  This paper contributes multivariate versions of seven commonly used elastic
similarity and distance measures for time series data analytics. Elastic
similarity and distance measures are a class of similarity measures that 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.
