  Local community detection consists of finding a group of nodes closely
related to the seeds, a small set of nodes of interest. Such group of nodes are
densely connected or have a high probability of being connected internally than
their connections to other clusters in the network. Existing local community
detection methods focus on finding either one local community that all seeds
are most likely to be in or finding a single community for each of the seeds.
However, a seed member usually belongs to multiple local overlapping
communities. In this work, we present a novel method of detecting multiple
local communities to which a single seed member belongs. The proposed method
consists of three key steps: (1) local sampling with Personalized PageRank
(PPR); (2) using the sparseness generated by a sparse nonnegative matrix
factorization (SNMF) to estimate the number of communities in the sampled
subgraph; (3) using SNMF soft community membership vectors to assign nodes to
communities. The proposed method shows favorable accuracy performance and a
good conductance when compared to state-of-the-art community detection methods
by experiments using a combination of artificial and real-world networks.

Social and Information Networks;Physics and Society