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This is a Quantitative Study study (also classified as: Experimental Study).

September 30, 2025MathematicsOpen Access

Information-Geometric Models in Data Analysis and Physics

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This framework develops insights into data structures on Riemannian manifolds, suggesting new information theories.

The study reveals how geometric insights inform data analysis, emphasizing curvature in statistical representations.
Utilizing Fisher information metrics, the framework captures local and global data relationships across various scales.
Methods include gradient flow lines and kernel-based principal component analysis, respecting intrinsic geometry principles.
This approach may lead to significant advancements by elucidating physical systems through geometrically-informed information theory.

Bernal‐Casas et al. (2025) studied this question.

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