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Knot data analysis using multiscale Gauss link integral

组织者

瓦西里·戈尔布诺夫 , Taras Panov , 尼古拉·莱舍提金 , 吴杰 , 邬荣领 , 杨卓科

演讲者

Fengling Li

时间

2025年04月14日 20:00 至 21:00

地点

A6-101

线上

Zoom 468 248 1222 (BIMSA)

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-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. This is a joint work with Li Shen, Hongsong Feng, Fengchun Lei, Jie Wu and Guo-Wei Wei.