Abstract
Uncovering community structures is important for understanding networks. Currently, several nonnegative matrix factorization algorithms have been proposed for discovering community structure in complex networks. However, these algorithms exhibit some drawbacks, such as unstable results and inefficient running times. In view of the problems, a novel approach that utilizes an initialized Bayesian nonnegative matrix factorization model for determining community membership is proposed. First, based on singular value decomposition, we obtain simple initialized matrix factorizations from approximate decompositions of the complex network’s adjacency matrix. Then, within a few iterations, the final matrix factorizations are achieved by the Bayesian nonnegative matrix factorization method with the initialized matrix factorizations. Thus, the network’s community structure can be determined by judging the classification of nodes with a final matrix factor. Experimental results show that the proposed method is highly accurate and offers competitive performance to that of the state-of-the-art methods even though it is not designed for the purpose of modularity maximization.
Highlights
Many complex systems in the real world have the form of networks whose edges are linked by nodes or vertices
We present a novel and running time efficient method for community detection based on Bayesian nonnegative matrix factorization (BNMF) with a simple
When the community structure is not clear, our method produces a unique solution, as represented by the red line, which is better than the BNMF results in terms of the average modularity
Summary
Many complex systems in the real world have the form of networks whose edges are linked by nodes or vertices. In these networks, there are many sub-graphs, called communities or modules, which have a high density of internal links. A number of methods have been developed for community detection in which an objective function is maximized or minimized. One of these community detection methods is nonnegative matrix factorization (NMF), which was proposed by Lee and Seung [3]. Wild et al [9] use ‘‘Clustering Centroid’’, which uses the centroid vector for initialization Another important initialization method is NNDSVD (nonnegative double singular value decomposition), which was proposed by C. NNDSVD uses the rank-2 matrix with the nearest positive approximation as its initialization and obtains better results than other initialization methods. The merits of this approach are as follows: i) computationally efficient and stable, ii) high accuracy in determining the membership of networks, and iii) overcoming the drawbacks of the maximum modularity criterion
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