The article introduces LieBN, a novel batch normalization technique tailored for Riemannian manifolds, particularly symmetric positive definite (SPD) matrices. Through a comprehensive analysis, the authors revisit existing methods, propose new frameworks, and present rigorous experimental results demonstrating that LieBN outperforms traditional Euclidean normalization in applications such as EEG classification. The work includes detailed theoretical underpinnings, experiments validating the effectiveness of LieBN, and discussions on its relevance to deep learning. The findings emphasize the significance of adapting normalization methods to the geometric properties of data for improved machine learning outcomes.
The new LieBN framework provides a systematic way to extend batch normalization to Riemannian manifolds, specifically catering to SPD (symmetric positive definite) matrices.
We demonstrate through experiments that LieBN significantly enhances performance in processing SPD data, surpassing traditional Euclidean techniques in various applications.
#batch-normalization #riemannian-geometry #spd-matrices #deep-learning #machine-learning-experiments
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