  Measuring similarities between unlabeled time series trajectories is an
important problem in domains as diverse as medicine, astronomy, finance, and
computer vision. It is often unclear what is the appropriate metric to use
because of the complex nature of noise in the trajectories (e.g. different
sampling rates or outliers). Domain experts typically hand-craft or manually
select a specific metric, such as dynamic time warping (DTW), to apply on their
data. In this paper, we propose Autowarp, an end-to-end algorithm that
optimizes and learns a good metric given unlabeled trajectories. We define a
flexible and differentiable family of warping metrics, which encompasses common
metrics such as DTW, Euclidean, and edit distance. Autowarp then leverages the
representation power of sequence autoencoders to optimize for a member of this
warping distance family. The output is a metric which is easy to interpret and
can be robustly learned from relatively few trajectories. In systematic
experiments across different domains, we show that Autowarp often outperforms
hand-crafted trajectory similarity metrics.
