Graph theoretic and stochastic block models integrated with matrix factorization for community detection

In this work we describe a novel method to integrate graph theoretic and stochastic block models by using matrix factorization for the purposes of data mining interesting patterns. Complex networks represent pairwise patterns of connectivity between nodes and can reveal much information terms of the relationships between entities. Further information on these relationships can be extracted through a careful analysis of the shared communities they coexist with. Here we use the strengths of stochastic block models which are widely used for community detection and are a natural extension of complex networks. However, numerous false positive community affiliations are often identified. We integrate the two types of network with a non negative matrix factorization function. We test and validate our methods against other competing systems on several data sets