Quasi Zigzag Persistence - A Topological Framework for Analyzing Time-Varying Data

Explore a mathematical framework for analyzing time-varying data through Quasi Zigzag Persistent Homology (QZPH) in this 50-minute conference talk. Learn how this innovative approach integrates multiparameter persistence and zigzag persistence to create a stable topological invariant that captures both static and dynamic features across different scales. Discover the efficient algorithm developed to compute this invariant and examine its practical applications in machine learning tasks, particularly in sleep-stage detection where it demonstrates effectiveness in capturing evolving patterns within time-varying datasets. Gain insights into how topological data analysis can be applied to understand complex temporal structures and enhance predictive models for dynamic systems.