NNC: A Nearest Neighbors Constraint-based Metric Learning for Multivariate Time Series Classification

Multivariate time series (MTS) classification has gained significant attention as a prominent research area in recent years. Studies using Mahalanobis distance-based dynamic time warping along with metric learning algorithms have reported significant results. Existing metric learning approaches, such as large margin nearest neighbor, seek to optimize a loss function with two components: one that reduces the distance between samples with the same label and another that increases the distance between samples with different labels. However, these two terms play an opposite role in some situations and it is difficult to explore a way to balance such two competitive terms. In this paper, we introduce a nearest neighbors constraint (NNC) model designed for MTS classification. In NNC, a data-adaptive Mahalanobis distance-based dynamic time warping distance metric is designed to compute the distance between two MTS. To learn the Mahalanobis distance, a concise and effective loss function is developed. Instead of scanning all triplets, NNC only employs the triplets which violate the rule that an MTS's k nearest neighbors should share the same label with it to learn the Mahalanobis distance. Experiments on 9 public MTS datasets demonstrate that the proposed model achieves competitive performance.