Proximity Preserving Nonnegative Matrix Factorization

Abstract

We consider the problem of community detection. Although network embedding and representation learning methods are recently getting popular, we claim that they fall into suboptimal solutions for community detection, because they are based on indirect approach, which requires to apply clustering methods such as k-means to the embedding/representation vectors. We present PPNMF, proximity preserving nonnegative matrix factorization for community detection. The idea of PPNMF is three-fold. 1) PPNMF is based on direct approach: it directly minimizes its loss function for community detection. 2) Users can control the importance of observed edges over unobserved edges. 3) PPNMF can precisely capture the effects of the first-order and second-order proximities of vertexes to communities. Also, PPNMF employs the Adamic Adar index as the second-order proximity. The experiments validate that PPNMF performs better or comparable to existing methods in various real datasets for the tasks of community detection.