Time series analysis is a fundamental data mining task that has made encouraging progress in many real-world scenarios. Supervised training methods based on empirical risk minimization have proven their effectiveness on specific tasks and datasets. However, the acquisition of well-annotated data is costly, and a large amount of unlabeled series data is under-utilized. Due to distributional shifts across various domains and different patterns of interest across multiple tasks. The problem of cross-domain multi-task migration remains a significant challenge. To address these problems, this article proposes a novel cross-domain approach based on Wave Quantization for Time Series (termed as WQ4TS), which can be combined with any advanced time series model and applied to diverse downstream tasks. Specifically, we transfer the data from different domains into a common spectral latent space and enable the model to learn the temporal pattern knowledge of different domains directly from the common space and utilize it for the inference of downstream tasks, thereby mitigating the challenge of heterogeneous migration. The establishment of spectral latent space brings at least three benefits, cross-domain migration capability thus adapting to zero- and few-shot scenarios without relying on priori knowledge, general compatible cross-domain framework without changing the existing model structure, and robust modeling capability thus achieving SOTA results in multiple downstream tasks. To demonstrate the effectiveness of the proposed approach, we conduct extensive experiments including three important tasks: forecasting, imputation, and classification. And three common real-world scenarios are simulated: full-data, few-shot, and zero-shot. The proposed WQ4TS achieves the best performance on 87.5% of all tasks. Concretely, WQ4TS achieved 25.8% and 44.1% improvements in MSE metric for few-shot and zero-shot forecasting tasks, respectively, and demonstrated excellent 24.9% increase in average accuracy on few-shot classification tasks. The source codes of WQ4TS are publicly available on https://github.com/Xiang-Kai/WQ4TS .

Graph Neural Networks (GNNs) have demonstrated remarkable effectiveness across various tasks but are often hindered by their high computational overhead. GNN-to-MLP distillation provides a promising remedy by transferring knowledge from complex GNNs to lightweight MLPs. However, existing methods largely overlook the differences in aggregation mechanisms and heterogeneous architectures. Simplifying such intricate information into MLP potentially causes information loss or distortion, ultimately resulting in suboptimal performance. This paper proposes an aggregation mechanism enhanced GNN distillation framework (AMEND). AMEND introduces multi-scope aggregation context preservation to replicate the teacher's broad aggregation scopes and an aggregation-enhanced centered kernel alignment method to match the teacher's aggregation patterns. To ensure efficient and robust knowledge transfer, we integrate a manifold mixup strategy, enabling the student to capture the teacher's insights into mixed data distributions. Experimental results on 8 standard and 4 large-scale datasets demonstrate that AMEND consistently outperforms state-of-the-art distillation methods.

Multivariate Time Series Classification (MTSC) is a fundamental data mining task, which is widely applied in the fields like health care and energy management. However, the existing MTSC methods are mostly adapted from univariate versions and model the static patterns among series in the time domain. We argue they fail to capture the inter-dependencies across variables and rarely consider the unique dynamic features in multilevel frequencies, which are susceptible to signal noise and lack sufficient feature extraction capability to achieve satisfactory classification accuracy. To address these issues, we propose a novel framework called Multilevel Dynamic Wavelet Graph Neural Network (MagNet) , which effectively captures inherent temporal-frequency dependencies in multivariate time series data in a global view, facilitating the information flow among inter-related variables and leveraging learnable Graph Neural Networks (GNNs) to uncover dynamic frequency dependencies. We propose an orthogonal temporal convolution layer that utilizes soft orthogonal losses to constrain features learned at different frequency components to reduce feature redundancy. Additionally, we introduce a hierarchical graph coarsening operator to address the flat learning challenges in traditional GNNs. Our dynamic wavelet GNN and hierarchical coarsening enable deep model stacking and end-to-end learning. Extensive experiments on 30 UEA benchmarks demonstrate that our method outperforms the state-of-the-art baselines in the MTSC tasks.

Time series analysis has a wide range of applications in the fields of weather forecasting, traffic management, fault detection, intelligent operation, etc. In the real world, time series typically consist of dynamic fluctuations and mixtures of periodicities, which bring challenges on modeling and analyzing their patterns. To overcome the complexities, a common approach is to decompose long-term time series into sub-components for easier analysis. Unlike conventional time series decomposition that decouples a series into the trend and seasonal parts, we proposed a novel triple decomposition method to decouple a long-term series into three components: trend-part, regular-part, and fluctuant-part. Notably, the third part is a particular component that represents the dynamic spectral fluctuation in time series with the formulation of spectrum gradient. Based on triple decomposition, we propose a novel task-general deep learning model called TS3Net for long-term series analysis. It introduces a temporal-frequency block (TF-Block) with a multi-branch structure to expand the time series into a 2D temporal-frequency distribution. Subsequently, deep representation can be learned by a vision architecture that captures the dynamic variations from the complex multi-periodic series. The decomposed components are processed by TS3Net individually, and their results are integrated to form the final result for time series analysis. We conduct extensive experiment based on six open datasets to evaluate the proposed method in comparison with 10 baselines. Numerical results show that TS3Net significantly outperforms the state-of-the-art methods on both time series forecasting and imputation tasks. The source codes of TS3Net are publicly available on https://github.com/Xiang-Kai/TS3Net.