Community Detection In Complex Network Based On Mixed Gauss Model

Complex network is the basic structure of complex system and the tool of study complex system. It has powerful ability of description, and has been widely used in various disciplines. In recent years, the researchers found that all the complex networks of different disciplines have community structure.Detection community structure in the network can help people to analyze various characteristics of complex networks. With the new application field expanded constantly, complex system problems gradually diversified, complex network topology structure and properties is also more complex. It is put forward higher requirements for speed and accuracy of the community detecting algorithm. Although there are many algorithms for community finding, but few of them can effectively depict network characteristics and seek out community structure rapidly and exactly.This paper proposes a new model for detecting community——Gaussian Mixture Model which based on principal component analysis. In this model, it is assumed that the different community structure in same network is generated by different Gaussian model, namely different community has different formation mechanism. This assumption is more accord with the reality. For the parameters in the model, we use expectation maximization algorithm to solve. Because of the large scale of complex networks, reduce the time complexity is the key of the research, at the beginning of the algorithm. In order to make the algorithm more efficient, the principal component analysis has been used to reduce the dimension of the adjacency matrix.Through a series of classic experiments on actual networks and compared with the existing community detecting algorithms, we can found that our model is more flexible and can be used to deal with different types of networks, such as weight networks, directed networks, overlap networks. At the same time, the results of algorithm are more accurate and consistent with the actual division of the network. Adjacency matrix dimension has been reduced by using principal component analysis. The final results had little impact, if the principal component contribution reached more than ninety percent. This makes our algorithm can handle large and complex networks, such as biological network, internet network, social network, etc.