  Learning low-dimensional representations on graphs has proved to be effective
in various downstream tasks. However, noises prevail in real-world networks,
which compromise networks to a large extent in that edges in networks propagate
noises through the whole network instead of only the node itself. While
existing methods tend to focus on preserving structural properties, the
robustness of the learned representations against noises is generally ignored.
In this paper, we propose a novel framework to learn noise-free node
representations and eliminate noises simultaneously. Since noises are often
unknown on real graphs, we design two generators, namely a graph generator and
a noise generator, to identify normal structures and noises in an unsupervised
setting. On the one hand, the graph generator serves as a unified scheme to
incorporate any useful graph prior knowledge to generate normal structures. We
illustrate the generative process with community structures and power-law
degree distributions as examples. On the other hand, the noise generator
generates graph noises not only satisfying some fundamental properties but also
in an adaptive way. Thus, real noises with arbitrary distributions can be
handled successfully. Finally, in order to eliminate noises and obtain
noise-free node representations, two generators need to be optimized jointly,
and through maximum likelihood estimation, we equivalently convert the model
into imposing different regularization constraints on the true graph and noises
respectively. Our model is evaluated on both real-world and synthetic data. It
outperforms other strong baselines for node classification and graph
reconstruction tasks, demonstrating its ability to eliminate graph noises.
