ADAPTIVE SPATIAL-TEMPORAL INCEPTION GRAPH CONVOLUTION NETWORKS FOR MULTI-STEP SPATIAL-TEMPORAL DATA FORECASTING

Abstract

Spatial-temporal data forecasting is of great importance for industries such as telecom network operation and transportation management. However, spatialtemporal data are inherent with complex spatial-temporal correlations and behaves heterogeneities among the spatial and temporal aspects, which makes the forecasting remain as a very challenging task though recently great work has been done. In this paper, we propose a novel model, Adaptive Spatial-Temporal Inception Graph Convolution Networks (ASTI-GCN), to solve the multi-step spatial-temporal data forecasting problem. The model proposes multi-scale spatial-temporal joint graph convolution block to directly model the spatial-temporal joint correlations without introducing elaborately constructed mechanisms. Moreover inception mechanism combined with the graph node-level attention is introduced to make the model capture the heterogeneous nature of the graph adaptively. Our experiments on three real-world datasets from two different fields consistently show ASTI-GCN outperforms the state-of-the-art performance. In addition, ASTI-GCN is proved to generalize well.

1. INTRODUCTION

Spatial-temporal data forecasting has attracted attention from researchers due to its wide range of applications and the same specific characteristics of spatial-temporal data. Typical applications include mobile traffic forecast (He et al., 2019) , traffic road condition forecast (Song et al., 2020; Yu et al., 2017; Guo et al., 2019; Zheng et al., 2020; Li et al., 2017) , on-demand vehicle sharing services passenger demand forecast (Bai et al., 2019) and geo-sensory time series prediction (Liang et al., 2018) etc. The accurate forecast is the foundation of many real-world applications, such as Intelligent Telecom Network Operation and Intelligent Transportation Systems (ITS). Specifically, accurate traffic forecast can help transportation agencies better control traffic scheduling and reduce traffic congestion; The traffic volumes prediction of the wireless telecommunication network plays an important role for the network operation and optimization, for example, it can help to infer the accurate sleep periods (low traffic periods) of the base stations to achieve energy saving without sacrificing customer experience. However, as we all know, accurate spatialtemporal data forecasting faces multiple challenges. First, it is inherent with complex spatial-temporal correlations. In the spatialtemporal graph, different neighbors may have different impacts on the central location at the same time step, as the bold lines shown in Fig- ure1 , which called spatial correlations.Different historical observations of the same location influence the future moments of itself variously due to temporal correlations. The observations of different neighbors at historical moments can directly affect the central node at future time steps due to the spatial-temporal joint correlations. As shown in Figure1, the information of the spatialtemporal network can propagate along the spatial and temporal dimensions simultaneously, and the transmission process can be discontinuous due to complex external factors, which result in spatialtemporal joint correlations of the spatial-temporal data in a short period. Spatial-temporal data is heterogenous in both spatial and temporal dimensions (Song et al., 2020) . Nodes in different regions of the graph have various properties and local spatial structures, so the corresponding data distribution can be different. For example, the traffic flow distribution of urban and suburban areas are quite different, while the traffic of urban area is denser and that of suburban area is relatively sparse. Besides, the traffic flow in the same region also exhibit heterogeneity in different time periods. For example, the mobile traffic in business district would decrease at night compared to the daytime, while it's opposite in the residential district. In addition, multi-step time series forecasting is often accompanied by error accumulation problem. Typical methods like RNNs often cause error accumulation due to iterative forecasting, leading to rapid deterioration of the long-term prediction accuracy. (Yu et al., 2017; Zheng et al., 2020) . Most of the previous work is mainly to solve the above challenges. To model the spatial-temporal dependency, STGCN (Yu et al., 2017) and DCRNN (Li et al., 2017) extract spatial and temporal correlations separately. ASTGCN (Guo et al., 2019) introduced spatial and temporal attention to model the dynamic spatial and temporal correlations. STG2Seq (Bai et al., 2019) aimed at using GCN to capture spatial and temporal correlations simultaneously. But they all didn't consider the spatialtemporal joint correlations and heterogeneity. Different from the above methods, STSGCN (Song et al., 2020) used multiple local spatial-temporal graphs to model the spatial-temporal synchronous correlations and spatial-temporal heterogeneity of the local adjacent time steps. But STSGCN can only model the spatial-temporal synchronous correlations of its defined local spatial-temporal graphs and it is equipped with complex structure. In this paper, we propose a novel model called ASTI-GCN, Adaptive spatial-temporal Inception Graph Convolutional Networks, to address the above issues with multi-step spatial-temporal data forecasting. We propose the spatial-temporal joint convolution to directly model the spatial-temporal joint correlations without introducing elaborately constructed mechanisms. And we introduce the inception mechanism to build multi-scale spatial-temporal features to adapt to graph nodes with different properties. Then, to achieve the heterogeneity modeling, we construct the spatial-temporal Inception Graph Convolution Module, which combined the spatial-temporal inception mechanism with the graph attention to build the adaptive ability of graph nodes with different properties. After multiple spatial-temporal inception-GCMs, two decoder modules named sequence decoder and short-term decoder are designed to directly establish the relationships between the historical and future time steps to alleviate error accumulation. Overall, our main contributions are summarized as follows: • We propose a novel spatial-temporal joint graph convolution network to directly capture spatial-temporal correlations. Moreover, we introduce inception with graph attention to adaptively model the graph heterogeneity. • We propose to combine the sequence decoder and short-term decoder together for multistep forecasting to model direct relationships between historical and future time steps to alleviate the error propagation. • We evaluate our model on three real-world datasets from two fields, and the experimental results show that our model achieves the best performances among all the eight baselines with good generalization ability.

2. RELATED WORK

Spatial-temporal data information can be extracted using the deep learning method from European space, such as ConvLSTM (Xingjian et al., 2015) , PredRNN (Gowrishankar & Satyanarayana, 2009) and so on. However, most of the spatial-temporal data in real scenes are graph data with complex and changeable relationships.Common timing prediction models, such as HA and ARIMA (Williams & Hoel, 2003) , cannot be simply migrated to such scenarios. Graph based methods like DCRNN (Li et al., 2017) modeled traffic flow as a diffusion process on a directed graph. Spatial dependencies and temporal dependencies are captured by bidirectional random walk and DCGRU based



Figure 1: Spatial-temporal correlations.

