TTS-Norm: Forecasting Tensor Time Series via Multi-Way Normalization

Tensor time series (TTS) data, a generalization of one-dimensional time series on a high-dimensional space, is ubiquitous in real-world applications. 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. However, properly coping with the TTS is a much more challenging task, due to its high-dimensional and complex inner structure. In this article, we start by revealing the structure of TTS data from afn statistical view of point. Then, in line with this analysis, we perform Tensor Time Series forecasting via a proposed Multi-way Normalization (TTS-Norm), which effectively disentangles multiple heterogeneous low-dimensional substructures from the original high-dimensional structure. Finally, we design a novel objective function for TTS forecasting, accounting for the numerical heterogeneity among different low-dimensional subspaces of TTS. Extensive experiments on two real-world datasets verify the superior performance of our proposed model.¹