Frequency Analysis for Graph Convolution Network
Authors: Hoang NT, Takanori Maehara
Keywords: graph signal processing, frequency analysis, graph convolution neural network, simplified convolution network, semi-supervised vertex classification
TL;DR: We study the filtering effect of GCN and SGC on benchmark datasets, find that all datasets are low-frequency and state-of-the-art models do not work in high-frequency settings.
Abstract: In this work, we develop quantitative results to the learnablity of a two-layers Graph Convolutional Network (GCN). Instead of analyzing GCN under some classes of functions, our approach provides a quantitative gap between a two-layers GCN and a two-layers MLP model. Our analysis is based on the graph signal processing (GSP) approach, which can provide much more useful insights than the message-passing computational model. Interestingly, based on our analysis, we have been able to empirically demonstrate a few case when GCN and other state-of-the-art models cannot learn even when true vertex features are extremely low-dimensional. To demonstrate our theoretical findings and propose a solution to the aforementioned adversarial cases, we build a proof of concept graph neural network model with stacked filters named Graph Filters Neural Network (gfNN).