  Graph clustering has been studied extensively on both plain graphs and
attributed graphs. However, all these methods need to partition the whole graph
to find cluster structures. Sometimes, based on domain knowledge, people may
have information about a specific target region in the graph and only want to
find a single cluster concentrated on this local region. Such a task is called
local clustering. In contrast to global clustering, local clustering aims to
find only one cluster that is concentrating on the given seed vertex (and also
on the designated attributes for attributed graphs). Currently, very few
methods can deal with this kind of task. To this end, we propose two quality
measures for a local cluster: Graph Unimodality (GU) and Attribute Unimodality
(AU). The former measures the homogeneity of the graph structure while the
latter measures the homogeneity of the subspace that is composed of the
designated attributes. We call their linear combination as Compactness.
Further, we propose LOCLU to optimize the Compactness score. The local cluster
detected by LOCLU concentrates on the region of interest, provides efficient
information flow in the graph and exhibits a unimodal data distribution in the
subspace of the designated attributes.
