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（TTS）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，尤其是涉及多源时空数据的监测系统（如交通需求与空气污染物）。相较于近年来备受关注并取得显著进展的时间序列或多变量时间序列建模，张量时间序列的研究尚显不足。由于张量时间序列具有高维且复杂的内部结构，对其进行恰当处理是一项更具挑战性的任务。本文提出了一种新颖的TTS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TTS数据集上的实验结果表明，我们的方法相较于最先进的基线模型具有优越性。代码与数据已发布至https://github.com/beginner-sketch/GMRL。