Time-series prediction has become a prominent challenge, especially when the data are described as sequences of multiway arrays. Because noise and redundancy may exist in the tensor representation of a time series, we focus on solving the problem of high-order time-series prediction under a tensor decomposition framework and develop two novel multilinear models: 1) the multilinear orthogonal autoregressive (MOAR) model and 2) the multilinear constrained autoregressive (MCAR) model. The MOAR model is designed to preserve as much information as possible from the original tensorial data under orthogonal constraints. The MCAR model is an enhanced version that is developed by replacing orthogonal constraints with an inverse decomposition error term. For both models, we project the original tensor into subspaces spanned by basis matrices to facilitate the discovery of the intrinsic temporal structure embedded in the original tensor. To build connections among consecutive slices of the tensor, we generalize a traditional autoregressive model to tensor form to better preserve the temporal smoothness. Experiments conducted on four publicly available datasets demonstrate that our proposed methods converge within a small number of iterations during the training stage and achieve promising results compared with state-of-the-art methods.

中文翻译：

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用于时间序列预测的高阶时间相关模型学习


时间序列预测已成为一个突出的挑战，特别是当数据被描述为多路数组的序列时。由于时间序列的张量表示中可能存在噪声和冗余，因此我们专注于解决张量分解框架下的高阶时间序列预测问题，并开发了两种新颖的多线性模型：1）多线性正交自回归（MOAR）模型和 2) 多线性约束自回归 (MCAR) 模型。 MOAR 模型旨在在正交约束下保留原始张量数据中尽可能多的信息。 MCAR模型是通过用逆分解误差项代替正交约束而开发的增强版本。对于这两个模型，我们将原始张量投影到由基础矩阵跨越的子空间中，以方便发现嵌入在原始张量中的内在时间结构。为了在张量的连续切片之间建立连接，我们将传统的自回归模型推广为张量形式，以更好地保持时间平滑性。在四个公开可用的数据集上进行的实验表明，我们提出的方法在训练阶段在少量迭代内收敛，并与最先进的方法相比取得了有希望的结果。