Clustering using the fisher-rao distance

2016 ◽  
Author(s):  
Joao E. Strapasson ◽  
Julianna Pinele ◽  
Sueli I. R. Costa
Keyword(s):  
Rao Distance

scholarly journals On the second Feng-Rao distance of Algebraic Geometry codes related to Arf semigroups

2018 ◽  
Vol 86 (12) ◽  
pp. 2893-2916 ◽  
Author(s):  
José I. Farrán ◽  
Pedro A. García-Sánchez ◽  
Benjamín A. Heredia
Keyword(s):  
Algebraic Geometry ◽  
Algebraic Geometry Codes ◽  
Rao Distance ◽  
Arf Semigroups

scholarly journals An unbalanced optimal transport splitting scheme for general advection-reaction-diffusion problems

2019 ◽  
Vol 25 ◽  
pp. 8 ◽  
Author(s):  
Thomas Gallouët ◽  
Maxime Laborde ◽  
Léonard Monsaingeon
Keyword(s):  
Optimal Transport ◽  
Diffusion Processes ◽  
Reaction Diffusion ◽  
Wasserstein Distance ◽  
Diffusion Problem ◽  
Constructive Method ◽  
Interacting Species ◽  
General Scalar ◽  
Minimizing Movements ◽  
Rao Distance

In this paper, we show that unbalanced optimal transport provides a convenient framework to handle reaction and diffusion processes in a unified metric setting. We use a constructive method, alternating minimizing movements for the Wasserstein distance and for the Fisher-Rao distance, and prove existence of weak solutions for general scalar reaction-diffusion-advection equations. We extend the approach to systems of multiple interacting species, and also consider an application to a very degenerate diffusion problem involving a Gamma-limit. Moreover, some numerical simulations are included.

scholarly journals Color Texture Classification Using Rao Distance between Multivariate Copula Based Models

2011 ◽  
pp. 498-505 ◽  
Author(s):  
Ahmed Drissi El Maliani ◽  
Mohammed El Hassouni ◽  
Nour-Eddine Lasmar ◽  
Yannick Berthoumieu ◽  
Driss Aboutajdine
Keyword(s):  
Texture Classification ◽  
Rao Distance ◽  
Multivariate Copula ◽  
Color Texture

scholarly journals On Voronoi Diagrams on the Information-Geometric Cauchy Manifolds

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 713 ◽  
Author(s):  
Frank Nielsen
Keyword(s):  
Voronoi Diagram ◽  
Voronoi Diagrams ◽  
Information Geometry ◽  
Square Root ◽  
Chi Square ◽  
Scale Parameters ◽  
Leibler Divergence ◽  
Finite Set ◽  
Metric Distance ◽  
Rao Distance

We study the Voronoi diagrams of a finite set of Cauchy distributions and their dual complexes from the viewpoint of information geometry by considering the Fisher-Rao distance, the Kullback-Leibler divergence, the chi square divergence, and a flat divergence derived from Tsallis entropy related to the conformal flattening of the Fisher-Rao geometry. We prove that the Voronoi diagrams of the Fisher-Rao distance, the chi square divergence, and the Kullback-Leibler divergences all coincide with a hyperbolic Voronoi diagram on the corresponding Cauchy location-scale parameters, and that the dual Cauchy hyperbolic Delaunay complexes are Fisher orthogonal to the Cauchy hyperbolic Voronoi diagrams. The dual Voronoi diagrams with respect to the dual flat divergences amount to dual Bregman Voronoi diagrams, and their dual complexes are regular triangulations. The primal Bregman Voronoi diagram is the Euclidean Voronoi diagram and the dual Bregman Voronoi diagram coincides with the Cauchy hyperbolic Voronoi diagram. In addition, we prove that the square root of the Kullback-Leibler divergence between Cauchy distributions yields a metric distance which is Hilbertian for the Cauchy scale families.

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