Partial ordered Wasserstein distance for sequential data

Measuring the distance between data sequences is a challenging problem, especially in the presence of outliers and local distortions. Existing measures typically align the two sequences before calculating their distance based on the difference between the corresponding elements. However, those alignments are not flexible enough to accommodate local distortions and severe effects of outliers. In this article, we propose a novel distance, termed as Partial Ordered Wasserstein (POW), which is flexible to align two sequences and robust w.r.t outliers. We further analyze some properties of the proposed distance, and show that POW enables a simple way to automatically and adaptively select the amount of transported mass, so as to accommodate outliers. Two different applications of POW are then studied: time -series classification and multi -step localization. Finally, we conduct extensive experiments on widely available public datasets to evaluate the performance of the proposed distances. Experimental results, obtained via a thorough experimental protocol, show the performance superiority of POW over several existing distance measures. Our Python source code is available on https://github.com/TungDP/Partial-Ordered-Wasserstein-Distance