  There are now a broad range of time series classification (TSC) algorithms
designed to exploit different representations of the data. These have been
evaluated on a range of problems hosted at the UCR-UEA TSC Archive
(www.timeseriesclassification.com), and there have been extensive comparative
studies. However, our understanding of why one algorithm outperforms another is
still anecdotal at best. This series of experiments is meant to help provide
insights into what sort of discriminatory features in the data lead one set of
algorithms that exploit a particular representation to be better than other
algorithms. We categorise five different feature spaces exploited by TSC
algorithms then design data simulators to generate randomised data from each
representation. We describe what results we expected from each class of
algorithm and data representation, then observe whether these prior beliefs are
supported by the experimental evidence. We provide an open source
implementation of all the simulators to allow for the controlled testing of
hypotheses relating to classifier performance on different data
representations. We identify many surprising results that confounded our
expectations, and use these results to highlight how an over simplified view of
classifier structure can often lead to erroneous prior beliefs. We believe
ensembling can often overcome prior bias, and our results support the belief by
showing that the ensemble approach adopted by the Hierarchical Collective of
Transform based Ensembles (HIVE-COTE) is significantly better than the
alternatives when the data representation is unknown, and is significantly
better than, or not significantly significantly better than, or not
significantly worse than, the best other approach on three out of five of the
individual simulators.
