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Time Series Decomposition Using the Fréchet Distance

Authors Anne Driemel , Jan Höckendorff , Ioannis Psarros , Christian Sohler

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LIPIcs.ESA.2026.96.pdf
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ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Time Series Analysis
  • Fréchet Distance
  • Approximation Algorithms

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Abstract

In this paper, we introduce a new data analysis problem that aims to decompose a set of univariate time series into a small set of k base curves of length at most l such that the sum of Fréchet distances of the time series to a "Fréchet combination" of the base curves is minimized. Here, a Fréchet combination allows to combine individually scaled base curves using a k-dimensional traversal. We call the problem of finding a set of optimal base curves the Fréchet decomposition problem and we consider two variants: (a) the base curves can be arbitrary curves of bounded length and (b) the curves come from a given finite set of candidate curves. We think of the Fréchet decomposition problem as a Fréchet variant of principal component analysis. For the case of a single base curve we develop a (1+ε)-approximation algorithm for the Fréchet decomposition problem. Additionally we give an exact algorithm for the projection distance problem that asks to compute the distance of one given time series to a given set of k base curves. This allows us to design an exact algorithm for the Fréchet decomposition problem for general k when curves come from a fixed candidate set.

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Anne Driemel, Jan Höckendorff, Ioannis Psarros, and Christian Sohler. Time Series Decomposition Using the Fréchet Distance. In 34th Annual European Symposium on Algorithms (ESA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 388, pp. 96:1-96:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ESA.2026.96

Author Details

Anne Driemel
  • University of Bonn, Germany
Jan Höckendorff
  • University of Cologne, Germany
Ioannis Psarros
  • Archimedes, Athena Research Center, Greece
Christian Sohler
  • University of Cologne, Germany

Funding

  • Driemel, Anne: Affiliated with Lamarr Institute for Machine Learning and Artificial Intelligence; Supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project Number 459420781.
  • Höckendorff, Jan: Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project Number 459420781.
  • Psarros, Ioannis: This work has been partially supported by project MIS 5154714 of the National Recovery and Resilience Plan Greece 2.0 funded by the European Union under the NextGenerationEU Program.
  • Sohler, Christian: Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project Number 459420781.

Supplementary Materials

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