Elastic similarity and distance measures for multivariate time series

Ahmed Shifaz, Charlotte Pelletier, François Petitjean, Geoffrey I. Webb

Research output: Contribution to journalArticleResearchpeer-review

8 Citations (Scopus)


This paper contributes multivariate versions of seven commonly used elastic similarity and distance measures for time series data analytics. Elastic similarity and distance measures can compensate for misalignments in the time axis of time series data. We adapt two existing strategies used in a multivariate version of the well-known Dynamic Time Warping (DTW), namely, Independent and Dependent DTW, to these seven measures. While these measures can be applied to various time series analysis tasks, we demonstrate their utility on multivariate time series classification using the nearest neighbor classifier. On 23 well-known datasets, we demonstrate that each of the measures but one achieves the highest accuracy relative to others on at least one dataset, supporting the value of developing a suite of multivariate similarity and distance measures. We also demonstrate that there are datasets for which either the dependent versions of all measures are more accurate than their independent counterparts or vice versa. In addition, we also construct a nearest neighbor-based ensemble of the measures and show that it is competitive to other state-of-the-art single-strategy multivariate time series classifiers.

Original languageEnglish
Pages (from-to)2665–2698
Number of pages34
JournalKnowledge and Information Systems
Publication statusPublished - Jun 2023


  • Dependent measures
  • Dynamic time warping
  • Elastic distance measures
  • Elastic similarity measures
  • Independent measures
  • Multivariate similarity measures
  • Multivariate time series
  • Multivariate time series classification

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