PERSISTENT DIRECTED FLAG LAPLACIAN

Topological data analysis (TDA) has had enormous success in science and engineering in the past decade. Persistent topological Laplacians (PTLs) overcome some limitations of persistent homology, a key technique in TDA, and provide substantial insight to the behavior of various geometric and topologi...

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Bibliographic Details
Published inFoundations of data science Vol. 7; no. 3; p. 737
Main Authors Jones, Benjamin, Wei, Guo-Wei
Format Journal Article
LanguageEnglish
Published United States 01.09.2025
Subjects
Persistent topological Laplacians
clique complex
directed flag Laplacians
Primary: 55N31
directed flag complex
topological data analysis
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ISSN2639-8001
2639-8001
DOI10.3934/fods.2024048

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Summary:Topological data analysis (TDA) has had enormous success in science and engineering in the past decade. Persistent topological Laplacians (PTLs) overcome some limitations of persistent homology, a key technique in TDA, and provide substantial insight to the behavior of various geometric and topological objects. This work extends PTLs to directed flag complexes, which are an exciting generalization to flag complexes, also known as clique complexes, that arise naturally in many situations. We introduce the directed flag Laplacian and show that the proposed persistent directed flag Laplacian (PDFL) is a distinct way of analyzing these flag complexes. Example calculations are provided to demonstrate the potential of the proposed PDFL in real world applications.
ISSN:2639-8001
2639-8001
DOI:10.3934/fods.2024048