Diffusion Graph Neural Ordinary Differential Equation Network for Traffic Prediction

Traffic prediction is the cornerstone of the intelligent transportation system (ITS), and accurate prediction is essential for planning route, alleviating traffic pressure, and optimizing public transportation resource allocation. Although many methods have been proposed, they still have deficiencies in capturing the spatial-temporal dependence of traffic data. In specific, their network structures are usually discrete, making it is challenging to continuously model the dynamic spatial-temporal patterns of the road network. Besides, static graph structure of the road network is not sufficient to express dynamic traffic patterns. In this paper, we propose a diffusion graph neural ordinary differential equation network (DGODE) to address the above challenges for traffic prediction. Firstly, DGODE represents the node relationships of the road network as a bidirectional spatial graph and the node relationships of the time as a unidirectional temporal graph, and then generates an adaptive diffusion matrix to explore potential node relationships and capture spatial and temporal dependencies. Next, the neural ordinary differential equation (NODE) is introduced to contin-uously model the dynamical change of traffic network, making it possible to capture global dependence at a deeper network structure. Since the solution of the ordinary differential equation is determined by the initial state, we design the structure with a jump link to supplement the spatial-temporal information in the historical data. Finally, the experimental evaluation on four real-world datasets shows that DGODE is significantly superior to several baseline methods.

[1]  Yaying Zhang,et al.  Spatial-Temporal Interactive Dynamic Graph Convolution Network for Traffic Forecasting , 2022, ArXiv.

[2]  Noseong Park,et al.  Graph Neural Controlled Differential Equations for Traffic Forecasting , 2021, AAAI.

[3]  Guojie Song,et al.  Spatial-Temporal Graph ODE Networks for Traffic Flow Forecasting , 2021, KDD.

[4]  Yulia R. Gel,et al.  Z-GCNETs: Time Zigzags at Graph Convolutional Networks for Time Series Forecasting , 2021, ICML.

[5]  Li Mengzhang,et al.  Spatial-Temporal Fusion Graph Neural Networks for Traffic Flow Forecasting , 2020, AAAI.

[6]  Youfang Lin,et al.  Spatial-Temporal Synchronous Graph Convolutional Networks: A New Framework for Spatial-Temporal Network Data Forecasting , 2020, AAAI.

[7]  Zewen Li,et al.  A Survey of Convolutional Neural Networks: Analysis, Applications, and Prospects , 2020, IEEE Transactions on Neural Networks and Learning Systems.

[8]  Jian Tang,et al.  Continuous Graph Neural Networks , 2019, ICML.

[9]  Hanghang Tong,et al.  Graph convolutional networks: a comprehensive review , 2019, Computational Social Networks.

[10]  Jing Jiang,et al.  Graph WaveNet for Deep Spatial-Temporal Graph Modeling , 2019, IJCAI.

[11]  David Duvenaud,et al.  Neural Ordinary Differential Equations , 2018, NeurIPS.

[12]  Jieping Ye,et al.  Deep Multi-View Spatial-Temporal Network for Taxi Demand Prediction , 2018, AAAI.

[13]  Zhanxing Zhu,et al.  Spatio-temporal Graph Convolutional Neural Network: A Deep Learning Framework for Traffic Forecasting , 2017, IJCAI.

[14]  Cyrus Shahabi,et al.  Diffusion Convolutional Recurrent Neural Network: Data-Driven Traffic Forecasting , 2017, ICLR.

[15]  Xavier Bresson,et al.  CayleyNets: Graph Convolutional Neural Networks With Complex Rational Spectral Filters , 2017, IEEE Transactions on Signal Processing.

[16]  Gregory D. Hager,et al.  Temporal Convolutional Networks for Action Segmentation and Detection , 2016, 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[17]  Xiuwen Yi,et al.  DNN-based prediction model for spatio-temporal data , 2016, SIGSPATIAL/GIS.

[18]  Yu Zheng,et al.  Deep Spatio-Temporal Residual Networks for Citywide Crowd Flows Prediction , 2016, AAAI.

[19]  Max Welling,et al.  Semi-Supervised Classification with Graph Convolutional Networks , 2016, ICLR.

[20]  Xavier Bresson,et al.  Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering , 2016, NIPS.

[21]  Donald F. Towsley,et al.  Diffusion-Convolutional Neural Networks , 2015, NIPS.

[22]  Yoshua Bengio,et al.  Learning Phrase Representations using RNN Encoder–Decoder for Statistical Machine Translation , 2014, EMNLP.

[23]  Said M. Easa,et al.  Supervised Weighting-Online Learning Algorithm for Short-Term Traffic Flow Prediction , 2013, IEEE Transactions on Intelligent Transportation Systems.

[24]  Hans van Lint,et al.  Short-Term Traffic and Travel Time Prediction Models , 2012 .

[25]  Alessio Micheli,et al.  Neural Network for Graphs: A Contextual Constructive Approach , 2009, IEEE Transactions on Neural Networks.

[26]  J. Beran.  Time series analysis , 2003 .

[27]  S. Hochreiter,et al.  Long Short-Term Memory , 1997, Neural Computation.

[28]  Alexander J. Smola,et al.  Support Vector Regression Machines , 1996, NIPS.

[29]  G. Box,et al.  Distribution of Residual Autocorrelations in Autoregressive-Integrated Moving Average Time Series Models , 1970 .

[30]  Yitong Ma,et al.  DSTAGNN: Dynamic Spatial-Temporal Aware Graph Neural Network for Traffic Flow Forecasting , 2022, ICML.

[31]  A. Micheli,et al.  The Infinite Contextual Graph Markov Model , 2022, ICML.

[32]  Elif Derya Übeyli,et al.  Recurrent Neural Networks , 2018 .

[33]  Vladimir N. Vapnik,et al.  The Nature of Statistical Learning Theory , 2000, Statistics for Engineering and Information Science.