Abstract
Community detection is a fundamental problem in the analysis of complex networks. Recently, many researchers have concentrated on the detection of overlapping communities, where a vertex may belong to more than one community. However, most current methods require the number (or the size) of the communities as a priori information, which is usually unavailable in real-world networks. Thus, a practical algorithm should not only find the overlapping community structure, but also automatically determine the number of communities. Furthermore, it is preferable if this method is able to reveal the hierarchical structure of networks as well. In this work, we firstly propose a generative model that employs a nonnegative matrix factorization (NMF) formulization with a l2,1 norm regularization term, balanced by a resolution parameter. The NMF has the nature that provides overlapping community structure by assigning soft membership variables to each vertex; the l2,1 regularization term is a technique of group sparsity which can automatically determine the number of communities by penalizing too many nonempty communities; and hence the resolution parameter enables us to explore the hierarchical structure of networks. Thereafter, we derive the multiplicative update rule to learn the model parameters, and offer the proof of its correctness. Finally, we test our approach on a variety of synthetic and real-world networks, and compare it with some state-of-the-art algorithms. The results validate the superior performance of our new method.
Highlights
Many real-world systems can be represented as complex networks, where the vertices represent the components of the systems and the links represent the interactions between them
We first describe our generative model, and present an algorithm based on nonnegative matrix factorization to learn the parameters of the model
The methods compared include: Louvain method [20] and Infomap [29], both of which are the most popular hard-partitioning methods; CPM [4], which is one of the most widely used overlapping community detection method; Fuzzy Infomap (F-Infomap) [30], which is an extension of Infomap to detect overlapping communities; SNMF [11] and BNMTF [12], which are the model-based methods based on nonnegative matrix factorization (NMF)
Summary
Many real-world systems can be represented as complex networks, where the vertices represent the components of the systems and the links represent the interactions between them. In complex networks, they share some common properties such as the small-world property [1] and power-law degree distributions [2]. Community structure, one of the most important inherent properties in complex networks, attracts a lot of attentions. It is regarded as groups of vertices with denser connections within groups but sparser connections between them [3]. It is PLOS ONE | DOI:10.1371/journal.pone.0119171 March 30, 2015
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