Title: COMMUNITY PRESERVING NODE EMBEDDING. Abstract: Detecting communities or the modular structure of real-life networks (e.g. a social
network or a product purchase network) is an important task because the way a
network functions is often determined by its communities.
The traditional approaches to community detection involve modularity-based approaches,
which generally speaking, construct partitions based on heuristics that
seek to maximize the ratio of the edges within the partitions to those between
them. Node embedding approaches, which represent each node in a graph as a
real-valued vector, transform the problem of community detection in a graph to
that of clustering a set of vectors. Existing node embedding approaches are primarily
based on first initiating uniform random walks from each node to construct
a context of a node and then seeks to make the vector representation of
the node close to its context. However, standard node embedding approaches do
not directly take into account the community structure of a network while constructing
the context around each node. To alleviate this, we explore two different
threads of work. First, we investigate the use of biased random walks (specifically,
maximum entropy based walks) to obtain more centrality preserving embedding
of nodes, which we hypothesize may lead to more effective clusters in the embedded
space. Second, we propose a community structure aware node embedding
approach where we incorporate modularity-based partitioning heuristics into
the objective function of node embedding. We demonstrate that our proposed approach
for community detection outperforms a number of modularity-based baselines
as well as K-means on a standard node-embedded vector space (specifically,
node2vec) on a wide range of real-life networks of different sizes and densities.