Yuran Jin

Hao Shu, Jicheng Li, Yu Jin et al.

Non-random missing data is a ubiquitous yet undertreated flaw in multidimensional time series, fundamentally threatening the reliability of data-driven analysis and decision-making. Pure low-rank tensor completion, as a classical data recovery method, falls short in handling non-random missingness, both methodologically and theoretically. Hankel-structured tensor completion models provide a feasible approach for recovering multidimensional time series with non-random missing patterns. However, most Hankel-based multidimensional data recovery methods both suffer from unclear sources of Hankel tensor low-rankness and lack an exact recovery theory for non-random missing data. To address these issues, we propose the temporal isometric delay-embedding transform, which constructs a Hankel tensor whose low-rankness is naturally induced by the smoothness and periodicity of the underlying time series. Leveraging this property, we develop the \textit{Low-Rank Tensor Completion with Temporal Isometric Delay-embedding Transform} (LRTC-TIDT) model, which characterizes the low-rank structure under the \textit{Tensor Singular Value Decomposition} (t-SVD) framework. Once the prescribed non-random sampling conditions and mild incoherence assumptions are satisfied, the proposed LRTC-TIDT model achieves exact recovery, as confirmed by simulation experiments under various non-random missing patterns. Furthermore, LRTC-TIDT consistently outperforms existing tensor-based methods across multiple real-world tasks, including network flow reconstruction, urban traffic estimation, and temperature field prediction. Our implementation is publicly available at https://github.com/HaoShu2000/LRTC-TIDT.

Hao Shu, Jicheng Li, Yu Jin et al.

In recent years, the prediction of multidimensional time series data has become increasingly important due to its wide-ranging applications. Tensor-based prediction methods have gained attention for their ability to preserve the inherent structure of such data. However, existing approaches, such as tensor autoregression and tensor decomposition, often have consistently failed to provide clear assertions regarding the number of samples that can be exactly predicted. While matrix-based methods using nuclear norms address this limitation, their reliance on matrices limits accuracy and increases computational costs when handling multidimensional data. To overcome these challenges, we reformulate multidimensional time series prediction as a deterministic tensor completion problem and propose a novel theoretical framework. Specifically, we develop a deterministic tensor completion theory and introduce the Temporal Convolutional Tensor Nuclear Norm (TCTNN) model. By convolving the multidimensional time series along the temporal dimension and applying the tensor nuclear norm, our approach identifies the maximum forecast horizon for exact predictions. Additionally, TCTNN achieves superior performance in prediction accuracy and computational efficiency compared to existing methods across diverse real-world datasets, including climate temperature, network flow, and traffic ride data. Our implementation is publicly available at https://github.com/HaoShu2000/TCTNN.