ArticleFoundations of data science (Springfield, Mo.)2025
PERSISTENT INTERACTION TOPOLOGY IN DATA ANALYSIS.
Article in Foundations of data science (Springfield, Mo.), 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 7 papers.
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Who cites it
7 citing papers in PubMed.
- Interaction topology theory deciphers multiscale codes of MOF-like materials.Science advances · 2026Article
- Disrupted Higher-Order Topology in OCD Brain Networks Revealed by Hodge Laplacian - an ENIGMA Study.bioRxiv : the preprint server for biology · 2026Article
- Topological data analysis and topological deep learning beyond persistent homology: a review.Artificial intelligence review · 2026Article
- Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real-World Data.Advanced intelligent discovery · 2025Article
- A Review of Topological Data Analysis and Topological Deep Learning in Molecular Sciences.Journal of chemical information and modeling · 2025Review
- Persistent Topological Laplacians-A Survey.Mathematics (Basel, Switzerland) · 2025Article
- Evolutionary Khovanov homology.AIMS mathematics · 2024Article
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3 authors.
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Abstract
Topological data analysis, as a tool for extracting topological features and characterizing geometric shapes, has had tremendous success across diverse fields. Its key mathematical techniques include persistent homology and the recently developed persistent Laplacians. However, classic mathematical models like simplicial complexes often struggle to provide a localized topological description for interactions or individual elements within a complex system involving a specific set of elements. In this work, we introduce persistent interaction homology and persistent interaction Laplacian that emphasize individual interacting elements in the system. We demonstrate the stability of persistent interaction homology as a persistent module. Furthermore, for a finite discrete set of points in the Euclidean space, we provide the construction of persistent interaction Vietoris-Rips complexes and compute their interaction homology and interaction Laplacians. The proposed methods hold significant promise for analyzing heterogeneously interactive data and emphasizing specific elements in data. Their utility for data science is demonstrated with applications to molecules.
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