Quasi Zigzag Persistence: A Topological Framework for Analyzing Time-Varying Data
This addresses the problem of analyzing evolving patterns in time-varying datasets for applications such as sleep-stage detection, representing an incremental advancement by combining existing topological methods.
The paper tackles the analysis of time-varying data by proposing Quasi Zigzag Persistent Homology (QZPH), a framework that integrates multiparameter and zigzag persistence to capture static and dynamic features, and demonstrates its effectiveness in enhancing machine learning models for tasks like sleep-stage detection.
In this paper, we propose Quasi Zigzag Persistent Homology (QZPH) as a framework for analyzing time-varying data by integrating multiparameter persistence and zigzag persistence. To this end, we introduce a stable topological invariant that captures both static and dynamic features at different scales. We present an algorithm to compute this invariant efficiently. We show that it enhances the machine learning models when applied to tasks such as sleep-stage detection, demonstrating its effectiveness in capturing the evolving patterns in time-varying datasets.