Research On Complex Network Kernel Methods And Functions Backbones Based On Higher-Order Structure

In our real world,many complex systems can be modeled as a complex network for analysis.In recent years,the structure and functions of complex networks have received increasing attention.As the scale of complex networks continues to grow,it becomes more and more difficult to understand the network topology and functions.Therefore,it becomes challenging to filter redundant information of the network and characterize the network structure.In this case,studying the kernel methods of complex networks and extracting the backbones of complex networks can simplify the representation of the network and help us understand and statistically the topology and function of the network.Most of the existing researches attach importance to the statistical heterogeneity of connection patterns in complex networks,such as the low-order structure of the network: edges and points,which leads to the neglect of many valuable functional information in the network.At the same time,a large number of studies have revealed that the structure and function of the network can be reflected by some higher-order structural design principles of the network.Therefore,in this paper,we analyze the limitations of the traditional complex network kernel methods and network backbone extraction methods,and propose a kernel method based on higher-order structure Graphlet roles correlation and two methods to extract the functional backbone of the network based on the higher-order structure Motif.The main work of this article includes the following two aspects:First,a kernel method GRK for complex networks based on Graphlet roles correlation is proposed.First of all,through analysis,the correlation of the Graphlet roles of the network is closely related to the topology and function of the network.On this basis,we propose a new positive definite kernel method GRK and define it.The GRK core mainly generates the corresponding Graphlet role degree matrix by counting the Graphlet roles corresponding to each node in the network.Then,based on the Graphlet roles degree matrix of the network,the Pearson correlation of the Graphlet roles is calculated to map the structural similarity between the two networks.Finally,we applied the GRK kernel method to support vector machines to classify and predict five standard bioinformatics data sets to verify the performance of the kernel method.Second: Two methods for extracting network function backbones based on Motif:one is the global threshold method based on Motif(Motif-GT method),and the otheris the difference filtering method based on Motif(Motif-DF method).Firstly,according to the standardized saliency eigenvalue SP analysis,the saliency Motif structure set in the network is identified.Based on the saliency Motif structure set,the Motif weight attribute is added to the edges in the network.The Motif-GT method extracts effective edges by setting a global threshold,while the Motif-DF method filters important nodes and edges in the network based on the null hypothesis to extract the network backbone.We applied our method on four real-world networks,and analyzed the performance of the evaluation method by analyzing the size of the network backbone at a certain edge ratio and three metrics that characterize the network function.