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Open AccessFeature PaperArticle
Understanding Higher-Order Interactions in Information Space
by
Herbert Edelsbrunner
Herbert Edelsbrunner 1,
Katharina Ölsböck
Katharina Ölsböck 1 and
Hubert Wagner
Hubert Wagner 2,*
1
ISTA (Institute of Science and Technology Austria), 3400 Klosterneuburg, Austria
2
Department of Mathematics, University of Florida, Gainesville, FL 32611, USA
*
Author to whom correspondence should be addressed.
Entropy 2024, 26(8), 637; https://doi.org/10.3390/e26080637 (registering DOI)
Submission received: 19 June 2024
/
Revised: 19 July 2024
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Accepted: 20 July 2024
/
Published: 27 July 2024
Abstract
Methods used in topological data analysis naturally capture higher-order interactions in point cloud data embedded in a metric space. This methodology was recently extended to data living in an information space, by which we mean a space measured with an information theoretical distance. One such setting is a finite collection of discrete probability distributions embedded in the probability simplex measured with the relative entropy (Kullback–Leibler divergence). More generally, one can work with a Bregman divergence parameterized by a different notion of entropy. While theoretical algorithms exist for this setup, there is a paucity of implementations for exploring and comparing geometric-topological properties of various information spaces. The interest of this work is therefore twofold. First, we propose the first robust algorithms and software for geometric and topological data analysis in information space. Perhaps surprisingly, despite working with Bregman divergences, our design reuses robust libraries for the Euclidean case. Second, using the new software, we take the first steps towards understanding the geometric-topological structure of these spaces. In particular, we compare them with the more familiar spaces equipped with the Euclidean and Fisher metrics.
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MDPI and ACS Style
Edelsbrunner, H.; Ölsböck, K.; Wagner, H.
Understanding Higher-Order Interactions in Information Space. Entropy 2024, 26, 637.
https://doi.org/10.3390/e26080637
AMA Style
Edelsbrunner H, Ölsböck K, Wagner H.
Understanding Higher-Order Interactions in Information Space. Entropy. 2024; 26(8):637.
https://doi.org/10.3390/e26080637
Chicago/Turabian Style
Edelsbrunner, Herbert, Katharina Ölsböck, and Hubert Wagner.
2024. "Understanding Higher-Order Interactions in Information Space" Entropy 26, no. 8: 637.
https://doi.org/10.3390/e26080637
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