2025/05/15 by Simon Schindler, Schindler, Simon, Saverio Messineo +6
Computer Science · Engineering · #Algebraic Topology (math.AT) #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Machine Learning (stat.ML) #Signal Processing (eess.SP) #Slime Mold and Myxomycetes Research #Time Series Analysis and Forecasting #Topological and Geometric Data Analysis #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2505.10004
openalex publication_date 2025/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Many multi-variate time series obtained in the natural sciences and engineering possess a repetitive behavior, as for instance state-space trajectories of industrial machines in discrete automation. Recovering the times of recurrence from such a multi-variate time series is of a fundamental importance for many monitoring and control tasks. For a periodic time series this is equivalent to determining its period length. In this work we present a persistent homology framework to estimate recurrence times in multi-variate time series with different generalizations of cyclic behavior (periodic, repetitive, and recurring). To this end, we provide three specialized methods within our framework that are provably stable and validate them using real-world data, including a new benchmark dataset from an injection molding machine.