Knot data analysis using multiscale Gauss link integral

• 成果类型: Article
• 署名作者: Then, Li; Feng, Hongsong; Li, Fengling; Lei, Fengchun; Wu, Jie; Wei, Guo-Wei
• 署名单位: Michigan State University; Dalian University of Technology; Michigan State University; Michigan State University
• 刊物名称: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
• ISSN/ISSBN: 0027-11333
• DOI: 10.1073/pnas.2408431121
• 发表日期: 2024-10-15
• 关键词: normal-mode analysis; network model; prediction; collection

摘要

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-& agrave;-go-go-Related Gene potassium channel blockade screening, and quantitative toxicity assessment. Our KDA opens a research area-knot deep learning-in data science.