Building Deep Networks on Grassmann Manifolds

By Zhiwu Huang, Jiqing Wu, Luc Van Gool. 2016

198 citations recorded by the source corpus.

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.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Geometry and Topology

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Jiwen Lu
2. Jie Zhou
3. Yongming Rao
4. Zhiwu Huang
5. Cuntai Guan
6. Luc Van Gool
7. Thomas Probst
8. Chengde Wan

In Computer Vision and Pattern Recognition

1. Jie Zhou
2. Jiwen Lu
3. Yongming Rao
4. Luc Van Gool
5. Yang Liu
6. Dacheng Tao
7. Yi Yang
8. Chen Change Loy

In Geometry and Topology

1. Jiwen Lu
2. Yongming Rao
3. Jie Zhou
4. Zhiwu Huang
5. Luc Van Gool

Citations in the corpus

• Deep Learning on Lie Groups for Skeleton-Based Action Recognition (2016, background): “Moreover, recently some deep learning models have emerged [10, 7, 28, 25, 18, 21] that deal with data in a nonEuclidean domain.”
• Attention-Aware Deep Reinforcement Learning for Video Face Recognition (2017, methodology): “There have been a variety of studies on how to effectively integrate information across frames for video face representation [6, 18, 21, 28, 43].”
• Federated Transfer Learning for EEG Signal Classification (2020, background): “The paradigm of deep neural networks on SPD matrices has been proposed to interpolate, manipulate and classify SPD matrices in bunch of application areas [14], [15], [16], [17].”