This article discusses Riemannian normalization methods on Lie groups, emphasizing the importance of LieBN for SPD manifolds. The paper highlights the structural properties of Lie groups, particularly the role of left-invariant metrics in simplifying complex geometries. Through various experimental results, the authors demonstrate how LieBN serves as a natural extension of traditional Euclidean normalization, presenting significant accuracy benefits in tasks such as EEG classification and addressing challenges in scaling and backpropagation of matrix functions. Overall, it aims to advance understanding and application of normalization techniques in machine learning on manifolds.
This paper explores Riemannian normalization on Lie groups, particularly focusing on implementing LieBN for the SPD manifolds and addressing the nuances of structure and performance.
A Lie graph is integral in understanding Riemannian geometry, and the use of left-invariant metrics simplifies the complex interactions within Lie groups.
The LieBN approach emerges as a novel technique to generalize Euclidean normalization, showcasing clear advantages in performance across various experiments involving SPD manifold applications.
We delve into experimental results which underscore the practicality of LieBN, notably in domain-specific contexts such as EEG classification, which exhibit promising accuracy improvements.
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