High-Order Temporal Correlation Model Learning for Time-Series Prediction

Abstract

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.

A truncated SVD-based ARIMA model for multiple QoS prediction in mobile edge computing

“…However, these methods predict QoS values sequence by sequence, which may lead to high computational costs when predicting a large amount of sequences. Jing et al [20] represented a multiple temporal sequence as a matrix and generalized the AutoRegressive (AR) model by applying it to the temporal sequence matrix. Shi et al [4] proposed a temporal sequence prediction method for short temporal sequences.…”

Demystifying Deep Learning in Predictive Spatiotemporal Analytics: An Information-Theoretic Framework

“…Bahadori et al [16] treated the spatiotemporal data as tensors and proposed a low-rank tensor learning framework for spatiotemporal prediction. Furthermore, the spatial autocorrelation [17], temporal autocorrelation [18], and high-order temporal correlation [19] have been modeled as constraints and integrated into the tensor factorization frameworks for the PSTA task.…”

Block Hankel Tensor ARIMA for Multiple Short Time Series Forecasting

“…Furthermore, we could do long-term forecasting by using prior foretasted values in last steps. Although this way may lead to error accumulation to some degree, it becomes more practical for real-world applications (Jing et al 2018).…”

“…Multiple TS arising from real applications can be reformulated as a matrix or even a high-order tensor (multi-way data) naturally. For example, the spatio-temporal grid of ocean data in meteorology can be shaped as a fourth-order tensor TS, wherein four factors are jointly represented as latitude, longitude, grid points and time (Jing et al 2018). When dealing with tensors, traditional linear TSF models require reshaping TS into vectors.…”

“…Taking this advantage, tensor decomposition-based approaches can handle multiple TS simultaneously and achieve good forecasting performance (Dunlavy, Kolda, and Acar 2011;Li et al 2015;Tan et al 2016;Bhanu et al 2018;Faloutsos et al 2018). For example, Tucker decomposition integrated with AR model was proposed (Jing et al 2018) to obtain the multilinear orthogonality AR (MOAR) model and the multilinear constrained AR model for high-order TSF. Moreover, some works incorporate decomposition with neural networks for more complex tensorial TS Ma et al 2019).…”