Order-Preserving Metric Learning for Mining Multivariate Time Series

Multivariate time series (MTS) analysis is an increasingly popular research topic in recent years due to the vast amount of MTS data that are being generated in numerous fields such as genomics research, health informatics, finance and abnormal detection. The particularity of the data makes it a challenging task, e.g., missing data, different sampling frequencies, and random noise. Moreover, each instance depends not only on its past values but also has some dependency on other instances, and there exist discriminatory order-dependent characteristics. To address these challenges, in this paper, we introduce an order-preserving metric learning framework for multivariate time series prediction. Specifically, we adopt quadruplet-wise constraints which can encompass pair-wise and triplet-wise constraints to model similarity from complex label relations. To preserve the inherent temporal relationships of the instances in MTS, order-preserving Wasserstein distance is integrated to the framework to measure dissimilarity between MTS data, where the inverse difference moment regularization enforces flow-network with local homogeneous structures and the KL-divergence with a prior distribution regularization prevents flow-network between instances with faraway temporal locations. Besides the regularizations on flow-network, the ground measurement of the Wasserstein distance is replaced by Mahalanobis distance to increase its discrimination capability. An alternating iteration strategy is proposed to jointly optimize the Mahalanobis distance matrix in the ground measurement and the flow-network of Wasserstein distance. Extensive experiments on real-world clinical data from critical care are provided to demonstrate the effectiveness of the proposed method on sepsis prediction task.