Analysis Of Complex Network Structures Based On Statistical Inference

Complex networks, a set of nodes connected by a set of edges, provide a powerful tool to represent many real-world complex systems, such as world wide web, internet of things, ecological networks, neural networks and social networks. Community detection as one of the most important tasks for complex network analysis has attracted considerable multidisciplinary researchers’ attention. During the past several years, a large number of community detection methods have been proposed by researchers from diverse disciplines. However, there are still several challenges, including overlapping community detection, heterogeneous network community detection, network structure exploration,application of network communities and others.This thesis proposes several statistical inference based models to overcome problems mentioned above, mainly including overlapping community detection and structural regularity exploration. In the case of overlapping community detection, we focus on signed networks and weighted networks, in which the former considers the edge polarity(i.e.,positive and negative), while the latter considers the edge strength(i.e., strong and weak).In the case of structural regularity exploration, we focus on homogeneous networks and heterogeneous networks, in which the former are composed of mono-nodes and monoedges, while the latter are composed of multi-nodes(e.g., nodes with attributes) or multiedges(e.g., multi-dimensional edges). The main contents are as follows.The first study focuses on overlapping community detection in signed networks based on a mixture model. Most of the existing algorithms for community detection in signed networks aim at providing a hard-partition of the network whereby any node should belong to a community or not. However, overlapping communities widely exist in many real-world networks. We propose a signed probabilistic mixture model to detect overlapping communities in undirected signed networks. It is a variant of the probabilistic mixture model which generates positive and negative links with different probabilities.Experiments on a number of signed networks show that our model can detect overlapping communities and outperforms other state-of-the-art models.The second study focuses on overlapping community detection in weighted networks based on a Bayesian approach. One existing probabilistic mixture model performs well on overlapping community detection in weighted networks. The main shortcoming of this model lies in that in some networks it allows some nodes not to belong to any community, leading them fail in these networks. We propose a Bayesian mixture network model to detect overlapping communities in weighted networks. The model avoids the abovementioned problem by introducing several prior knowledge. Experiments on a number of real and synthetic networks show that our model can detect overlapping communities and identifies community structures as the same as other state-of-the-art models.The third study focuses on automatic exploration of structural regularities in complex networks based on a Bayesian nonparametric model. Most existing structure exploration methods need to specify either a group number or a certain type of structure when they are applied to a network. In the real world, however, not only the group number but also the certain type of structure that a network has are usually unknown in advance. We propose a Bayesian nonparametric mixture model to automatically explore structural regularities in complex networks without any prior knowledge about the group number or the certain type of structure. The model extends an existing mixture model which can explore the structural regularities but need to specify the community number to a Bayesian nonparametric framework and adopts the Dirichlet proccess to automatically determine the group number. Experiments conducted on a large number of networks with different structures show that our model can explore structural regularities and determine the group number automatically and identify network structures as the same as other state-of-the-art models. In addition, we also apply the Bayesian nonparametric mixture model to friend recommendation for improving recommendation performance.The fourth study focuses on automatic exploration of structural regularities in heterogeneous networks based on a Bayesian nonparametric model. Two types of heterogeneous networks: networks with node attributes and multidimensional networks, are considered in our studies. One main challenge of networks with node attributes is how to apply attribute information for improvement. We propose a Bayesian nonparametric attribute model to automatically explore structural regularities in networks with node attributes. It aggregates the node links and attributes via a shared hidden variable. Experiments on a number of networks with node attributes show that our model can explore structural regularities and determine the group number automatically and identify network structures as the same as other state-of-the-art models. The main limitation of existing structure exploration methods for multidimensional networks lies in that they need to specify a certain type of structure, such as community structure. We propose a multidimensional Bayesian nonparametric mixture model to automatically explore structural regularities in multidimensional networks. The model first extracts structural features from each dimension via a structural regularity exploration model and then aggregates these features to explore the structural regularities of multidimensional networks via an existing clustering method. Experiments on a number of multidimensional networks show our model can identify community structures or mixture structures as the same as other state-of-the-art models and outperform other models in networks with disassortative structure.