Uncovering Community Structures with Initialized Bayesian Nonnegative Matrix Factorization by Xianchao Tang, Tao Xu, Xia Feng, and, Guoqing Yang.
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.
Some titles grab you by the lapels and say, “READ ME!,” don’t they? 😉
I found the first paragraph a much friendlier summary of why you should read this paper (footnotes omitted):
Many complex systems in the real world have the form of networks whose edges are linked by nodes or vertices. Examples include social systems such as personal relationships, collaborative networks of scientists, and networks that model the spread of epidemics; ecosystems such as neuron networks, genetic regulatory networks, and protein-protein interactions; and technology systems such as telephone networks, the Internet and the World Wide Web . In these networks, there are many sub-graphs, called communities or modules, which have a high density of internal links. In contrast, the links between these sub-graphs have a fairly lower density . In community networks, sub-graphs have their own functions and social roles. Furthermore, a community can be thought of as a general description of the whole network to gain more facile visualization and a better understanding of the complex systems. In some cases, a community can reveal the real world network’s properties without releasing the group membership or compromising the members’ privacy. Therefore, community detection has become a fundamental and important research topic in complex networks.
If you think of “the real world network’s properties” as potential properties for identification of a network as a subject or as properties of the network as a subject, the importance of this article becomes clearer.
Being able to speak of sub-graphs as subjects with properties can only improve our ability to compare sub-graphs across complex networks.
BTW, all the data used in this article is available for downloading: http://dx.doi.org/10.6084/m9.figshare.1149965
I first saw this in a tweet by Brian Keegan.