Original title: Knot data analysis using multiscale Gauss link integral
Authors: Li Shen, Hongsong Feng, Fengling Li, Fengchun Lei, Jie Wu, Guo-Wei Wei
Discovering a New Path for Knots: The Power of Multiscale Gauss Link Integrals in Data Analysis
Over the years, a potent technique called topological data analysis (TDA) has revolutionized data science. At its core lies persistent homology, tracking key properties in datasets via algebraic topology. Despite the prominence of knot theory in math, its practical use is hindered by localization and quantization limitations.
In response, a breakthrough emerges: knot data analysis (KDA). By melding curve segmentation and multiscale analysis into the Gauss link integral, the innovative multiscale Gauss link integral (mGLI) emerges. It not only grasps the overall topological makeup of knots but also delves into local structures and connections at multiple scales.
This pioneering mGLI surpasses existing methods, notably enhancing protein flexibility analysis, outshining earlier persistent homology-based approaches. The fusion of artificial intelligence (AI) and KDA extends its applicability beyond knots to various curve-like datasets, opening new avenues in data exploration.
Original article: https://arxiv.org/abs/2311.12834