  Recent advances in time series classification have largely focused on methods
that either employ deep learning or utilize other machine learning models for
feature extraction. Though successful, their power often comes at the
requirement of computational complexity. In this paper, we introduce GeoStat
representations for time series. GeoStat representations are based off of a
generalization of recent methods for trajectory classification, and summarize
the information of a time series in terms of comprehensive statistics of
(possibly windowed) distributions of easy to compute differential geometric
quantities, requiring no dynamic time warping. The features used are intuitive
and require minimal parameter tuning. We perform an exhaustive evaluation of
GeoStat on a number of real datasets, showing that simple KNN and SVM
classifiers trained on these representations exhibit surprising performance
relative to modern single model methods requiring significant computational
power, achieving state of the art results in many cases. In particular, we show
that this methodology achieves good performance on a challenging dataset
involving the classification of fishing vessels, where our methods achieve good
performance relative to the state of the art despite only having access to
approximately two percent of the dataset used in training and evaluating this
state of the art.
