  Network (or graph) embedding is the task to map the nodes of a graph to a
lower dimensional vector space, such that it preserves the graph properties and
facilitates the downstream network mining tasks. Real world networks often come
with (community) outlier nodes, which behave differently from the regular nodes
of the community. These outlier nodes can affect the embedding of the regular
nodes, if not handled carefully. In this paper, we propose a novel unsupervised
graph embedding approach (called DMGD) which integrates outlier and community
detection with node embedding. We extend the idea of deep support vector data
description to the framework of graph embedding when there are multiple
communities present in the given network, and an outlier is characterized
relative to its community. We also show the theoretical bounds on the number of
outliers detected by DMGD. Our formulation boils down to an interesting minimax
game between the outliers, community assignments and the node embedding
function. We also propose an efficient algorithm to solve this optimization
framework. Experimental results on both synthetic and real world networks show
the merit of our approach compared to state-of-the-arts.
