Beyond Low-pass Filtering: Graph Convolutional Networks with Automatic Filtering

TL;DR

This paper introduces AutoGCN, a novel graph convolutional network that captures the full spectrum of graph signals and automatically adjusts filter bandwidth, overcoming limitations of traditional low-pass filters.

Contribution

AutoGCN is the first to automatically adapt filter bandwidth in spectral graph convolution, capturing high-frequency signals and improving performance.

Findings

AutoGCN outperforms baseline methods significantly.

It captures full spectrum of graph signals.

AutoGCN is localized in space and based on spectral theory.

Abstract

Graph convolutional networks are becoming indispensable for deep learning from graph-structured data. Most of the existing graph convolutional networks share two big shortcomings. First, they are essentially low-pass filters, thus the potentially useful middle and high frequency band of graph signals are ignored. Second, the bandwidth of existing graph convolutional filters is fixed. Parameters of a graph convolutional filter only transform the graph inputs without changing the curvature of a graph convolutional filter function. In reality, we are uncertain about whether we should retain or cut off the frequency at a certain point unless we have expert domain knowledge. In this paper, we propose Automatic Graph Convolutional Networks (AutoGCN) to capture the full spectrum of graph signals and automatically update the bandwidth of graph convolutional filters. While it is based on graph spectral theory, our AutoGCN is also localized in space and has a spatial form. Experimental results show that AutoGCN achieves significant improvement over baseline methods which only work as low-pass filters.