Application Of Spectral Clustering Combined With Nystr(?)m Method In Multilayer Network

Traditional network science research object only includes single object type and relationship,ignoring the heterogeneity of the object and the diversity of the relationship.Multilayer Network is the expansion and extension of traditional network.Each layer of network node belongs to different object types,and each layer of network node is closely related.At present,the main research content is to explore its network topology structure and its nature,dynamic characteristics and generation mechanism,network design principle and application,etc.However,the research on finding the internal channel of multi-layer network through clustering is relatively less.Starting from the traditional spectral clustering,this paper assumes the data distribution and constructs the adjacency matrix according to the data structure characteristics of multi-layer network,simplifies the process of spectral clustering solution by means of the Nystrom method,realizes the clustering of multi-layer network.It is worth noting that it is practical to simplify the calculation by Nystrom method.According to the mathematical derivation,the simplified clustering process only uses the underlying intra-layer relationship and the inter-layer relationship,ignoring the upper-layer intra-layer relationship.When the latter has less impact on the whole network,the clustering effect is better,otherwise the clustering effect will be greatly reduced.In addition,the number of real categories is not known in real life.This paper also explores the possibility of using the eigenvalue distribution of the adjacency matrix to determine the number of categories.This method works well in most scenarios.Finally,this paper compares the robust of this method and other methods with cervical cancer data in the TCGA database,and the methods proposed in this paper have achieved good results in two-layer network.