# Hybrid Graph Models for Traffic Prediction
## 1 Introduction  
Traffic prediction is of great significance for optimizing urban traffic systems, improving traffic efficiency, reducing congestion, and improving environmental quality. Recently, many countries have been committed to developing intelligent transportation systems. As an indispensable part of traffic prediction, obtaining real-time traffic conditions can help people better arrange travel plans and share resources [1; 2; 3; 4; 5; 6]. Traffic prediction aims to estimate future road conditions from the historical state recorded by the traffic system [7; 8; 9; 10]. A real-time and accurate grasp of road conditions plays an important role in traffic management and resource allocation. However, the complex spatial correlation and nonlinear temporal dependence of the traffic network pose great challenges to obtaining accurate traffic prediction. Although many works have achieved excellent predictive performance, accurate traffic prediction still faces the following challenges, as shown in Figure 1:  
Figure 1: Complex spatial–temporal correlations. (1) Complex spatial correlation. Node \(O\) received different impacts from adjacent nodes (such as \(A\), \(B\), \(C\), \(D\)) at different time steps. Capturing the dynamic relationship between nodes is crucial to improving predictive performance. (2) Nonlinear temporal dependence. Node \(B\) is influenced by its own node and adjacent nodes at the previous state and the influence weight \(\beta_{i}\) changes dynamically over time. Traditional traffic prediction methods such as the autoregressive integral moving average algorithm (ARIMA) [11] or Kalman filter extract time series information of the traffic network based on time stationary assumption. Traditional methods have achieved great success in traffic prediction. However, the flexibility of these methods is limited due to the complex spatial correlations and nonlinear temporal dependencies of the traffic network. Due to the powerful feature representation ability of deep learning, deep learning-based methods have made breakthroughs in computer vision, natural language processing, and traffic prediction. Deep learning-based methods automatically learn the rich spatial-temporal information of traffic data through deep neural networks. The temporal signal of a traffic network can be regarded as a sequence-to-sequence model, and the temporal interactivity of nodes can be extracted by the 1D convolution operations in traffic prediction. Compared with 1D convolutional neural networks, recurrent neural networks (RNNs) have attracted extensive attention because these methods can model long-range temporal information [12]. However, RNNs learning-based methods are prone to the vanishing gradient, which makes the backbone network unable to effectively train and learn deep semantic information. In the spatial dimension, convolutional neural networks (CNNs) have excellent feature extraction capabilities on the Euclidean data structure. However, the spatial distribution of the traffic network nodes can be regarded as a non-Euclidean data structure, which leads to the fact that CNNs learning-based methods have not been widely used in traffic prediction. In recent years, graph neural networks (GNNs) have received extensive attention due to their excellent results on non-Euclidean structures [13; 14; 15; 16]. The GNNs, which can roughly be divided into the spectral domain and spatial domain, update the state of the current node by aggregating the information of adjacent nodes. However, the adjacency matrix generated based on distance or similarity has several limitations.These methods are subjective and incomplete and cannot represent the potential correlation of the traffic network. For example, as shown in Figure 1, node \(O\) represents a commercial area and node \(D\) is a residential area. Although node \(O\) and node \(D\) are far apart in space, they have a strong correlation. In this paper, we propose a novel Hybrid Graph Model (HGM) to extract rich spatial-temporal information about the traffic network.