ArticleFoundations of data science (Springfield, Mo.)2026
Persistent Stanley-Reisner Theory.
Article in Foundations of data science (Springfield, Mo.), 2026. 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.
- CAKR: commutative algebra k-mer representations for genomics.Nature communications · 2026Article
- Commutative Algebra Modeling in Materials Science - A Case Study on Metal-Organic Frameworks (MOFs).Journal of chemical information and modeling · 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
- CAP: Commutative algebra prediction of protein-nucleic acid binding affinities.Machine learning: science and technology · 2025Article
- Article
- CAML: Commutative Algebra Machine Learning─A Case Study on Protein-Ligand Binding Affinity Prediction.Journal of chemical information and modeling · 2025Article
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2 authors.
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Abstract
Topological data analysis (TDA) has emerged as an effective approach in data science, with its key technique, persistent homology, rooted in algebraic topology. Although alternative approaches based on differential topology, geometric topology, and combinatorial Laplacians have been proposed, combinatorial commutative algebra has hardly been developed for machine learning and data science. In this work, we introduce persistent Stanley-Reisner theory to bridge commutative algebra, combinatorial algebraic topology, machine learning, and data science. We propose persistent h-vectors, persistent f-vectors, persistent graded Betti numbers, persistent facet ideals, and facet persistence modules. Stability analysis indicates that these algebraic invariants are stable against geometric perturbations. We employ a machine learning prediction on a molecular dataset to demonstrate the utility of the proposed persistent Stanley-Reisner theory for practical applications.
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