Persistent path Laplacian

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2023Embargo end date: 01 Jan 2022Publisher:American Institute of Mathematical Sciences (AIMS)Journal:Foundations of Data Science, volume 5, pages 26-55 (eissn: 2639-8001,

Copyright policy )Funded by:NSF | III: Medium: De Rham-Hodg..., NIH | Synergistic integration o..., NSF | Collaborative Research: I... +2 projects

Authors: Wang, Rui; Wei, Guo-Wei;

doi: 10.3934/fods.2022015 , 10.48550/arxiv.2206.03991

pmid: 37841699

pmc: PMC10575407

arXiv: 2206.03991

Persistent path Laplacian

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Abstract

Path homology proposed by S.-T.Yau and his co-workers provides a new mathematical model for directed graphs and networks. Persistent path homology (PPH) extends the path homology with filtration to deal with asymmetry structures. However, PPH is constrained to purely topological persistence and cannot track the homotopic shape evolution of data during filtration. To overcome the limitation of PPH, persistent path Laplacian (PPL) is introduced to capture the shape evolution of data. PPL's harmonic spectra fully recover PPH's topological persistence and its non-harmonic spectra reveal the homotopic shape evolution of data during filtration.

30 page, 7 figures

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Keywords

Topological data analysis, spectral graph theory, persistent Laplacian, simultaneous geometric and topological analyses, Persistent homology and applications, topological data analysis, persistent homology, spectral data analysis, topological data analysis, Mathematics - Spectral Theory, FOS: Mathematics, Algebraic Topology (math.AT), Mathematics - Algebraic Topology, Spectral Theory (math.SP)

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