Generalized ordered Wasserstein distance for sequential data

Tung Doan, Hiep To, Thi Hong Vuong, Muriel Visani, Atsuhiro Takasu, Khoat Than

Abstract: Many practical tasks often require computation of similarity or distance between two sequences. Existing distance measures for sequential data typically align the two sequences, using the differences between the elements in the two sequences. However, such alignments are often not generalized enough to accommodate complex relationships between two sequences. In this article, we propose a novel distance, called Generalized Ordered Wasserstein (GOW), which uses a weighted combination of basis functions to capture both linear and nonlinear relationships between the two sequences. We analyze several properties of the proposed distance and show that GOW generalizes some existing distances and more expressive. Particularly, GOW enables automatic and adaptive selection of the basis functions, which is really beneficial to practical applications. Extensive experiments on widely available public datasets validate effectiveness and show superior performance of GOW over several existing distances. Our code is available at https://github.com/TungDP/GOW.

External IDs:dblp:journals/pr/DoanTVVTT26