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.

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Abstract

Matrix

Radar

Understanding Multi-Group Attention in AI Models

LieBN on SPD Manifolds: Showcasing Our LieBN Framework

Read My Stories

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Make resilience your competitive advantage

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

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