Graph Representation Learning With Complex Structure:Research And Application

The contemporary period is marked by an exponential surge in data.As the car-rier of information,data exhibits an escalating trend of diversity and complexity,notably in practical domains like communication networks,social networks,biological networks,and transportation networks.The scientific community commonly labels such data,which deviate from Euclidean space definitions and represent structural relationships through net-work topology,as non-Euclidean data,encompassing graphs,hypergraphs,and dynamic graphs.Diverging from conventional serialized or grid-structured data,such as audios,im-ages,and videos,the data is irregular(graphs),multivariate(hypergraphs),and dynamic(dynamic graphs).Graph representation learning methods proficiently capture intricate topological relationships and nuanced semantic information within non-Euclidean data,thereby serving as a crucial tool for uncovering concealed information embedded in these relationships.This dissertation centers on a series of theoretical and methodological is-sues in graph representation learning methods and extends their application to practical scenarios.The specific research endeavors are outlined below:To address the issues of slow convergence and convergence oscillation in graph rep-resentation learning methods,particularly in irregular arranged scenarios,this dissertation introduces a regularized graph neural network based on approximate fractional order gradi-ent descent.By designing an approximate calculation strategy for fractional gradients,the fractional order chain rule calculation in the backpropagation process is approximated as the product operation of multiple gradients,thereby reducing the computational complex-ity of fractional gradients.By regularizing the graph neural network to learn parameters and limiting the size of model parameters,the stability of neural network convergence is ensured.Experiments on citation and community network datasets demonstrate that the fractional order graph neural network achieves higher classification performance than other graph embedding methods and first-order graph neural networks,with a faster con-vergence rate than first-order graph neural networks.To tackle the challenges of oversmoothing and overfitting in hypergraph representa-tion learning methods,particularly in multivariate and multi-modal scenarios,this disser-tation introduces a multi-modal hypergraph neural network based on parametric filtering and feature sampling.By designing a parameterized filter,hypergraph signals with differ-ent frequency components in the graph domain are extracted,which allows flexible learn-ing of the importance of different-order neighboring nodes in the hypergraph structure.Furthermore,the random feature sampling enriches the originally limited training sample space,enabling joint predictions of multiple probability matrices.By introducing a single hypergraph model,hyperedge and node features belonging to different modes are merged,achieving multi-modal graph data representation and learning.Compared to other base-line models for hypergraph learning and multi-modal learning,the proposed multi-modal hypergraph neural network achieves higher recognition accuracy on hypergraph datasets and multi-modal datasets.To address the issue of dynamic correlation between network parameters and node features in dynamic graph representation learning methods,this dissertation introduces a discrete dynamic graph neural network.By incorporating Gated Recurrent Unit net-work layers,the weight parameters of graph neural network layers at each time step are encoded to ensure the temporal correlation of the network parameters.By integrating Long Short-Term Memory neural network layers,the temporal features of nodes embed-ded through graph neural networks are processed,ensuring the temporal correlation of the embedded node features.Experiments on dynamic edge prediction,edge classification,and node classification tasks,demonstrate that the proposed dynamic graph neural net-work attains higher recognition accuracy and superior generalization ability compared to dynamic graph baseline models.This dissertation further selects the wireless communication scenario,encompassing the characteristics of the three complex structural scenarios mentioned above - irregularity,multi-connectivity and multi-modality,and dynamics.Focusing on the typical problem of power allocation optimization in wireless communication scenarios,the practical appli-cation of graph representation learning methods is explored.First,dynamic graph mod-els are employed to model the pairwise connection relationships between transceivers in ad-hoc networks,capturing the dynamic topological structures under varying numbers of transceivers.Next,dynamic hypergraph models are used to model the high-order implicit multi-connectivity relationships between base stations and multiple users in cellular net-works,capturing the dynamic topological structures under different numbers of base sta-tions and user devices.Designing the synchronous training loss function,the models are adaptable to time-varying channel state information and dynamic topological structures,ensuring strong generalization and transfer learning capabilities.To validate the effective-ness of the proposed power allocation scheme,experiments are conducted on three wire-less communication channel models - the Gaussian channel model,ad-hoc network model,and cellular network model.For the Gaussian channel model and ad-hoc network model,graph neural networks outperform other power allocation schemes in terms of achievable rates and inference speed.For the cellular network model,hypergraph neural networks achieve outstanding data rates.This provides practical validation and demonstration for the application of graph representation learning methods in real communication scenarios.