  Network embedding has become a hot research topic recently which can provide
low-dimensional feature representations for many machine learning applications.
Current work focuses on either (1) whether the embedding is designed as an
unsupervised learning task by explicitly preserving the structural connectivity
in the network, or (2) whether the embedding is a by-product during the
supervised learning of a specific discriminative task in a deep neural network.
In this paper, we focus on bridging the gap of the two lines of the research.
We propose to adapt the Generative Adversarial model to perform network
embedding, in which the generator is trying to generate vertex pairs, while the
discriminator tries to distinguish the generated vertex pairs from real
connections (edges) in the network. Wasserstein-1 distance is adopted to train
the generator to gain better stability. We develop three variations of models,
including GANE which applies cosine similarity, GANE-O1 which preserves the
first-order proximity, and GANE-O2 which tries to preserves the second-order
proximity of the network in the low-dimensional embedded vector space. We later
prove that GANE-O2 has the same objective function as GANE-O1 when negative
sampling is applied to simplify the training process in GANE-O2. Experiments
with real-world network datasets demonstrate that our models constantly
outperform state-of-the-art solutions with significant improvements on
precision in link prediction, as well as on visualizations and accuracy in
clustering tasks.
