# STA-GCN: Spatial-Temporal Self-Attention Graph Convolutional Networks for Traffic-Flow Prediction
## 2 Literature Review  
As mentioned above traffic-flow prediction providing typical time-series prediction is one of the essential parts of ITS, which is still a challenging issue. Over the past decades, various models and techniques were employed in traffic-flow prediction, which can be roughly divided into model-driven and data-driven approaches [16; 17]. The model-driven approaches mainly depend on mathematical statistics or historical observations in constructing parametric models, which include time-series models, Kalman filtering models, spectral analyses, etc. Many classic models are proposed for traffic-flow prediction, such as the autoregression moving-average model (ARMA) and autoregression integral moving-average model (ARIMA) [18; 19]. However, parametric models, which are easily affected by external environmental factors, do not effectively deal with the non-linear issue of traffic. Compared to model-driven methods, data-driven methods mainly focus on the relationship between input and output rather than the model parameters. Example models include SVR, Kalman filtering, and artificial neural networks (ANNs) [20], which clearly illustrate non-linear mapping capability for prediction and weakness in learning the spatio-temporal characteristics of network traffic flow. Recently, the data-driven models of traffic-flow prediction have shifted to deep-learning methods in terms of the temporal and spatial features. For instance, the graph convolutional network (GCN) extends convolutional operations from structured data to graph-structured data, mainly through spatial domain convolutions [21] and spectral domain convolutions [22]. Regarding spatial domain convolutions, [PERSON] et al. [23] modeled traffic flow as a diffusion process on a directed graph and proposed the diffusion convolutional recurrent neural network (DCRNN), which captures spatial correlations based on bidirectional random walks to predict traffic flow on large road networks. [PERSON] et al. [24] added spatial-temporal correlations between adjacent matrices of a graph and constructed a prediction framework using a combination of spatial domain convolutional layers and gated linear units. [PERSON] et al. [25] argued that explicit graph structures are not sufficient to represent node relationships in real-world graphs and proposed the Graph WaveNet architecture based on node-embedding learning. The graph convolutional layer in this architecture extracts structural features between nodes through spatial domain convolutions. Regarding spectral domain convolutions, [PERSON] et al. [26] proposed a general graph convolutional framework based on the graph Laplacian matrix, and [PERSON] et al. [27] optimized this method using Chebyshev polynomials to approximate feature decomposition. [PERSON] et al. [28] designed a dynamic Laplacian matrix that incorporates tensor decomposition to better capture spatial-temporal changes, and constructed a corresponding dynamic spatial-temporal graph convolutional neural network (DGCNN). On the other hand, the Transformer model [29], proposed in 2017, is a novel foundational model that holds equal importance to CNN and RNN. In recent years, the Transformer model has made significant progress in both NLP and CV fields, and its core algorithm, the self-attention mechanism, has been widely developed and applied. [PERSON] et al. [30] used self-attention layers to process graph-structured data through neural networks and achieved state-of-the-art results. [PERSON] et al. [31] used Transformer to capture temporal correlations in traffic flow and combined these with GNN, which can capture spatial dependencies, to build a spatial-temporal traffic-flow prediction model. [PERSON] et al. [32] used a self-attention mechanism to simultaneously capture spatial and temporal dependencies of traffic-state changes, but when capturing spatial dependencies, the computational cost was excessively high due to the large number of spatial nodes.