High-dimensional low-rank three-way tensor autoregressive time series predictor

Recently, tensor time-series forecasting has gained increasing attention, whose core requirement is how to perform dimensionality reduction. In this paper, we establish a least square optimization model by combining tensor singular value decomposition (t-SVD) with autoregression (AR) to forecast thi...

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Vydáno v:Expert systems with applications Ročník 299; s. 130104
Hlavní autoři: Wang, Haoning, Zhang, Liping
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Ltd 01.03.2026
Témata:
Alternating minimization algorithm
Autoregression
Tensor singular value decomposition
Tensor time series forecasting
Autoregression
Tensor singular value decomposition
Tensor time series forecasting
Alternating minimization algorithm
ISSN:0957-4174
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Shrnutí:Recently, tensor time-series forecasting has gained increasing attention, whose core requirement is how to perform dimensionality reduction. In this paper, we establish a least square optimization model by combining tensor singular value decomposition (t-SVD) with autoregression (AR) to forecast third-order tensor time-series, which has great benefit in computational complexity and dimensionality reduction. We divide such an optimization problem using fast Fourier transformation and t-SVD into four decoupled subproblems, whose variables include regressive coefficient, f-diagonal tensor, left and right orthogonal tensors, and propose an efficient forecasting algorithm via alternating minimization strategy, called Low-rank Tensor Autoregressive Predictor (LOTAP), in which each subproblem has a closed-form solution. Numerical experiments indicate that, compared to Tucker-decomposition-based algorithms, LOTAP achieves a speed improvement ranging from 2 to 6 times while maintaining accurate forecasting performance in all four baseline tasks. In addition, this algorithm is applicable to a wider range of tensor forecasting tasks because of its more effective dimensionality reduction ability.
ISSN:0957-4174
DOI:10.1016/j.eswa.2025.130104