1.The application of gyro-structures on SPD manifolds and correlation matrices is indeed novel, but the paper does not clearly articulate the theoretical significance or unique advantages of using Power-Euclidean (PE) geometry over existing approaches like Affine-Invariant (AI) or Log-Euclidean (LE) methods. The work seems incremental without providing substantial theoretical or empirical evidence that PE geometry offers practical improvements beyond computational convenience. Especially, while gyro-structures are presented as an extension to non-Euclidean spaces, the paper does not establish a strong need or motivation for this approach within the broader context of machine learning or geometry-based learning. It lacks a thorough discussion on why gyro-structures would fundamentally enhance SPD or correlation matrix-based learning in a way that current methods do not.
2.Some key theoretical concepts and mathematical operations, such as those in gyrovector space theory and correlation matrix manifold construction, are highly technical and lack intuitive explanations. Additional clarification or simplified summaries would improve accessibility for readers unfamiliar with advanced Riemannian geometry.
3.On the experiments part, the related discussion lacks interpretive insights that would elucidate why the proposed gyro-structures outperform existing methods. In addition, while the paper compares its methods against SPD-based models and a few gyro-structure-based approaches, it lacks comparison with other state-of-the-art methods that might not rely on gyro-structures. This omission makes it unclear whether the proposed approach actually outperforms simpler or more commonly used techniques in manifold-based learning.
3.On the experiments part, the related discussion lacks interpretive insights that would elucidate why the proposed gyro-structures outperform existing methods. In addition, while the paper compares its methods against SPD-based models and a few gyro-structure-based approaches, it lacks comparison with other state-of-the-art methods that might not rely on gyro-structures. This omission makes it unclear whether the proposed approach actually outperforms simpler or more commonly used techniques in manifold-based learning.