Neural Computing and Applications

, Volume 29, Issue 9, pp 413–424 | Cite as

Structural regularity exploration in multidimensional networks via Bayesian inference

  • Yi Chen
  • Xiaolong Wang
  • Buzhou Tang


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.


Multidimensional networks Network structure Structural regularity exploration Mixture model Bayesian nonparametric theory 



This paper is supported in part by Grants: National 863 Program of China (2015AA015405), NSFCs (National Natural Science Foundations of China) (61573118, 61402128, 61473101 and 61472428), Special Foundation for Technology Research Program of Guangdong Province (2015B010131010), Strategic Emerging Industry Development Special Funds of Shenzhen (20151013161937, JSGG20151015161015297 and JCYJ20160531192358466), Innovation Fund of Harbin Institute of Technology (HIT.NSRIF.2017052), Program from the Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education (93K172016K12) and CCF-Tencent Open Research Fund (RAGR20160102).

Compliance with ethical standards

Conflict of interest

The article is an extension of the paper entitled “Structural regularity exploration in multidimensional networks” published in the 22nd International Conference on Neural Information Processing (ICONIP 2015).

Supplementary material

521_2017_3041_MOESM1_ESM.doc (268 kb)
Supplementary material 1 (DOC 268 kb)


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Copyright information

© The Natural Computing Applications Forum 2017

Authors and Affiliations

  1. 1.Department of Computer Science and TechnologyShenzhen Graduate School, Harbin Institute of TechnologyShenzhenChina
  2. 2.School of Computer Science and TechnologyHarbin Institute of TechnologyHarbinChina

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