Unraveling Spatial-Temporal and Out-of-Distribution Patterns for Multivariate Time Series Classification

Time series in the real world exhibit complexity due to their diverse features and temporal patterns evolving over time. The evolving nature represents a multidimensional temporal out-of-distribution (MT-OOD) phenomenon. Nevertheless, the majority of current research fail to account for the MT-OOD phenomenon. Although particular methods (i.e, DIVERSIFY) acknowledge the OOD phenomenon, they merely address the single temporal dimension OOD. To tackle the intricate and demanding MT-OOD, we propose a novel method by leveraging Spatial-Temporal dynamics and Out-of-distribution Patterns, named STOP, to unravel the complex interplay of spatial and temporal factors to discern patterns that lie beyond conventional distributions. By converting each variable of a multivariate time series into a subgraph and fusing these subgraphs, STOP is able to capture both the inter-correlations within each variable and intra-correlations across different variables. To model the MT-OOD property, we further extract out-of-distribution patterns from the spatial-temporal subgraphs, which are then seamlessly integrated into the constructed graph that fortifies the framework for more resilient classification outcomes. Extensive experiments on real-world datasets validates the effectiveness of STOP, asserting its superiority in multivariate time series classification.