Building Deep Networks on Grassmann Manifolds

Zhiwu Huang, Jiqing Wu, Luc Van Gool

Published 2016-11-17Version 1

Representing the data on Grassmann manifolds is popular in quite a few image and video recognition tasks. In order to enable deep learning on Grassmann manifolds, this paper proposes a deep network architecture which generalizes the Euclidean network paradigm to Grassmann manifolds. In particular, we design full rank mapping layers to transform input Grassmannian data into more desirable ones, exploit orthogonal re-normalization 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 turn the resulting Grassmannian data into Euclidean forms for regular output layers. To train the deep network, we exploit a stochastic gradient descent setting on manifolds where the connection weights reside on, and study a matrix generalization of backpropagation to update the structured data. We experimentally evaluate the proposed network for three computer vision tasks, and show that it has clear advantages over existing Grassmann learning methods, and achieves results comparable with state-of-the-art approaches.