FourierGNN：从纯图视角重新思考多元时间序列预测
FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective
AI总结：
针对现有GNN方法时空建模分离的问题，提出纯图视角的FourierGNN，通过超变量图统一时空依赖，并在傅里叶空间实现高效预测，在七个数据集上以更少参数取得更优性能。
摘要：
多元时间序列（MTS）预测在众多行业中具有重大意义。当前最先进的基于图神经网络（GNN）的预测方法通常需要同时使用图网络（如GCN）和时间网络（如LSTM），分别捕捉序列间（空间）动态和序列内（时间）依赖。然而，这两种网络的不确定兼容性给手工模型设计带来了额外负担。此外，分离的空间和时间建模天然违背了现实世界中统一的时空相互依赖关系，这在很大程度上阻碍了预测性能。为克服这些问题，我们探索了一个有趣的方向：直接应用图网络，并从纯图视角重新思考MTS预测。我们首先定义了一种新颖的数据结构——超变量图（hypervariate graph），它将每个序列值（无论变量还是时间戳）视为图节点，并将滑动窗口表示为时空全连接图。这一视角统一考虑了时空动态，并将经典MTS预测重新表述为对超变量图的预测。随后，我们提出了一种新颖架构——傅里叶图神经网络（FourierGNN），通过堆叠我们提出的傅里叶图算子（FGO）在傅里叶空间执行矩阵乘法。FourierGNN具有充分的表达能力，并实现了更低的复杂度，能够有效且高效地完成预测。此外，我们的理论分析揭示了FGO在时域中与图卷积的等价性，进一步验证了FourierGNN的有效性。在七个数据集上的大量实验表明，与最先进的方法相比，我们以更高的效率和更少的参数实现了优越的性能。
英文摘要：
Multivariate time series (MTS) forecasting has shown great importance in numerous industries. Current state-of-the-art graph neural network (GNN)-based forecasting methods usually require both graph networks (e.g., GCN) and temporal networks (e.g., LSTM) to capture inter-series (spatial) dynamics and intra-series (temporal) dependencies, respectively. However, the uncertain compatibility of the two networks puts an extra burden on handcrafted model designs. Moreover, the separate spatial and temporal modeling naturally violates the unified spatiotemporal inter-dependencies in real world, which largely hinders the forecasting performance. To overcome these problems, we explore an interesting direction of directly applying graph networks and rethink MTS forecasting from a pure graph perspective. We first define a novel data structure, hypervariate graph, which regards each series value (regardless of variates or timestamps) as a graph node, and represents sliding windows as space-time fully-connected graphs. This perspective considers spatiotemporal dynamics unitedly and reformulates classic MTS forecasting into the predictions on hypervariate graphs. Then, we propose a novel architecture Fourier Graph Neural Network (FourierGNN) by stacking our proposed Fourier Graph Operator (FGO) to perform matrix multiplications in Fourier space. FourierGNN accommodates adequate expressiveness and achieves much lower complexity, which can effectively and efficiently accomplish the forecasting. Besides, our theoretical analysis reveals FGO's equivalence to graph convolutions in the time domain, which further verifies the validity of FourierGNN. Extensive experiments on seven datasets have demonstrated our superior performance with higher efficiency and fewer parameters compared with state-of-the-art methods.
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