3 papers
math.HO2025
Topological Data Analysis and Topological Deep Learning Beyond Persistent Homology -- A Review
Zhe Su, Xiang Liu, Layal Bou Hamdan +4
Topological data analysis (TDA) is a rapidly evolving field in applied mathematics and data science that leverages tools from topology to uncover robust, shape-driven insights in c…
math.GT2024
Multiscale Jones Polynomial and Persistent Jones Polynomial for Knot Data Analysis
Ruzhi Song, Fengling Li, Jie Wu +2
Many structures in science, engineering, and art can be viewed as curves in 3-space. The entanglement of these curves plays a crucial role in determining the functionality and phys…
math.GT2023
Knot data analysis using multiscale Gauss link integral
Li Shen, Hongsong Feng, Fengling Li +3
In the past decade, topological data analysis (TDA) has emerged as a powerful approach in data science. The main technique in TDA is persistent homology, which tracks topological i…