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

• URL: http://arxiv.org/abs/2502.16049v1
• Date: Sat, 22 Feb 2025 02:53:26 GMT
• Title: Quasi Zigzag Persistence: A Topological Framework for Analyzing Time-Varying Data
• Authors: Tamal K. Dey, Shreyas N. Samaga,
• Abstract summary: We propose Quasi Zigzag Persistent Homology (QZPH) as a framework for analyzing time-varying data.<n>We introduce a stable topological invariant that captures both static and dynamic features at different scales.<n>We show that it enhances the machine learning models when applied to tasks such as sleep-stage detection.
• Score: 0.25322020135765466
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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-evolving datasets.

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