The Hellinger distance as used for the representation of serological ABO distances among earlier human populations

Juhasz, Ference

doi:10.1007/bf00284654

Cited by 4 publications

(1 citation statement)

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“…Some exemplary applications of the Bhattacharyya arccos distance B 1/2,1,1 (Q, P) can be found e.g. in Rao [301] and Juhasz [177] for cluster analysis of human populations, in Martin-Fernandez et al [251] for general hierarchical clustering, Greenacre [141] for metric scaling, and in Chen et al [79] for clustering high-dimensional microbial data from RNA sequencing.…”

Section: As a Further Example Considermentioning

confidence: 99%

A precise bare simulation approach to the minimization of some distances. Foundations

Broniatowski¹,

Stummer²

2021

Preprint

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In information theory -as well as in the adjacent fields of statistics, machine learning, artificial intelligence, signal processing and pattern recognition -many flexibilizations of the omnipresent Kullback-Leibler information distance (relative entropy) and of the closely related Shannon entropy have become frequently used tools. To tackle corresponding constrained minimization (respectively maximization) problems by a newly developed dimension-free bare (pure) simulation method, is the main goal of this paper. Almost no assumptions (like convexity) on the set of constraints are needed, within our discrete setup of arbitrary dimension, and our method is precise (i.e., converges in the limit). As a side effect, we also derive an innovative way of constructing new useful distances/divergences. To illustrate the core of our approach, we present numerous examples. The potential for widespread applicability is indicated, too; in particular, we deliver many recent references for uses of the involved distances/divergences and entropies in various different research fields (which may also serve as an interdisciplinary interface).

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Section: As a Further Example Considermentioning

confidence: 99%

A precise bare simulation approach to the minimization of some distances. Foundations

Broniatowski¹,

Stummer²

2021

Preprint

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A Precise Bare Simulation Approach to the Minimization of Some Distances. I. Foundations

Broniatowski¹,

Stummer

2023

IEEE Trans. Inform. Theory

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The constrained minimization (respectively maximization) of directed distances and of related generalized entropies is a fundamental task in information theory as well as in the adjacent fields of statistics, machine learning, artificial intelligence, signal processing and pattern recognition. In our previous paper "A precise bare simulation approach to the minimization of some distances. I. Foundations", we obtained such kind of constrained optima by a new dimension-free precise bare (pure) simulation method, provided basically that (i) the underlying directed distance is of f −divergence type, and that (ii) this can be connected to a light-tailed probability distribution in a certain manner. In the present paper, we extend this approach such that constrained optimization problems of a very huge amount of directed distances and generalized entropies -and beyond -can be tackled by a newly developed dimension-free extended bare simulation method, for obtaining both optima as well as optimizers. Almost no assumptions (like convexity) on the set of constraints are needed, within our discrete setup of arbitrary dimension, and our method is precise (i.e., converges in the limit). For instance, we cover constrained optimizations of arbitrary f −divergences, Bregman distances, scaled Bregman distances and weighted ℓr−distances. The potential for wide-spread applicability is indicated, too; in particular, we deliver many recent references for uses of the involved distances/divergences in various different research fields (which may also serve as an interdisciplinary interface).

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Charakterystyka serologiczna populacji wsi Wielkie Drogi w pobliżu Krakowa

Swornowski¹

2022

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The Hellinger distance as used for the representation of serological ABO distances among earlier human populations

Cited by 4 publications

References 4 publications

A precise bare simulation approach to the minimization of some distances. Foundations

A precise bare simulation approach to the minimization of some distances. Foundations

A Precise Bare Simulation Approach to the Minimization of Some Distances. I. Foundations

Charakterystyka serologiczna populacji wsi Wielkie Drogi w pobliżu Krakowa

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