PERSISTENT HYPERDIGRAPH HOMOLOGY AND PERSISTENT HYPERDIGRAPH LAPLACIANS

Hypergraphs are useful mathematical models for describing complex relationships among members of a structured graph, while hyperdigraphs serve as a generalization that can encode asymmetric relationships in the data. However, obtaining topological information directly from hyperdigraphs remains a ch...

Full description

Saved in:
Bibliographic Details
Published inFoundations of data science Vol. 5; no. 4; p. 558
Main Authors Chen, Dong, Liu, Jian, Wu, Jie, Wei, Guo-Wei
Format Journal Article
LanguageEnglish
Published United States 01.12.2023
Subjects
18G85
filtration
Topological hyperdigraph Laplacians
homology
persistence
Secondary: 05C65
Primary: 55N31
Topological hyperdigraph
Online AccessGet full text
ISSN2639-8001
2639-8001
DOI10.3934/fods.2023010

Cover

More Information
Summary:Hypergraphs are useful mathematical models for describing complex relationships among members of a structured graph, while hyperdigraphs serve as a generalization that can encode asymmetric relationships in the data. However, obtaining topological information directly from hyperdigraphs remains a challenge. To address this issue, we introduce hyperdigraph homology in this work. We also propose topological hyperdigraph Laplacians, which can extract both harmonic spectra and non-harmonic spectra from directed and internally organized data. Moreover, we introduce persistent hyperdigraph homology and persistent hyperdigraph Laplacians through filtration, enabling the capture of topological persistence and homotopic shape evolution of directed and structured data across multiple scales. The proposed methods offer new multiscale algebraic topology tools for topological data analysis.
ISSN:2639-8001
2639-8001
DOI:10.3934/fods.2023010