  Research into the classification of time series has made enormous progress in
the last decade. The UCR time series archive has played a significant role in
challenging and guiding the development of new learners for time series
classification. The largest dataset in the UCR archive holds 10 thousand time
series only; which may explain why the primary research focus has been in
creating algorithms that have high accuracy on relatively small datasets.
  This paper introduces Proximity Forest, an algorithm that learns accurate
models from datasets with millions of time series, and classifies a time series
in milliseconds. The models are ensembles of highly randomized Proximity Trees.
Whereas conventional decision trees branch on attribute values (and usually
perform poorly on time series), Proximity Trees branch on the proximity of time
series to one exemplar time series or another; allowing us to leverage the
decades of work into developing relevant measures for time series. Proximity
Forest gains both efficiency and accuracy by stochastic selection of both
exemplars and similarity measures.
  Our work is motivated by recent time series applications that provide orders
of magnitude more time series than the UCR benchmarks. Our experiments
demonstrate that Proximity Forest is highly competitive on the UCR archive: it
ranks among the most accurate classifiers while being significantly faster. We
demonstrate on a 1M time series Earth observation dataset that Proximity Forest
retains this accuracy on datasets that are many orders of magnitude greater
than those in the UCR repository, while learning its models at least 100,000
times faster than current state of the art models Elastic Ensemble and COTE.
