  As graph data collected from the real world is merely noise-free, a practical
representation of graphs should be robust to noise. Existing research usually
focuses on feature smoothing but leaves the geometric structure untouched.
Furthermore, most work takes L2-norm that pursues a global smoothness, which
limits the expressivity of graph neural networks. This paper tailors
regularizers for graph data in terms of both feature and structure noises,
where the objective function is efficiently solved with the alternating
direction method of multipliers (ADMM). The proposed scheme allows to take
multiple layers without the concern of over-smoothing, and it guarantees
convergence to the optimal solutions. Empirical study proves that our model
achieves significantly better performance compared with popular graph
convolutions even when the graph is heavily contaminated.
