  Dynamic time warping (DTW) is an effective dissimilarity measure in many time
series applications. Despite its popularity, it is prone to noises and
outliers, which leads to singularity problem and bias in the measurement. The
time complexity of DTW is quadratic to the length of time series, making it
inapplicable in real-time applications. In this paper, we propose a novel time
series dissimilarity measure named RobustDTW to reduce the effects of noises
and outliers. Specifically, the RobustDTW estimates the trend and optimizes the
time warp in an alternating manner by utilizing our designed temporal graph
trend filtering. To improve efficiency, we propose a multi-level framework that
estimates the trend and the warp function at a lower resolution, and then
repeatedly refines them at a higher resolution. Based on the proposed
RobustDTW, we further extend it to periodicity detection and outlier time
series detection. Experiments on real-world datasets demonstrate the superior
performance of RobustDTW compared to DTW variants in both outlier time series
detection and periodicity detection.
