Research On Geometric Network Models And Application

Complex network is the theory of describing entity relation in complex systems.Many complex relations in the real world can be represented by complex networks.Generally,realistic networks exhibit strong regularity which includes the scale-free feature,high clustering,small-world effect and network community structure.Research shows that the real network structure is essentially related to geometric space.The relevant properties of geometric space can be used to describe the statistical characteristics of the network.Using geometric network models to study complex networks is the main research method in the field of complex networks.In this paper,by a unified framework of geometric network model,we study network generation,complex networks representation and the applications of geometrically complex networks.The research content includes:(1)We study the dynamic geometric network generation model.In order to describe the dynamic features of the real network structure,we proposed a dynamic geometric network generation model.Based on the description of the formation process of connecting edges over time as a Poisson/Hawks stochastic process,the proposed model can simultaneously describe the dynamic and structural properties of real network.We derives the key characteristics of complex network,such as the average degree,clustering coefficient,and average path length.Theories and experiments show that the proposed model can accurately reproduce real network generation process.Scale-free,high clustering,small-world and community features can be generated simultaneously.(2)We investigate hyperbolic representation of weighted complex networks.Geometric network model reproduces real network generation.In this paper,we specifically considers networks embedding in hyperbolic space based on weighted hyperbolic network generative model.Aiming at the non-convex characteristics of the embedding optimization problem,we proposes a hyperbolic embedding method of the weighted network based on the eigendecomposition of the Laplacian matrix,the greedy algorithm and the parameterized gradient optimization algorithm.This method prevents hyperbolic embedding optimization from falling into the local maxima.Experiments show the hyperbolic embedding representation has the capability to preserve node similarities and achieves good performance in link prediction,node classification and network navigation.(3)We study geometric random network based artificial neural networks.Traditional neural network models are usually based on artificially designed network structures.As an application of geometric network models,we discusses the performance of artificial neural networks with geometric characteristics and real network features.We use geometric complex network model to simulate the network structure with real network characteristics,and uses it to design neural network architecture.Based on deep learning technology,a neural network model based on geometric network is constructed.Numerical results show that the network structure with real network characteristics has good classification performance,and its performance exceeds that of the currently widely used neural network structure.Based on the geometric neural network model,we also study the relationship between neural network structure and performance,as well as the relationship between node location and its classification function.The results show that high-performance networks generally have the characteristics of sparseness,homogeneity,and local connection;the network nodes distributed in adjacent geometric regions are related in classification function;sparse networks have a strong ability to resist node failure.