  Time series clustering is the act of grouping time series data without
recourse to a label. Algorithms that cluster time series can be classified into
two groups: those that employ a time series specific distance measure; and
those that derive features from time series. Both approaches usually rely on
traditional clustering algorithms such as $k$-means. Our focus is on distance
based time series that employ elastic distance measures, i.e. distances that
perform some kind of realignment whilst measuring distance. We describe nine
commonly used elastic distance measures and compare their performance with
k-means and k-medoids clustering. Our findings are surprising. The most popular
technique, dynamic time warping (DTW), performs worse than Euclidean distance
with k-means, and even when tuned, is no better. Using k-medoids rather than
k-means improved the clusterings for all nine distance measures. DTW is not
significantly better than Euclidean distance with k-medoids. Generally,
distance measures that employ editing in conjunction with warping perform
better, and one distance measure, the move-split-merge (MSM) method, is the
best performing measure of this study. We also compare to clustering with DTW
using barycentre averaging (DBA). We find that DBA does improve DTW k-means,
but that the standard DBA is still worse than using MSM. Our conclusion is to
recommend MSM with k-medoids as the benchmark algorithm for clustering time
series with elastic distance measures. We provide implementations in the aeon
toolkit, results and guidance on reproducing results on the associated GitHub
repository.
