Hypergraph Neural Networks For Complex Higher-order Relationships

Graphs are widely used in fields as diverse as social networks,recommendation networks,and biochemical networks,depending on how effectively they describe paired relationships that exist in various networks of the real world.Driven by artificial intelligence and deep learning,graph neural networks have gained fast development and have been widely studied in application fields such as social analysis,financial analysis,and chemical analysis.However,many real-world networks exhibit complex and diverse relationships between objects,such as research collaboration networks,protein networks,etc.If these complex relationships are directly represented as pairwise relationships by graphs,it will lead to information loss.As an extension of graphs,hypergraphs are a more flexible modeling tool,which can naturally display higher-order relationships that cannot be fully characterized by graphs,making up for the shortcomings of graphs.Based on this,hypergraph neural networks have received a lot of attention,having gradually become an important technology and a new research direction in deep learning.In particular,that is a very important research applying hypergraph neural networks to node classification tasks.This thesis is rooted in hypergraph neural networks for higher-order relationships,with node classification tasks as the starting point.It focuses on several issues that need improvement in depth,width,and hypergraph filters of current hypergraph neural networks.Three hypergraph neural network models are proposed to solve these problems and enrich the hypergraph neural network system.The main research contents of this thesis are as follows:(1)A method for constructing deep hypergraph neural networks is proposed.Firstly,to solve the problem that the structure of a hypergraph neural network is not easy to deepen,using sampling hyperedges to enhance the robustness and randomness of the data while reducing message passing and alleviating overfitting.Secondly,to address common issues in deep networks,such as oversmoothing,introducing identity mapping,and residual connections to design hypergraph convolutional layers suitable for deep network structures.Then,using the hypergraph neural network HGNN and the hypergraph wavelet neural network HWNN as the basic hypergraph convolutional layers,the deep hypergraph neural networks Deep HGNN and Deep HWNN are designed by selectively combining the three techniques.Finally,the experiments are carried out on two 3D datasets for visual object classification,and the results show that the proposed deep models can deepen the network structure and improve the classification accuracy.(2)A hypergraph neural network based on an autoregressive moving average filter is proposed.Firstly,in response to the lack of research on filters in existing hypergraph neural networks,the detailed analysis and deduction of hypergraph convolutional layers are conducted from the perspective of hypergraph filters.Secondly,to compensate for the shortcomings of the hypergraph convolution with a polynomial filter,a new hypergraph convolution layer based on the autoregressive moving average ARMA filter is designed,which can obtain a more flexible frequency response.Thirdly,to effectively utilize multi-modal data,two kinds of hypergraph neural network models are designed according to the different execution orders of hypergraph fusion and hypergraph convolution.In addition,to consider multi-modal data,two kinds of hypergraph neural network models were proposed,based on the different order of performing hypergraph fusion and hypergraph convolution.Finally,the experiments were conducted on two common datasets,the citation network and 3D object,the results showed that the proposed hypergraph neural network model not only improved classification accuracy but also fully utilized the multi-modal features of the data.(3)A double-channel hypergraph neural network based on hypergraph convolution and a line graph of hypergraph is proposed.Firstly,to solve the problem of ignoring the hyperedge topology in previous studies,the line graph of the hypergraph is used to describe the inlining of the hyperedge effectively.Secondly,to reduce the computational cost,the graph wavelet transform is used to realize the convolution operation and design the hypergraph line graph wavelet neural network.Then,to simultaneously get the node topology and edge topology information of the hypergraph,a dual-channel learning mode is adopted to integrate hypergraph convolution and a line graph of hypergraph convolution to develop a dual-channel hypergraph neural network depended on hypergraph convolution and graph wavelet.Finally,the experiments are done on three types of public datasets,citation network,3D object,and cooking network,and the results show that the proposed method can improve the accuracy of node classification and enhance the robustness of the model.In a word,this thesis mainly provides the theoretical basis and technical support for hypergraph neural networks in tasks such as node classification.As a new research direction in deep learning of artificial intelligence,hypergraph neural networks have a short development history and abundant research content,so it has vital theoretical value and engineering significance to study hypergraph neural networks.