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 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. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Preliminaries 2 Preliminaries 3. Revisiting Normalization 3.1 Revisiting Euclidean Normalization 3.1 Revisiting Euclidean Normalization 3.2 Revisiting Existing RBN 3.2 Revisiting Existing RBN 4 Riemannian Normalization on Lie Groups 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 LieBN on the Lie Groups of SPD Manifolds and 5.1 Deformed Lie Groups of SPD Manifolds 5.2 LieBN on SPD Manifolds 5.2 LieBN on SPD Manifolds 6 Experiments 6 Experiments 6.1 Experimental Results 6.1 Experimental Results 7 Conclusions, Acknowledgments, and References 7 Conclusions, Acknowledgments, and References APPENDIX CONTENTS APPENDIX CONTENTS A Notations A Notations B Basic layes in SPDnet and TSMNet B Basic layes in SPDnet and TSMNet C Statistical Results of Scaling in the LieBN C Statistical Results of Scaling in the LieBN D LieBN as a Natural Generalization of Euclidean BN D LieBN as a Natural Generalization of Euclidean BN E Domain-specific Momentum LieBN for EEG Classification E Domain-specific Momentum LieBN for EEG Classification F Backpropagation of Matrix Functions F Backpropagation of Matrix Functions G Additional Details and Experiments of LieBN on SPD manifolds G Additional Details and Experiments of LieBN on SPD manifolds H Preliminary Experiments on Rotation Matrices H Preliminary Experiments on Rotation Matrices I Proofs of the Lemmas and Theories in the Main Paper 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 Implementation details: This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. available on arxiv 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. Authors: 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.

Part of HackerNoon's growing list of open-source research papers, promoting free access to academic material.

Abstract

Matrix

Radar

How We Implemented Our Three Families of LieBN to SPD Neural Networks

About Author

Comments

TOPICS

THIS ARTICLE WAS FEATURED IN

Related Stories

A Brief Review of the Lie Group and the Geometries of SPD Manifolds

A Lie Group Approach to Riemannian Batch Normalization

Revisiting Euclidean Normalization: A Second Look

Revisiting Existing RBN: Developing Riemannian Normalization Approaches Tailored for Manifolds

Riemannian Normalization on Lie Groups

LieBN on SPD Manifolds: Showcasing Our LieBN Framework

A Brief Review of the Lie Group and the Geometries of SPD Manifolds

A Lie Group Approach to Riemannian Batch Normalization

Revisiting Euclidean Normalization: A Second Look

Revisiting Existing RBN: Developing Riemannian Normalization Approaches Tailored for Manifolds

Riemannian Normalization on Lie Groups

LieBN on SPD Manifolds: Showcasing Our LieBN Framework

Light-Mode

Classic

Newspaper

Minty

Dark-Mode

Neon Noir

Minty

HN StartUps