Research On Statistical Generalization And Expression Ability Of Graph Neural Networks

Graph-structured data is ubiquitous,such as: social networks,transportation networks,etc.Therefore,how to mine the rich semantic information in graph data is a very valuable topic.Graph neural networks,as one of the powerful methods for processing graph data,have attracted extensive research in the past two years.However,there are still two major challenges in modeling graph data using graph neural networks:(1)How to overcome the degradation of the performance of graph neural networks in deep models.(2)How to solve the problem that it is difficult to obtain data with labels in real-world.The above two challenges greatly limit the generalization and expression ability of graph neural networks.In response to this problem,this paper first examines the graph neural network of the deep architecture,then,the theoretical study of statistical generalization analysis of graph convolutional networks is carried out.And the expression ability of graph convolutional networks is studied,and generalized to heterogeneous graph neural networks.Subsequently,unsupervised graph neural networks that do not use label data were further studied.In summary,the research content and innovation points of this paper are summarized as follows:1.Based on the statistical generalization analysis of graph convolutional networks,a graph convolutional network based on simplified stacking is proposed.The message-passing of the graph convolutional network is easily coupled with feature extraction,resulting in weak feature extraction ability.This paper designs a simplified stacking classifier to efficiently extract the features of the graph data,and then use the aggregation layer to further fuse the extracted data.In addition,the convergence theorem of the statistical generalization boundary of graph convolutional neural networks is proposed,and the proof is given by the contraction property of Rademacher complexity,the definition of Frobenius norm and Cauchy-Schwarz inequality.Experiments have shown that the proposed method can deepen the network and further improve the performance of the model.2.The expression ability of the graph convolutional network was studied.Aiming at the problem of weak expression ability of graph convolutional networks,this paper uses the organic integration of multi-scale information and self-attention mechanism to adaptively make the model focus on learning multi-scale information,thereby improving the expression ability.In the node classification and graph classification tasks,the proposed method can effectively build a deep model and is superior to the current method.3.The expression ability of heterogeneous graph neural networks was performed,there is a problem of deep degradation of graph neural networks,and heterogeneous graph neural networks also exist.In this paper,a heterogeneous graph neural network based on similarity regularization and hierarchical fusion is designed for heterogeneous graphs.Two strategies can reduce the similarity of nodes and deepen the network,while improving the expression ability of the model.Sufficient experiments proved the effectiveness.4.The expression ability of unsupervised graph neural networks was carried out,for the problem of difficulty in obtaining graph data labels,this paper proposes an unsupervised method.Using the paradigm of contrast learning,a graph contrast learning method based on noise disturbance and adaptive filtering is proposed.The proposed method can be very elegant at generating high-quality samples for contrast learning,experimental surfaces,and the method in this paper does not use labels or even prefers supervised algorithms.