This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.

Search for Publication

Year(s) from:  to 
Keywords (separated by spaces):

Building Deep Networks on Grassmann Manifolds

Zhiwu Huang, Jiqing Wu, Luc Van Gool
Association for the Advancement of Artificial Intelligence (AAAI)
February 2018, in press


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 network, 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. We experimentally evaluate the proposed network for three visual classification tasks, and show that it has clear advantages over existing Grassmann learning methods, and achieves results comparable with state-of-the-art approaches.

Download in pdf format
  author = {Zhiwu Huang and Jiqing Wu and Luc Van Gool},
  title = {Building Deep Networks on Grassmann Manifolds },
  booktitle = {Association for the Advancement of Artificial Intelligence (AAAI)},
  year = {2018},
  month = {February},
  keywords = {},
  note = {in press}