The rapid growth of large datasets has led to a demand for novel approaches to extract valuable insights from intricate information. Graph theory provides a natural framework to model these relationships, but standard graphs may not capture the complex interdependence between components. Hypergraphs are a powerful extension of graphs that can represent higher-order relationships in the data. In this paper, we propose a novel approach to studying the structure of a dataset using hypergraph theory and a filtration method. Our method involves building a set of hypergraphs based on a variable distance parameter, enabling us to infer qualitative and quantitative information about the data structure. We apply our method to various sets of points, dynamical systems, signal models, and real electrophysiological data. Our results show that the proposed method can effectively differentiate between varying datasets, demonstrating its potential utility in a range of scientific applications.
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February 2024
Research Article|
February 29 2024
Filtration evolution of hypergraphs: A novel approach to studying multidimensional datasets Available to Purchase
Dalma Bilbao
;
Dalma Bilbao
(Data curation, Investigation, Software, Validation, Writing – review & editing)
1
Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)
, Buenos Aires C1425FQB Argentina
3
Facultad de Ciencia y Tecnología, Universidad Autónoma de Entre Ríos (UADER)
, Oro Verde, Entre Ríos 3105, Argentina
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Hugo Aimar
;
Hugo Aimar
(Conceptualization, Formal analysis, Funding acquisition, Investigation, Project administration, Writing – original draft, Writing – review & editing)
1
Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)
, Buenos Aires C1425FQB Argentina
3
Facultad de Ciencia y Tecnología, Universidad Autónoma de Entre Ríos (UADER)
, Oro Verde, Entre Ríos 3105, Argentina
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Diego M. Mateos
Diego M. Mateos
a)
(Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Software, Supervision, Visualization, Writing – original draft, Writing – review & editing)
1
Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)
, Buenos Aires C1425FQB Argentina
2
Instituto de Matemática Aplicada del Litoral (IMAL-CONICET-UNL), CCT CONICET
, Santa Fé 3000, Argentina
3
Facultad de Ciencia y Tecnología, Universidad Autónoma de Entre Ríos (UADER)
, Oro Verde, Entre Ríos 3105, Argentina
a)Author to whom correspondence should be addressed: [email protected]
Search for other works by this author on:
Dalma Bilbao
1,3
Hugo Aimar
1,3
Diego M. Mateos
1,2,3,a)
1
Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)
, Buenos Aires C1425FQB Argentina
3
Facultad de Ciencia y Tecnología, Universidad Autónoma de Entre Ríos (UADER)
, Oro Verde, Entre Ríos 3105, Argentina
2
Instituto de Matemática Aplicada del Litoral (IMAL-CONICET-UNL), CCT CONICET
, Santa Fé 3000, Argentina
a)Author to whom correspondence should be addressed: [email protected]
Chaos 34, 023142 (2024)
Article history
Received:
April 20 2023
Accepted:
February 01 2024
Citation
Dalma Bilbao, Hugo Aimar, Diego M. Mateos; Filtration evolution of hypergraphs: A novel approach to studying multidimensional datasets. Chaos 1 February 2024; 34 (2): 023142. https://doi.org/10.1063/5.0155459
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