# Time-Evolving Graph Convolutional Recurrent Network for Traffic Prediction
## 2 Related Work  
### Traffic Prediction Methods  
The methods of traffic prediction have been extensively researched. Traditional methods view this task as a univariant time-series regression and forecasting problem, using statistical signal processing models or classic machine-learning models, such as Auto-Regressive Integrated Moving Average (ARIMA) [3; 4], Kalman filtering [22; 23], Vector Auto-Regression (VAR) [24] and Support Vector Regression (SVR) [5]. However, these methods heavily rely on the stationary assumption, so they have limited representation space and can hardly capture the dynamics of real traffic. Meanwhile, they treat the sequences of different traffic nodes separately and therefore are incapable of utilizing the information of spatial dependency. With the emergence of deep-learning methods, some researchers employ CNN-based and RNN-based models in the tasks of traffic prediction. [PERSON] et al. [8] proposed a CNN-based residual network to model the citywide spatial correlations and predict the region crowd traffic. [PERSON] et al. [7] build a feature-level regression model with spatial and temporal features captured by a 1-D CNN and two LSTMs, respectively, in different time scales. These works show the advantages of deep-learning methods in modeling nonlinear spatiotemporal relationships. More recently, to tackle traffic data in irregular road topologies with non-Euclidean structures, graph neural networks have been widely used. Integrating graph networks such as GCN with other temporal models to construct spatiotemporal graph networks has become a new paradigm. We compare some typical works with our model and list the key components in Table 1 to show the gaps. [PERSON] et al. [12] model the spatial dependency of traffic with a diffusion process on the road distanced graph and replace the linear layer in GRU with diffusion convolution operation. [PERSON] et al. [13] propose the STGCN model, which stacks temporal 1-D CNN with ChebyNet [25] alternately and conducts prediction in a complete convolutional manner. Based on [13], [PERSON] et al. [15] also add spatial and temporal attention mechanisms to refine the correlations. Considering that the aforementioned works limit the inter-node adjacency to predefined distance graphs, some works attempt to extend the inter-node dependency to more views. [PERSON] et al. [16] design an augmented graph with adjacency along both the spatial and temporal dimension, and capture these two types of features with graph convolution synchronously. Following this idea, [PERSON] et al. [18] further add the time-series similarity subgraphs into the spatiotemporal augmented graph. [PERSON] et al. [19] propose an attentive bicomponent GCN based on both the road distance graph and its corresponding edge-wise line graph. [PERSON] et al. [14; 21] further equip graph convolution with static adaptive adjacency graphs and apply dilated convolution in the temporal dimension. However, in the works mentioned above, the adjacency graphs of traffic nodes are all static, and the graph convolutions are used to capture information in a fixed topology. In this way, some implicit dynamics of the inter-node dependency may be neglected. In contrast, our model takes advantage of evolving adjacency graphs at different time slots, and learns the dynamic spatial dependencies together with sequential signal features.