Table of Links
3. Revisiting Normalization
3.1 Revisiting Euclidean Normalization
4 Riemannian Normalization on Lie Groups
5 LieBN on the Lie Groups of SPD Manifolds and 5.1 Deformed Lie Groups of SPD Manifolds
7 Conclusions, Acknowledgments, and References
APPENDIX CONTENTS
B Basic layes in SPDnet and TSMNet
C Statistical Results of Scaling in the LieBN
D LieBN as a Natural Generalization of Euclidean BN
E Domain-specific Momentum LieBN for EEG Classification
F Backpropagation of Matrix Functions
G Additional Details and Experiments of LieBN on SPD manifolds
H Preliminary Experiments on Rotation Matrices
I Proofs of the Lemmas and Theories in the Main Paper
6 EXPERIMENTS
In this section, we implement our three families of LieBN to SPD neural networks. Following the previous work (Huang & Van Gool, 2017; Brooks et al., 2019b; Kobler et al., 2022a), we adopt three different applications: radar recognition on the Radar dataset (Brooks et al., 2019b), human action recognition on the HDM05 (M ¨uller et al., 2007) and FPHA (Garcia-Hernando et al., 2018) datasets, and EEG classification on the Hinss2021 dataset (Hinss et al., 2021). More details on datasets and hyper-parameters are exposed in App. G. Besides SPD neural networks, we also implement LieBN on special orthogonal groups and present some preliminary experiments (see App. H).
Implementation details: Note that our LieBN layers are architecture-agnostic and can be applied to any existing SPD neural network. In this paper, we focus on two network architectures: SPDNet
This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license.
Authors:
(1) Ziheng Chen, University of Trento;
(2) Yue Song, University of Trento and a Corresponding author;
(3) Yunmei Liu, University of Louisville;
(4) Nicu Sebe, University of Trento.