  Elastic similarity measures are a class of similarity measures specifically
designed to work with time series data. When scoring the similarity between two
time series, they allow points that do not correspond in timestamps to be
aligned. This can compensate for misalignments in the time axis of time series
data, and for similar processes that proceed at variable and differing paces.
Elastic similarity measures are widely used in machine learning tasks such as
classification, clustering and outlier detection when using time series data.
  There is a multitude of research on various univariate elastic similarity
measures. However, except for multivariate versions of the well known Dynamic
Time Warping (DTW) there is a lack of work to generalise other similarity
measures for multivariate cases. This paper adapts two existing strategies used
in multivariate DTW, namely, Independent and Dependent DTW, to several commonly
used elastic similarity measures.
  Using 23 datasets from the University of East Anglia (UEA) multivariate
archive, for nearest neighbour classification, we demonstrate that each measure
outperforms all others on at least one dataset and that there are datasets for
which either the dependent versions of all measures are more accurate than
their independent counterparts or vice versa. This latter finding suggests that
these differences arise from a fundamental property of the data. We also show
that an ensemble of such nearest neighbour classifiers is highly competitive
with other state-of-the-art multivariate time series classifiers.
