Extremal event graphs: A (stable) tool for analyzing noisy time series data

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Date

2023-01

Journal Title

Journal ISSN

Volume Title

Publisher

American Institute of Mathematical Sciences

Abstract

Local maxima and minima, or extremal events, in experimental time series can be used as a coarse summary to characterize data. However, the discrete sampling in recording experimental measurements suggests uncertainty on the true timing of extrema during the experiment. This in turn gives uncertainty in the timing order of extrema within the time series. Motivated by applications in genomic time series and biological network analysis, we construct a weighted directed acyclic graph (DAG) called an extremal event DAG using techniques from persistent homology that is robust to measurement noise. Furthermore, we define a distance between extremal event DAGs based on the edit distance between strings. We prove several properties including local stability for the extremal event DAG distance with respect to pairwise distances between functions in the time series data. Lastly, we provide algorithms, publicly free software, and implementations on extremal event DAG construction and comparison.

Description

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Foundations of Data Science following peer review. The definitive publisher-authenticated version [Extremal event graphs: A (stable) tool for analyzing noisy time series data. Foundations of Data Science 5, 1 p81-151 (2023)] is available online at: https://doi.org/10.3934/fods.2022019

Keywords

time series, topological data analysis, stability, directed graphs, biological networks

Citation

Robin Belton, Bree Cummins, Tomáš Gedeon, Brittany Terese Fasy. Extremal event graphs: A (stable) tool for analyzing noisy time series data. Foundations of Data Science, 2023, 5(1): 81-151. doi: 10.3934/fods.2022019
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