提出新型拓扑框架，捕捉时序数据的动态变化模式。
Quasi Zigzag Persistence: A Topological Framework for Analyzing Time-Varying Data
- 融合多参数与交错持久性，构建稳定拓扑不变量
- 在睡眠阶段识别任务中提升机器学习性能
- 适合研究随时间演变的数据结构与模式
本文提出准交错持久同调（QZPH）框架，通过整合多参数持久性和交错持久性，分析时序数据。我们引入一个稳定的拓扑不变量，可同时捕捉静态与动态特征在不同尺度下的表现。设计了高效算法用于计算该不变量。实验表明，将其应用于睡眠阶段检测等任务时，显著提升了机器学习模型性能，验证了其在捕捉时序数据演化模式方面的有效性。
原文摘要 · Abstract (English)
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.
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