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.

翻译：由于从真实世界收集的图表数据仅仅是无噪音的,因此,图表的实用表达方式应该对噪音具有很强的活力。现有的研究通常侧重于地貌平滑,但没有触及几何结构。此外,大多数工作都采用L2-norm,追求全球光滑,这限制了图形神经网络的表达性。本文从特征和结构噪音两方面对图形数据进行规范化,其中客观功能与乘数交替方向法(ADMM)有效解决。拟议办法允许在不担心过度悬浮的情况下采用多层,并确保与最佳解决方案趋同。 经验性研究证明,即使在图表受到严重污染的情况下,我们的模型也比流行的图形共变情况要好得多。