This paper focuses on spectral graph convolutional neural networks (ConvNets), where filters are defined as elementwise multiplication in the frequency domain of a graph. In machine learning settings where the dataset consists of signals defined on many different graphs, the trained ConvNet should generalize to signal on graphs unseen in the training set. It is thus important to transfer filters from one graph to the other. Transferability, which is a certain type of generalization capability, can be loosely defined as follows: if two graphs describe the same phenomenon, then a single filter/ConvNet should have similar repercussions on both graphs. This paper aims at debunking the common misconception that spectral filters are not transferable. We show that if two graphs discretize the same continuous metric space, then a spectral filter/ConvNet has approximately the same repercussion on both graphs. Our analysis is more permissive than the standard analysis. Transferability is typically described as the robustness of the filter to small graph perturbations and re-indexing of the vertices. Our analysis accounts also for large graph perturbations. We prove transferability between graphs that can have completely different dimensions and topologies, only requiring that both graphs discretize the same underlying continuous space.

本文重点介绍了频谱图卷积神经网络(ConvNets)并阐述了其在分析不同的图时的泛化能力，分析了滤波器的可转换性以及它们对顶点重编和大幅度图形扰动的鲁棒性，最终证明相同现象的不同图之间的滤波器可转换性。

谱图卷积神经网络的可传递性