Research On Models And Algorithms Of Graph Neural Networks

In the era of big data,there is a widespread interconnectivity among data,such as social networks,biological information networks,public opinion networks,and transportation networks.Graph data is an important carrier for expressing this type of data with interconnected characteristics.Currently,graph data analysis and mining have become an important trend in the development of the big data era.The breakthrough in graph data analysis technology will greatly promote the development of data science.However,as a typical non-Euclidean structured data,the irregular characteristics of graph data,such as the disorderliness of nodes and the inconsistency of neighbor numbers,pose new challenges to existing deep learning models and machine learning algorithms.Recently,graph neural networks,which combine the advantages of deep learning and graph computation,have rapidly emerged as a new type of graph representation learning tool.They have broad application prospects in production,scientific research(such as social networks,biological information,recommendation systems,and intelligent healthcare)and have attracted widespread attention from the academic and industrial communities.Their methods and application research are currently in an explosive period of development.However,there are still some key issues that need to be addressed in the research of graph neural networks: Currently,the basic theoretical research on graph neural networks is still in its infancy,and research on representation learning theory is still relatively lacking.In open environments,the robustness of existing graph neural networks is challenged when graph data is interfered with or biased.The performance of graph neural networks deteriorates when the number of layers increases,which seriously limits their application and promotion.Most graph neural networks focus on whole graph or node-level classification tasks,and there is little research on the applicability of graph neural networks in generative tasks.Regarding the above issues,the main research achievements of this thesis are as follows:(1)Regarding the theoretical research on representation learning of graph neural networks,we proposed a new framework for analyzing the expressive power of graph convolutional networks from a machine learning perspective,using function approximation theory.This approach enriches the representation learning theory of graph neural networks and provides new ideas for the basic theoretical research of graph neural networks,which is different from existing work that evaluates the expressive power of graph neural networks from a graph computation perspective using the Weisfeiler-Lehman(WL)graph isomorphism test.(2)To address the challenge of robustness in graph neural networks,we proposed a multi-view graph convolutional neural network model based on attention mechanism,which integrates multiple topological graph structure information to enhance the expressive power and robustness of graph neural networks.We theoretically demonstrated that the proposed multi-view graph convolutional network has stronger expressive power than a single-view graph convolutional network.In addition,we analyzed the robustness of the proposed multi-view graph neural network from an information theory perspective and showed that the robustness of the model is enhanced with an increase in the number of topological views.We also proposed a robust graph neural network based on a self-supervised learning architecture that combines the Dirichlet regularization constraint and the masking strategy in graph neural networks,thereby improving the robustness and weakly supervised learning ability of the graph neural network model.Extensive experimental results demonstrate the advantages of the proposed graph neural network model in terms of performance,robustness,and weakly supervised learning.(3)Regarding the over-smoothing,generalization,and construction of deep graph neural networks,theoretical analysis and effective deep graph convolutional networks are proposed.Firstly,the mathematical mechanism behind existing graph convolutional networks is systematically analyzed from the perspective of graph signal processing,providing theoretical guidance for designing effective graph filters(graph convolution strategies).At the same time,a theoretical explanation is given for the performance degradation phenomenon that occurs when existing graph convolutional networks are deepened.Based on the above theoretical results,an effective deep graph convolutional network is proposed by combining the graph aggregation strategy with attenuation of aggregation strength and the initial feature skip connection mechanism into the graph convolution operation,effectively alleviating the problem of performance degradation in deep graph convolutional networks.Finally,from the perspective of learning theory,the direct propagation Rademacher complexity analysis framework is used to theoretically analyze the generalization ability of the proposed deep graph convolutional network,ensuring its expressive power and generalization ability theoretically.(4)A deep graph neural network-based missing data completion method is proposed to address the applicability issues of graph neural networks in generation tasks.This method successfully utilizes the correlation characteristics between data using graph neural networks for typical generation problems such as missing data completion.Depending on the potential advantages of generative adversarial networks,the proposed data completion method no longer relies on explicit probability density functions in the inference process,making it more universally applicable in real-world scenarios.The theoretical support for the proposed data completion method is also provided for more general generation tasks,ensuring its effectiveness in theory.In summary,this thesis focuses on the challenges facing graph neural networks.It conducts in-depth research on the basic theoretical study of graph neural networks,new graph convolution techniques,deep graph neural network models,and their applications in typical generative tasks such as missing data completion.A series of novel graph neural network models are proposed,and a new framework for analyzing the expressive power of graph neural networks and the over-smoothing and generalization of deep graph neural networks is presented in theory.This provides new theoretical and technical support for the development and application of theoretical data analysis and mining in graph data.