A Nonnegative Matrix Factorization Approach for Multiple Local Community Detection

Abstract

Existing works on local community detection in social networks focus on finding one single community a few seed members are most likely to be in. In this work, we address a much harder problem of multiple local community detection and propose a Nonnegative Matrix Factorization algorithm for finding multiple local communities for a single seed chosen randomly in multiple ground truth communities. The number of detected communities for the seed is determined automatically by the algorithm. We first apply a Breadth-First Search to sample the input graph up to several levels depending on the network density. We then use Nonnegative Matrix Factorization on the adjacency matrix of the sampled subgraph to estimate the number of communities, and then cluster the nodes of the subgraph into communities. Our proposed method differs from the existing NMF-based community detection methods as it does not use“ argmax ” function to assign nodes to communities. Our method has been evaluated on real-world networks and shows good accuracy as evaluated by the F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> score when comparing with the state-of-the-art local community detection algorithm.