Augmenting graph convolutional neural networks with highpass filters

In this paper, we propose a graph neural network that employs high-pass filters in the convolutional layers. To do this, we depart from a linear model for the convolutional layer and consider the case of directed graphs. This allows for graph spectral theory and the connections between eigenfunctions over the graph and Fourier analysis to employ graph signal processing to obtain an architecture that “concatenates” low and high-pass filters to process data on a connected graph. This yields a method that is quite general in nature applicable to directed and undirected graphs and with clear links to graph spectral methods, Fourier analysis and graph signal processing. Here, we illustrate the utility of our graph convolutional approach to the classification using citation datasets and knowledge graphs. The results show that our method provides a margin of improvement over the alternative.