Framework for Designing Filters of Spectral Graph Convolutional Neural Networks in the Context of Regularization Theory

TL;DR

This paper introduces a generalized framework for designing spectral graph convolutional filters based on regularization theory, demonstrating improved performance in semi-supervised node classification tasks.

Contribution

It develops a unified framework linking spectral GCNN filters with regularization properties, including novel filters with better regularization behavior.

Findings

New filters outperform existing methods in semi-supervised node classification

Many state-of-the-art GCNN filters are special cases of the proposed framework

The framework provides a theoretical basis for regularization in spectral GCNNs

Abstract

Graph convolutional neural networks (GCNNs) have been widely used in graph learning. It has been observed that the smoothness functional on graphs can be defined in terms of the graph Laplacian. This fact points out in the direction of using Laplacian in deriving regularization operators on graphs and its consequent use with spectral GCNN filter designs. In this work, we explore the regularization properties of graph Laplacian and proposed a generalized framework for regularized filter designs in spectral GCNNs. We found that the filters used in many state-of-the-art GCNNs can be derived as a special case of the framework we developed. We designed new filters that are associated with well-defined regularization behavior and tested their performance on semi-supervised node classification tasks. Their performance was found to be superior to that of the other state-of-the-art techniques.