Beijing Institute of Mathematical Sciences and Applications

Vassily Gorbounov , Taras Panov , Nicolai Reshetikhin , Jie Wu , Rong Ling Wu , Zhuo Ke Yang

Fengling Li

Monday, April 14, 2025 8:00 PM - 9:00 PM

A6-101

Zoom 468 248 1222 (BIMSA)

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.