Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/309811 
Year of Publication: 
2023
Citation: 
[Journal:] Journal of Global Optimization [ISSN:] 1573-2916 [Volume:] 86 [Issue:] 4 [Publisher:] Springer US [Place:] New York, NY [Year:] 2023 [Pages:] 885-903
Publisher: 
Springer US, New York, NY
Abstract: 
Computing a sample mean of time series under dynamic time warping is NP-hard. Consequently, there is an ongoing research effort to devise efficient heuristics. The majority of heuristics have been developed for the constrained sample mean problem that assumes a solution of predefined length. In contrast, research on the unconstrained sample mean problem is underdeveloped. In this article, we propose a generic average-compress (AC) algorithm to address the unconstrained problem. The algorithm alternates between averaging (A-step) and compression (C-step). The A-step takes an initial guess as input and returns an approximation of a sample mean. Then the C-step reduces the length of the approximate solution. The compressed approximation serves as initial guess of the A-step in the next iteration. The purpose of the C-step is to direct the algorithm to more promising solutions of shorter length. The proposed algorithm is generic in the sense that any averaging and any compression method can be used. Experimental results show that the AC algorithm substantially outperforms current state-of-the-art algorithms for time series averaging.
Subjects: 
Time series averaging
Fréchet function
Heuristic
Nonconvex optimization
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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