Multivariate time series forecasting is crucial for various applications, such as financial investment, energy management, weather forecasting, and traffic optimization. However, accurate forecasting is challenging due to two main factors. First, real-world time series often show heterogeneous temporal patterns caused by distribution shifts over time. Second, correlations among channels are complex and intertwined, making it hard to model the interactions among channels precisely and flexibly. In this study, we address these challenges by proposing a general framework called \textbf{DUET}, which introduces \underline{DU}al clustering on the temporal and channel dimensions to \underline{E}nhance multivariate \underline{T}ime series forecasting. First, we design a Temporal Clustering Module (TCM) that clusters time series into fine-grained distributions to handle heterogeneous temporal patterns. For different distribution clusters, we design various pattern extractors to capture their intrinsic temporal patterns, thus modeling the heterogeneity. Second, we introduce a novel Channel-Soft-Clustering strategy and design a Channel Clustering Module (CCM), which captures the relationships among channels in the frequency domain through metric learning and applies sparsification to mitigate the adverse effects of noisy channels. Finally, DUET combines TCM and CCM to incorporate both the temporal and channel dimensions. Extensive experiments on 25 real-world datasets from 10 application domains, demonstrate the state-of-the-art performance of DUET.

翻译：多变量时间序列预测在金融投资、能源管理、气象预报和交通优化等众多应用中至关重要。然而，准确的预测面临两大主要挑战。首先，现实世界中的时间序列常因随时间发生的分布漂移而呈现异质性的时序模式。其次，通道间的相关性复杂且相互交织，难以精确而灵活地建模通道间的相互作用。在本研究中，我们通过提出一个名为 \textbf{DUET} 的通用框架来解决这些挑战，该框架在时序和通道维度上引入 \underline{双} 聚类以 \underline{增强} 多变量 \underline{时间} 序列预测。首先，我们设计了一个时序聚类模块（TCM），将时间序列聚类为细粒度的分布以处理异质性时序模式。针对不同的分布簇，我们设计了多种模式提取器以捕捉其内在的时序模式，从而对异质性进行建模。其次，我们引入了一种新颖的通道软聚类策略，并设计了一个通道聚类模块（CCM），该模块通过度量学习在频域中捕获通道间的关系，并应用稀疏化以减轻噪声通道的不利影响。最后，DUET 结合 TCM 和 CCM，以同时纳入时序和通道维度。在来自 10 个应用领域的 25 个真实世界数据集上进行的大量实验，证明了 DUET 的先进性能。