Graph Embedding Method Researches Based On Graph Signal Processing

We produce a large amount of data in our work and life.With the development,the data is recorded in storage devices.Most of the data is stored with the form of graph.Compared with data in euclidean space,the data of graph structure is more sparse and complex.Due to the characteristics of graph,the directly processing of it is inefficient.Therefore,acquiring better representation of graph to assist various tasks by proper designs becomes a eye-catching problem in researching.In this paper,we summarize the technology of graph representation methods firstly.For the three kinds of mainstream methods in graph embedding,matrix factorization,random walk and machine learning,we give out the advantages and disadvantages about them.Besides,we introduce graph signal processing(GSP)into graph embedding by employing Z-laplacian to evaluate time bias and graph wavelet to sample in space domain.It introduces spectral domains into graph.As a result,the new tools can get some new conclusions which can't be recovered by directly computation in the graph domains.Therefore,we can employ the related theories in graph signal processing,finding relations in the spectral domain and providing more information for graph embedding.By employing the theory of GSP,we modify the methods of graph embedding and propose three new algorithms.In this paper,we will combine the theory of graph signal processing with graph embedding.We get three new graph embedding algorithms by adjust settings and improve designs of original methods in graph embedding.Z-Net MF combines Z-laplacian,matrix factorization and random walk,and Node MF takes the thought of Node2 vec and design a new graph shift.The fusion of theories generates two kinds of matrix factorization based on biased random walk.They represent time domain biases and graph domain biases,which perform different properties.As for another method,it takes the graph structure representation ability of graph wavelets.The new methods,named Wave Sage employ graph wavelet as a sampling method of neighbors to improve the appearance of Graph Sage.We test the performance of these methods in multiple tasks and datasets,and the results of experiment prove that our methods have good performance and different properties comparing with original algorithms.In the end,we summarize our theories and give out the present problems and the research directions.