Tensor Graph Convolutional Neural Network Algorithm

Graph convolutional network can be regarded as an extension of the convolutional neural network on graph structure data,employed extensively in the citation network,traffic network,social network,protein network,and so on.Nowadays,the theoretical analysis of modeling static and homogeneous graph has been developed well,however,many real-life graph data do not satisfy the static and homogeneous characteristics.For example,a social network with multiple types of nodes and edges is heterogeneous,and a traffic network whose nodes’ states change over time is dynamic.With the limitations of computing power,memory capacity,and imperfect high-dimensional modeling theory,heterogeneous and spatial-temporal graph are sliced into multiple graphs and are separately modeled spatial dependency and heterogeneous/temporal dependency.However,this two-stage method fails to capture complex correlations in high-dimensional feature space.Based on tensor operation theories,this thesis comprehensively considers the modeling of high-dimensional complex dependencies,highdimensional data computation burden,and high-dimensional data storage and propose two types of tensor graph convolutional networks for the modeling of heterogeneous graph and spatial-temporal graph,moreover,the intelligent traffic monitoring system is developed by employing the proposed factorized spatial-temporal tensor graph convolutional algorithm.Specifically,the innovations of this article include:(1)A circulant tensor graph convolutional network(CTGCN)is proposed for complex dependencies modeling of heterogeneous graphs.Based on the tensor operation t-product,CTGCN derives the linear transformation of tensor space and integrates the diffusion of homogeneous information with the fusion of heterogeneous information into a unified tensor graph convolutional network.With the diagonalization of the circulant matrix constructed by the t-product operation,CTGCN is capable of avoiding calculation disasters and parametric disasters along with high-dimensional data modeling.Moreover,CTGCN also introduces a heterogeneous information attention mechanism fusion module to learn more discriminative graph node representations.Finally,experiments and related analysis on five node classification datasets demonstrate the efficiency and effectiveness of CTGCN for high-dimensional heterogeneous graph data modeling.We extend graph convolution into tensor space and propose a tensor graph convolution network to extract more discriminating features from spatial-temporal graph data.We further Besides,we can Extensive experiments on the three real-world datasets demonstrate that our method is more effective than traditional prediction methods,and achieves state-of-the-art performance.(2)A factorized spatial-temporal tensor graph convolutional network(factorized ST-TGCN)based on tensor decomposition is proposed for complex dependencies modeling of the spatial-temporal graph.Factorized ST-TGCN introduces Tucker decomposition to reduce the computational burden,which derives a unified tensor convolution that performs separate filtering in small-scale space,time,and feature modes.In addition,factorized ST-TGCN benefits from noise suppression of traffic data when discarding those trivial components in the process of tensor decomposition.Finally,extensive experiments on the two real-world datasets demonstrate that our method is more effective than traditional prediction methods,and achieves state-of-the-art performance.(3)An intelligent traffic monitoring system is developed by employing a factorized spatial-temporal tensor graph convolution model.The system displays real-time traffic status and predicted traffic status through visualized sensors speed data and predicted speed data,helping modern urban traffic plans.