ArticleAIMS mathematics2024
Persistent de Rham-Hodge Laplacians in Eulerian representation for manifold topological learning.
Article in AIMS mathematics, 2024. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 10 papers.
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Who cites it
10 citing papers in PubMed.
- Article
- Article
- Manifold topological deep learning for biomedical data.Nature communications · 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
- Manifold Topological Deep Learning for Biomedical Data.Research square · 2025Article
- Mayer-Homology Learning Prediction of Protein-Ligand Binding Affinities.Journal of computational biophysics and chemistry · 2025Article
- Persistent Topological Laplacians-A Survey.Mathematics (Basel, Switzerland) · 2025Article
- Topology-preserving Hodge decomposition in the Eulerian representation.Beijing journal of pure & applied mathematics · 2025Article
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Authors and funding
3 authors.
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Abstract
Recently, topological data analysis has become a trending topic in data science and engineering. However, the key technique of topological data analysis, i.e., persistent homology, is defined on point cloud data, which does not work directly for data on manifolds. Although earlier evolutionary de Rham-Hodge theory deals with data on manifolds, it is inconvenient for machine learning applications because of the numerical inconsistency caused by remeshing the involving manifolds in the Lagrangian representation. In this work, we introduced persistent de Rham-Hodge Laplacian, or persistent Hodge Laplacian (PHL), as an abbreviation for manifold topological learning. Our PHLs were constructed in the Eulerian representation via structure-persevering Cartesian grids, avoiding the numerical inconsistency over the multi-scale manifolds. To facilitate the manifold topological learning, we proposed a persistent Hodge Laplacian learning algorithm for data on manifolds or volumetric data. As a proof-of-principle application of the proposed manifold topological learning model, we considered the prediction of protein-ligand binding affinities with two benchmark datasets. Our numerical experiments highlighted the power and promise of the proposed method.
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