Publication Type

Conference Proceeding Article

Version

publishedVersion

Publication Date

2-2018

Abstract

Learning representations on Grassmann manifolds is popular in quite a few visual recognition tasks. In order to enable deep learning on Grassmann manifolds, this paper proposes a deep network architecture by generalizing the Euclidean network paradigm to Grassmann manifolds. In particular, we design full rank mapping layers to transform input Grassmannian data to more desirable ones, exploit re-orthonormalization layers to normalize the resulting matrices, study projection pooling layers to reduce the model complexity in the Grassmannian context, and devise projection mapping layers to respect Grassmannian geometry and meanwhile achieve Euclidean forms for regular output layers. To train the Grassmann networks, we exploit a stochastic gradient descent setting on manifolds of the connection weights, and study a matrix generalization of backpropagation to update the structured data. The evaluations on three visual recognition tasks show that our Grassmann networks have clear advantages over existing Grassmann learning methods, and achieve results comparable with state-of-the-art approaches.

Keywords

Artificial intelligence; Mapping; Matrix algebra; Network architecture; Stochastic systems

Discipline

Artificial Intelligence and Robotics | OS and Networks

Research Areas

Data Science and Engineering

Publication

Proceedings of the 32nd AAAI Conference on Artificial Intelligence,Louisiana, USA, 2018 February 2–7

First Page

3279

Last Page

3286

ISBN

9781577358008

Publisher

AAAI press

City or Country

California, USA

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