Tensor time series (TTS) data, a generalization of one-dimensional time series on a high-dimensional space, is ubiquitous in real-world scenarios, especially in monitoring systems involving multi-source spatio-temporal data (e.g., transportation demands and air pollutants). Compared to modeling time series or multivariate time series, which has received much attention and achieved tremendous progress in recent years, tensor time series has been paid less effort. Properly coping with the tensor time series is a much more challenging task, due to its high-dimensional and complex inner structure. In this paper, we develop a novel TTS forecasting framework, which seeks to individually model each heterogeneity component implied in the time, the location, and the source variables. We name this framework as GMRL, short for Gaussian Mixture Representation Learning. Experiment results on two real-world TTS datasets verify the superiority of our approach compared with the state-of-the-art baselines. Code and data are published on https://github.com/beginner-sketch/GMRL.

翻译：张量时间序列数据是一维时间序列在高维空间上的推广，在现实场景中普遍存在，尤其涉及多源时空数据（如交通需求和空气污染物）的监测系统中。与近年来备受关注且取得巨大进展的时间序列或多变量时间序列建模相比，张量时间序列的研究相对较少。由于张量时间序列具有高维和复杂的内在结构，正确处理该数据是一项更具挑战性的任务。本文提出了一种新颖的张量时间序列预测框架，旨在分别对时间、位置和源变量中隐含的每个异质性成分进行独立建模。我们将该框架命名为GMRL，即高斯混合表示学习（Gaussian Mixture Representation Learning）的缩写。在两个真实世界张量时间序列数据集上的实验结果表明，与最先进的基线方法相比，我们的方法具有优越性。相关代码和数据已发布于https://github.com/beginner-sketch/GMRL。