Adaptive spectral GNN and frequency enhanced self-attention for traffic forecasting

Abstract

In intelligent city, traffic forecasting has played a significant role in intelligent transportation system. Nowadays, many methods, which combine spectral graph neural network and self-attention, are proposed. However, they still have some limitations for traffic forecasting: 1) The polynomial basis of traditional spectral graph neural networks (GNN) is fixed, which limits their ability to learn spatial dependency of traffic data. 2) Some GNNs ignore the dynamic dependency of traffic data. 3) Traditional self-attention suffers from limited perception for long-term information, time delay, and global information. These defaults pose big challenge for traffic forecasting via limiting their ability of capturing spatial-temporal dependency, dynamic and heterogeneous nature in traffic data. From this perspective, we propose an adaptive spectral GNN and frequency enhanced self-attention (ASGFES) for traffic forecasting, which can effectively capture the spatial-temporal dependency, dynamic and heterogeneous nature in traffic data. Specifically, we first introduce an adaptive spectral graph neural network (ASGNN) for effectively capturing the spatial dependency via conducting adaptive polynomial basis. In addition, two dynamic long and short range attentive graphs are fed into the ASGNN for emphasizing the dynamicity in view of long and short range. Secondly, we introduce a normalized self-attention with damped exponential moving average (NSADEMA). Specifically, the normalized self-attention (NSA) can capture the necessary expressivity to learn all-pair interactions without the need for some extra operation such as positional encodings, multi-head operations, and so on. It can well obtain the temporal dependency and heterogeneity of traffic data. In addition, the DEMA, which is equipped into NSA, can enhance the perception for the inductive bias of traffic data in time domain. It can be aware of the time delay of traffic data. Thirdly, linear frequency learner with time-series decomposition (LFLTD) are developed for enhancing the ability of capturing the temporal dependency and heterogeneity. Specifically, time-series decomposition (TSD) facilitates the analysis and forecasting of complex time via capturing various hidden components such as the trend and seasonal components. Meanwhile, linear frequency learner (LFL) can learn global dependencies and concentrating on important part of frequency components with compact signal energy. At last, many experiments are performed on several public traffic datasets and demonstrate the proposed ASGFES can achieve better performance than other traffic forecasting methods.