Temporal Tensor Factorization: A Framework for Low-Rank Multilinear Time Series Forecasting

In the era of big data, there are increasing demands to forecast incomplete, sparse, and nonstationary data. The current research aims to solve these problems for multilinear time series through a combination of tensor autoregression and low-rank tensor factorization. We propose an expansion of TMF to second-order data: temporal tensor factorization (TTF). The current research aims to interpolate missing values via low-rank tensor factorization, which produces a latent time series. We perform forecasting in the latent space with a transform-based tensor autoregression (<tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{L}$</tex> -TAR) process. We present experimental results of the proposed method with other state-of-the-art methods on the benchmark datasets which include video imaging, dynamic networks, and energy usage.