## 1 Introduction  
Traffic speed prediction is an important part of the Intelligent Transportation System (ITS). Accurate and timely traffic prediction can assist in real-time dynamic traffic light control [1] and urban road planning, which will help alleviate the huge congestion problem as well as improve the safety and convenience of public transportation. Besides, traffic control in advance can prevent traffic paralysis, pedaling, and other events. Traffic speed prediction aims to predict future traffic speed based on a series of historical traffic speed observations. The three key complex factors affecting traffic speed are as follows:  
Factor 1: Global Spatial Dependencies. As shown in Figure 1, given the road network and sensors, the spatial correlations over different nodes on the traffic network are both local and global. Take Sensor 1 for example; the traffic status of its adjacent sensors (see Sensors 2 and 3) can influence that of Sensor 1. These are localized spatial correlations between sensors. In addition, the sensors (see Sensor 4) far from Sensor 1 can indirectly affect the traffic status of Sensor 1. Thus, all other sensors on the road network have impacts on Sensor 1. These are global spatial correlations between sensors. Figure 1, the traffic status at time \(t+1\) is more related to that of time \(t-l+1\), compared with that of time \(t\). In addition, we find that the trend of traffic speed over time in different workdays shows a high degree of similarity in Figure 1(a). Moreover, the trend of traffic speed on the same workday in different weeks is similar as well in Figure 1(b), which indicates that traffic speed renders both short-term neighboring and multiple long-term periodic dependencies. Thus, we consider the recent, daily, and weekly periodic patterns for traffic speed prediction simultaneously. Factor 3: External Factors. Traffic speed is significantly affected by external factors such as weather conditions, holidays, other special events, and so on. According to Figure 2(a), it is clearly shown that the traffic speed on holidays is different from that on normal days. In addition, it can be seen in Figure 2(b) that the traffic speed of a heavily rainy day is much lower than that of a sunny day. In addition to the above-mentioned key factors affecting traffic speed, there is uncertainty and inconsistency in the traffic data sensors collect, due to sensor failures, sensor maintenance, and other reasons. Several studies [2,3] have focused on evaluating and improving the reliability of sensors. To address the problem, in this paper, we also deal with the outliers and missing values in the traffic data, respectively. Studies on traffic prediction have never stopped in the past few decades. Early statistical methods [4,5] and traditional machine learning methods [6, 7, 8] for traffic prediction cannot model the non-linear temporal correlations of traffic data effectively, and they hardly consider spatial dependencies. In recent years, with the continuous development of deep learning, many researchers have applied deep-learning-based methods to the traffic domain. Some studies [9, 10, 11] combine convolutional neural networks (CNNs) and recurrent neural networks (RNNs) for traffic prediction, where CNNs are used to capture the spatial dependencies while RNNs are used to extract the temporal correlations of traffic data. Figure 1: The topological structure of the road network and complex spatial-temporal correlations between sensors. Figure 2: Multiple temporal dependencies of the traffic speed for PeMSD7. (PeMSD7 is a dataset containing traffic information from the sensors on the highways of Los Angeles County.) The main limitation of the aforementioned methods is that conventional convolution operations only capture the spatial characteristics of regular grid structures. They are not suitable for data with irregular topologies.