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

TL;DR

This paper introduces Quasi Zigzag Persistent Homology, a novel topological method that captures dynamic features in time-varying data, improving analysis and machine learning performance.

Contribution

It combines multiparameter and zigzag persistence into a new framework with an efficient algorithm for analyzing evolving datasets.

Findings

Enhances machine learning models for sleep-stage detection.

Provides a stable topological invariant for dynamic data.

Demonstrates effectiveness in capturing evolving patterns.

Abstract

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.