This article proposes a unified framework for Riemannian Batch Normalization (RBN) on Lie groups, addressing limitations in existing ad hoc methods. The framework emphasizes robust control over Riemannian mean and variance. Focusing on Symmetric Positive Definite (SPD) manifolds, the paper introduces three families of parameterized Lie groups that enhance normalization techniques for neural networks. The effectiveness of this approach is demonstrated through diverse experiments, including radar recognition, human action recognition, and EEG classification, showcasing its potential in applications involving manifold-valued measurements and improving deep learning outcomes in these domains.
This paper presents a unified framework for Riemannian Batch Normalization techniques on Lie groups, improving upon existing methods that were applied ad hoc to specific manifolds.
The proposed framework guarantees control over both the Riemannian mean and variance, essential for effective deep neural networks operating on manifold-valued measurements.
By generalizing existing Lie groups on Symmetric Positive Definite manifolds into three families of parameterized groups, we broaden the application of normalization techniques in diverse domains.
Through experiments on radar, human action recognition, and EEG classification, our approach demonstrates significant improvements over previous methods, solidifying its practical applications.
#riemannian-normalization #lie-groups #symmetric-positive-definite-manifolds #deep-neural-networks #machine-learning-applications
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