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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| Vydané v: | Expert systems with applications Ročník 299; s. 130104 |
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01.03.2026
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| ISSN: | 0957-4174 |
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| Abstract | 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. |
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| AbstractList | 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. |
| ArticleNumber | 130104 |
| Author | Wang, Haoning Zhang, Liping |
| Author_xml | – sequence: 1 givenname: Haoning orcidid: 0009-0002-0695-7527 surname: Wang fullname: Wang, Haoning email: whn22@mails.tsinghua.edu.cn – sequence: 2 givenname: Liping orcidid: 0000-0002-3839-9470 surname: Zhang fullname: Zhang, Liping email: lipingzhang@tsinghua.edu.cn |
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| Cites_doi | 10.1016/j.laa.2010.09.020 10.1016/j.ijforecast.2008.08.004 10.1016/j.cam.2023.115331 10.1016/j.engappai.2022.105452 10.1002/nla.2179 10.1016/j.ijforecast.2019.07.001 10.1007/s11045-013-0269-9 10.1109/TCYB.2021.3108847 10.1007/s10915-023-02411-2 10.1016/j.jeconom.2023.105544 10.1109/TPAMI.2019.2891760 10.1109/TIP.2017.2762595 10.1016/j.laa.2024.04.015 10.1137/07070111X 10.1109/TCSVT.2019.2901311 10.1109/TSP.2013.2269046 10.1109/TSP.2016.2639466 10.1090/mcom/4025 10.1109/TCYB.2019.2910151 10.1109/TCYB.2018.2832085 |
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| Keywords | Autoregression Tensor singular value decomposition Tensor time series forecasting Alternating minimization algorithm |
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| SubjectTerms | Alternating minimization algorithm Autoregression Tensor singular value decomposition Tensor time series forecasting |
| Title | High-dimensional low-rank three-way tensor autoregressive time series predictor |
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