IEEE Trans Pattern Anal Mach Intell. 2022 Jul;44(7):3496-3507. doi: 10.1109/TPAMI.2021.3054830. Epub 2022 Jun 3.
Popular graph neural networks implement convolution operations on graphs based on polynomial spectral filters. In this paper, we propose a novel graph convolutional layer inspired by the auto-regressive moving average (ARMA) filter that, compared to polynomial ones, provides a more flexible frequency response, is more robust to noise, and better captures the global graph structure. We propose a graph neural network implementation of the ARMA filter with a recursive and distributed formulation, obtaining a convolutional layer that is efficient to train, localized in the node space, and can be transferred to new graphs at test time. We perform a spectral analysis to study the filtering effect of the proposed ARMA layer and report experiments on four downstream tasks: semi-supervised node classification, graph signal classification, graph classification, and graph regression. Results show that the proposed ARMA layer brings significant improvements over graph neural networks based on polynomial filters.
流行的图神经网络在图上基于多项式谱滤波器实现卷积操作。在本文中，我们提出了一种受自回归移动平均 (ARMA) 滤波器启发的新型图卷积层，与多项式滤波器相比，它提供了更灵活的频率响应，对噪声更鲁棒，并且更好地捕捉全局图结构。我们提出了一种基于递归和分布式公式的 ARMA 滤波器的图神经网络实现，得到了一个在节点空间局部化的卷积层，并且可以在测试时转移到新的图上。我们进行了频谱分析来研究所提出的 ARMA 层的滤波效果，并在四个下游任务上进行了实验：半监督节点分类、图信号分类、图分类和图回归。结果表明，所提出的 ARMA 层在基于多项式滤波器的图神经网络上带来了显著的改进。
