Table of LinksAbstract and 1 Introduction2 Preliminaries3. Revisiting Normalization3.1 Revisiting Euclidean Normalization3.2 Revisiting Existing RBN4 Riemannian Normalization on Lie Groups5 LieBN on the Lie Groups of SPD Manifolds and 5.1 Deformed Lie Groups of SPD Manifolds5.2 LieBN on SPD Manifolds6 Experiments6.1 Experimental Results7 Conclusions, Acknowledgments, and References\APPENDIX CONTENTSA NotationsB Basic layes in SPDnet and TSMNetC Statistical Results of Scaling in the LieBND LieBN as a Natural Generalization of Euclidean BNE Domain-specific Momentum LieBN for EEG ClassificationF Backpropagation of Matrix FunctionsG Additional Details and Experiments of LieBN on SPD manifoldsH Preliminary Experiments on Rotation MatricesI Proofs of the Lemmas and Theories in the Main PaperA NOTATIONSFor better clarity, we summarize all the notations used in this paper in Tab. 6.\ B BASIC LAYERS IN SPDNET AND TSMNETSPDNet (Huang & Van Gool, 2017) is the most classic SPD neural network. SPDNet mimics the conventional densely connected feedforward network, consisting of three basic building blocks\\ \\where max(·) is element-wise maximization. BiMap and ReEig mimic transformation and nonlinear activation, while LogEig maps SPD matrices into the tangent space at the identity matrix for classification.\\ \C STATISTICAL RESULTS OF SCALING IN THE LIEBNIn this section, we will show the effect of our scaling (Eq. (14)) on the population. We will see that while the resulting population variance is generally agnostic, it becomes analytic under certain circumstances, such as SPD manifolds under LEM or LCM. As a result, Eq. (14) can normalize and transform the latent Gaussian distribution.\\ \\The above lemma implies that when ∆ is a constant, Y also follows a Gaussian distribution.\\ \\\ \\By Prop. C.3, we can directly obtain the following corollary.\\ \:::infoThis paper is available on arxiv under CC BY-NC-SA 4.0 DEED license.::::::infoAuthors:(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.:::\