ArticleProceedings of the National Academy of Sciences of the United States of America2024
Knot data analysis using multiscale Gauss link integral.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2024. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 12 papers.
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Who cites it
12 citing papers in PubMed.
- Topology-Aware Deep Learning on Higher-Order Structures for Drug Response Prediction.Advanced science (Weinheim, Baden-Wurttemberg, Germany) · 2026Article
- Topological deep learning for drug-target interaction, virtual screening, and docking scoring: a practical, benchmark-driven review.Briefings in bioinformatics · 2026Review
- Manifold topological deep learning for biomedical data.Nature communications · 2026Article
- Topological metrics as evolutionary and dynamical descriptors of conformational landscapes within protein families.PLoS computational biology · 2026Article
- Topological data analysis and topological deep learning beyond persistent homology: a review.Artificial intelligence review · 2026Article
- A Review of Topological Data Analysis and Topological Deep Learning in Molecular Sciences.Journal of chemical information and modeling · 2025Review
- Khovanov Laplacian and Khovanov Dirac for knots and links.Journal of physics. Complexity · 2025Article
- A review of machine learning methods for imbalanced data challenges in chemistry.Chemical science · 2025Review
- Manifold Topological Deep Learning for Biomedical Data.Research square · 2025Article
- Multi-scale Jones polynomial and persistent Jones polynomial for knot data analysis.AIMS mathematics · 2025Article
- Evolutionary Khovanov homology.AIMS mathematics · 2024Article
- Persistent de Rham-Hodge Laplacians in Eulerian representation for manifold topological learning.AIMS mathematics · 2024Article
Corrections and comments
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Authors and funding
6 authors.
Funding
Abstract
In the past decade, topological data analysis has emerged as a powerful algebraic topology approach in data science. Although knot theory and related subjects are a focus of study in mathematics, their success in practical applications is quite limited due to the lack of localization and quantization. We address these challenges by introducing knot data analysis (KDA), a paradigm that incorporates curve segmentation and multiscale analysis into the Gauss link integral. The resulting multiscale Gauss link integral (mGLI) recovers the global topological properties of knots and links at an appropriate scale and offers a multiscale geometric topology approach to capture the local structures and connectivities in data. By integration with machine learning or deep learning, the proposed mGLI significantly outperforms other state-of-the-art methods across various benchmark problems in 13 intricately complex biological datasets, including protein flexibility analysis, protein-ligand interactions, human Ether-à-go-go-Related Gene potassium channel blockade screening, and quantitative toxicity assessment. Our KDA opens a research area-knot deep learning-in data science.
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