Auto-weighted Sequential Wasserstein Distance and Application to Sequence Matching

Sequence matching problems have been central to the field of data analysis for decades. Such problems arise in widely diverse areas including computer vision, speech processing, bioinformatics, and natural language processing. However, solving such problems efficiently is difficult because one must consider temporal consistency, neighborhood structure similarity, robustness to noise and outliers, and flexibility on start-end matching points. This paper presents a proposal of a shape-aware Wasserstein distance between sequences building upon optimal transport (OT) framework. The proposed distance considers similarity measures of the elements, their neighborhood structures, and temporal positions. We incorporate these similarity measures into three ground cost matrixes of the OT formulation. The noteworthy contribution is that we formulate these measures as independent OT distances with a single shared optimal transport matrix, and adjust those weights automatically according to their effects on the total OT distance. Numerical evaluations suggest that the sequence matching method using our proposed Wasserstein distance robustly outperforms state-of-the-art methods across different real-world datasets.