Multivariate time series forecasting poses an ongoing challenge across various disciplines. Time series data often exhibit diverse intra-series and inter-series correlations, contributing to intricate and interwoven dependencies that have been the focus of numerous studies. Nevertheless, a significant research gap remains in comprehending the varying inter-series correlations across different time scales among multiple time series, an area that has received limited attention in the literature. To bridge this gap, this paper introduces MSGNet, an advanced deep learning model designed to capture the varying inter-series correlations across multiple time scales using frequency domain analysis and adaptive graph convolution. By leveraging frequency domain analysis, MSGNet effectively extracts salient periodic patterns and decomposes the time series into distinct time scales. The model incorporates a self-attention mechanism to capture intra-series dependencies, while introducing an adaptive mixhop graph convolution layer to autonomously learn diverse inter-series correlations within each time scale. Extensive experiments are conducted on several real-world datasets to showcase the effectiveness of MSGNet. Furthermore, MSGNet possesses the ability to automatically learn explainable multi-scale inter-series correlations, exhibiting strong generalization capabilities even when applied to out-of-distribution samples.

The problem of recovering data in multi-way arrays (i.e., tensors) arises in many fields such as image processing and computer vision, etc. In this paper, we present a novel method based on multi-linear n-rank and ℓ0norm optimization for recovering a low-n-rank tensor with an unknown fraction of its elements being arbitrarily corrupted. In the new method, the n-rank and ℓ0norm of the each mode of the given tensor are combined by weighted parameters as the objective function. In order to avoid relaxing the observed tensor into penalty terms, which may cause less accuracy problem, the minimization problem along each mode is accomplished by applying the augmented Lagrange multiplier method. The proposed approach is evaluated both on simulated data and real world data. Experimental results show that our proposed method tends to deliver higher-quality solutions with faster convergence rate compared with previous methods.