LieBN on the Lie Groups of SPD Manifolds and Deformed Lie Groups of SPD Manifolds

Table of Links

Abstract and 1 Introduction

2 Preliminaries

3. Revisiting Normalization

3.1 Revisiting Euclidean Normalization

3.2 Revisiting Existing RBN

4 Riemannian Normalization on Lie Groups

5 LieBN on the Lie Groups of SPD Manifolds and 5.1 Deformed Lie Groups of SPD Manifolds

5.2 LieBN on SPD Manifolds

6 Experiments

6.1 Experimental Results

7 Conclusions, Acknowledgments, and References

APPENDIX CONTENTS

A Notations

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