Exploring and visualizing temporal relations in multivariate time series

This paper introduces an approach to analyzing multivariate time series (MVTS) data through progressive temporal abstraction of the data into patterns characterizing the behavior of the studied dynamic phenomenon. The paper focuses on two core challenges: identifying basic behavior patterns of individual attributes and examining the temporal relations between these patterns across the range of attributes to derive higher-level abstractions of multi-attribute behavior. The proposed approach combines existing methods for univariate pattern extraction, computation of temporal relations according to the Allen's time interval algebra, visual displays of the temporal relations, and interactive query operations into a cohesive visual analytics workflow. The paper describes the application of the approach to real-world examples of population mobility data during the COVID-19 pandemic and characteristics of episodes in a football match, illustrating its versatility and effectiveness in understanding composite patterns of interrelated attribute behaviors in MVTS data. (c) 2023 The Authors. Published by Elsevier B.V. on behalf of Zhejiang University and Zhejiang University Press Co. Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).