linear activation function to the new SPD matrices, and design an eigenvalue logarithm layer to perform Riemannian computing on the resulting SPD matrices for regular output layers. For training the proposed deep network, we exploit a new backpropagation with a variant of stochastic gradient descent on Stiefel manifolds to update the structured connection weights and the involved SPD matrix data. We show through experiments that the proposed SPD matrix network can be simply trained and outperform existing SPD matrix learning and state-of-the-art methods in three typical visual classification tasks.

Keywords

Artificial intelligence; Eigenvalues and eigenfunctions; Geometry; Mathematical transformations; Network architecture; Stochastic systems; Video signal processing

Discipline

Artificial Intelligence and Robotics | OS and Networks

Research Areas

Data Science and Engineering

Publication

Proceedings of the 31st AAAI Conference on Artificial Intelligence, AAAI 2017, California, USA, 2017 February 4–9.

First Page

2036

Last Page

2042

Publisher

AAAI press

City or Country

California, USA

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