LieBN on the Lie Groups of SPD Manifolds and Deformed Lie Groups of SPD Manifolds
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Firstly, we extend the current Lie groups on SPD manifolds by the concept of deformation, resulting in three families of parameterized Lie groups.Companies Mentioned
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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
5 LIEBN ON THE LIE GROUPS OF SPD MANIFOLDS
This section showcases our Alg. 1 on SPD manifolds. Firstly, we extend the current Lie groups on SPD manifolds by the concept of deformation, resulting in three families of parameterized Lie groups. Subsequently, we construct LieBN layers based on these generalized Lie groups.
5.1 DEFORMED LIE GROUPS OF SPD MANIFOLDS
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.
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