Community Discovery Algorithm For Hybrid Multi-Layer Networks Based On Split Likelihood Framework

Network science has been widely used in computer science,social science,biology,statistics and other disciplines.Typical examples include social networks,transportation networks,brain networks,etc.Community structure is one of the most important network structure features in the process of complex network research.Network community discovery plays a key role in the in-depth analysis of large-scale actual community structure.At present,researching on network science mainly focuses on the study of the single chip networks.However,in practical situations,multi-layer networks are very common,and it is necessary to study them.For example,multi-layer social networks obtained from different social platforms,or multi-layer human brain network composed of brain samples of different ages.A variety of multi-layer community discovery methods have been proposed to study the shared community structure between multi chip networks,but most of them cannot be extended to large-scale multi-layer networks.In order to study the community discovery problem and of large-scale multi chip networks,In this paper,based on the Mixed ER Random Graph Model(MERM),a Maximum Maximazation(MM)algorithm is proposed based on the Expectation Maximization(EM)algorithm to study the problem of aggregating multiple networks into K classes without degradation of the community structure in each network,and gives the convergence proof of the algorithm.Then,based on the Mixed Stochastic Random Block Model(MSBM),the Mixed Split Likelihood Random Block Model(MSL-SBM)is proposed under the Split Likelihood(SL)framework,and the MMSL algorithm for multi-layer networks is proposed.The multi chip networks with multiple communities in each network are studied,the community structure in each network is obtained,and the multi chip networks are clustered into K classes,and the convergence of the MMSL algorithm is proved.In order to ensure the theoretical properties of the algorithm,under certain assumptions,the consistency of the MMSL algorithm is proved.Finally,through a large number of numerical simulations,the advantages of MM algorithm and MMSL algorithm in the accuracy and computational efficiency of the corresponding scenarios are verified respectively.The actual data analysis based on COBRE dataset further shows the practical application value of MMSL algorithm.