Research Of Unsupervised Graph Embedding Representation Learning Based On Gaussian Distribution

Deep learning has developed rapidly and has been applied in various fields.Whether it is for sound data,image data or text data,it has achieved certain results.However,due to the particularity of graph data,it is not easy to use deep learning methods on graph data.The information of graph structure is more and more widespread in various fields,and the research on graph embedding is gradually increasing.Large-scale graph structure information is more and more widespread in various fields.In recent years,the research on applying deep learning to graphs has gradually increased,so that the technology of graph analysis has made significant progress.For graph embedding and network representation technologies,many existing methods represent the nodes in the graph as point vectors in a low-dimensional space.However,this has a limitation: we don’t have information about the uncertainty of the representation.When describing a node in a complex graph by a single point only,uncertainty is inherent.Graph2 Gauss algorithm represents nodes as full Gaussian distributions,capturing the information about uncertainty of the representation.We mainly study how to represent nodes as Gaussian distributions more effectively in this paper.First,we propose that embedding nodes in Wasserstein space based on G2 G algorithm.The Graph2 Gauss algorithm embeds the nodes in the graph structure data into a Gaussian distributions,and measures the distance between the Gaussian distributions in the embedding space by KL divergence.Strictly speaking,KL divergence cannot actually be used as a measure of distance.For KL divergence,it does not have symmetry and does not satisfy the triangle inequality.Further,measuring the distance of nodes in the corresponding graph in the hidden space cannot maintain the transitivity of the graph.However,transitivity is one of the most important characteristics for graphs and networks.We use the Wasserstein distance to measure the distance between distributions when representing the nodes in the graph as a Gaussian distribution.Unlike KL divergence,Wasserstein distance satisfies characteristics such as symmetry and triangular inequality,making Wasserstein distance be a metric for measuring distance between distributions.Among them,satisfying triangular inequality ensures that Wasserstein distance can keep nodes transitive.Therefore,the Wasserstein distance is very suitable as an indicator for measuring two points in the hidden space.Through the comparison of experiments on five real-world data sets,we find that the method proposed in this paper can obtain leading effect and prove the effectiveness of the algorithm.Secondly,considering the generality of Gaussian distribution in the embedded space,we propose that improving G2 G algorithm using Householder Flow in this paper.When representing the nodes in the graph as Gaussian distributions,the Graph2 Gauss algorithm only focuses on the diagonal covariance form.This can reduce the computational complexity more or less,but makes the Gaussian distributions in the hidden space lack of generality and not flexible enough to match the real posterior.Due to the limitation of the shape of distributions in the hidden space,the Graph2 Gauss algorithm cannot fully express and match the true posterior distribution.Therefore,in order to improve the accuracy of the distribution in the hidden space,enriching the generated distribution is a feasible solution.We propose to use Householder Flow to generalize the Gaussian distribution in the hidden space.Extensive results on multiple datasets demonstrates the effectiveness of our improvement of G2 G algorithm based on Householder Flow.