Structural regularity exploration in multidimensional networks via Bayesian inference

Multidimensional networks, networks with multiple kinds of relations, widely exist in various fields in the real world, such as sociology, chemistry, biology and economics. One fundamental task of network analysis is to explore network structure, including assortative structure (i.e., community structure), disassortative structure (e.g., bipartite structure) and mixture structure, that is, to find structural regularities in networks. There are two aspects of structural regularity exploration: (1) group partition—how to partition nodes of networks into different groups, and (2) group number—how many groups in networks. Most existing structural regularity exploration methods for multidimensional networks need to pre-assume the structure type (e.g., the community structure) and to give the group number of networks, among which the structure type is a guide to group partition. However, the structure type and group number are usually unavailable in advance. To explore structural regularities in multidimensional networks well without pre-assuming which type of structure they have, we propose a novel feature aggregation method based on a mixture model and Bayesian theory, called the multidimensional Bayesian mixture (MBM) model. To automatically determine the group number of multidimensional networks, we further extend the MBM model using Bayesian nonparametric theory to a new model, called the multidimensional Bayesian nonparametric mixture (MBNPM) model. Experiments conducted on a number of synthetic and real multidimensional networks show that the MBM model outperforms other related models on most networks and the MBNPM model is comparable to the MBM model.