ArticleEntropy (Basel, Switzerland)2020
The Fisher-Rao Distance between Multivariate Normal Distributions: Special Cases, Bounds and Applications.
Article in Entropy (Basel, Switzerland), 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 9 papers.
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Who cites it
9 citing papers in PubMed.
- Multimodal Characterization of Acerola-Derived Gold Nanoparticles through Integrated Advanced Distributional Analysis.ACS omega · 2026Article
- RiTex: Harmonization of Radiomic Features Based on Riemannian Geometry.Journal of imaging · 2026Article
- Thermodynamic natural gradient descent (NGD-T) regulates natural-gradient steps by a geometric speed-cost bound.Scientific reports · 2026Article
- Fisher-Rao Distance for Finite-Energy Signal Manifolds: Geometric Foundations and Numerical Analysis.Entropy (Basel, Switzerland) · 2026Article
- Jeffreys Divergence and Generalized Fisher Information Measures on Fokker-Planck Space-Time Random Field.Entropy (Basel, Switzerland) · 2023Article
- A Simple Approximation Method for the Fisher-Rao Distance between Multivariate Normal Distributions.Entropy (Basel, Switzerland) · 2023Article
- Parameter estimation and uncertainty quantification using information geometry.Journal of the Royal Society, Interface · 2022Review
- An Elementary Introduction to Information Geometry.Entropy (Basel, Switzerland) · 2020Review
- On Voronoi Diagrams on the Information-Geometric Cauchy Manifolds.Entropy (Basel, Switzerland) · 2020Article
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3 authors.
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Abstract
The Fisher-Rao distance is a measure of dissimilarity between probability distributions, which, under certain regularity conditions of the statistical model, is up to a scaling factor the unique Riemannian metric invariant under Markov morphisms. It is related to the Shannon entropy and has been used to enlarge the perspective of analysis in a wide variety of domains such as image processing, radar systems, and morphological classification. Here, we approach this metric considered in the statistical model of normal multivariate probability distributions, for which there is not an explicit expression in general, by gathering known results (closed forms for submanifolds and bounds) and derive expressions for the distance between distributions with the same covariance matrix and between distributions with mirrored covariance matrices. An application of the Fisher-Rao distance to the simplification of Gaussian mixtures using the hierarchical clustering algorithm is also presented.
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