Research On Bayesian Stochastic Block Model For Noisy Network

Complex network is an abstract representation of complex system.Entities in the system are abstractly represented as network nodes,and interactions between entities are abstractly represented as network connections.Because of its universality,complex networks are widely used in sociology,biology,computer science and other disciplines.The research of related theories and methods has profound scientific significance.For the real network without any prior knowledge,how to explore its topology efficiently is an important task of complex network analysis.As a generation model,the stochastic block model based on Bayesian theory can deal with this problem well.Compared with single structure discovery,stochastic block model partitions the nodes in the network into their corresponding block structures by learning algorithm,which can discover many kinds of structures hidden in the network and the interaction between them.However,due to the complexity of the real system itself,there are inevitably some noisy nodes in the network,which behave abnormally and do not have a specific connection pattern.In the process of network partitioning,noisy nodes are randomly assigned to each block,which will affect the definition of block structure in stochastic block model to a large extent,and finally lead to the deviation of network topology structure from its real structure.In view of the above problems,this paper studies the stochastic block model for noisy network,and the main work is as follows:Firstly,this paper proposes a Bayesian stochastic block model for modeling noisy networks.As an extension method of stochastic block model,the model no longer uses connection density to define block structure,but partitions nodes according to the way of network generation,so it is more suitable for partitioning real networks without prior knowledge.At the same time,the model can learn different block connection probability,and then find out that many kinds of structures in the network even have a mixture of many kinds of structures.For the undirected network with noisy nodes,the model describes the connection between noisy nodes and other nodes in detail by combining the symmetry of the network,reduces the impact of noisy nodes on network structure partitioning,and improves the accuracy of noisy network structure discovery.Then,this paper chooses the variational Bayesian inference as the parameter learning strategy to learn the posterior distribution of each parameter in the model,and provides a complete derivation process.Besides,in the study of block model,how to determine the optimal number of blocks in the network is called the model selection problem,which is an important task for the model to automatically explore the network structure.In this paper,the evidence lower bound of the model is derived in detail,and it is used as the basis of model selection.The model selection function is verified by synthetic data set and real data set.Finally,by comparing with six state of the art algorithms in synthetic network and real network data set,the model in this paper has been proved to have good performance in dealing with the task of noisy network structure partitioning from three aspects: the accuracy of network structure partitioning,the diversity of structure discovery and the robustness of structure partitioning.This model is a typical generation model,so we can learn the relevant parameters of the network.The experiment shows that it has the ability to recover the parameters of the generated network.