Framework for Designing Filters of Spectral Graph Convolutional Neural Networks in the Context of Regularization Theory
This work addresses the design of filters in spectral GCNNs for graph learning, offering a regularization-based framework that improves performance in tasks like node classification, though it appears incremental as it generalizes existing methods.
The authors tackled the problem of designing filters for spectral graph convolutional neural networks (GCNNs) by proposing a generalized framework based on regularization theory using the graph Laplacian. They found that their new filters, which exhibit well-defined regularization behavior, achieved superior performance on semi-supervised node classification tasks compared to other state-of-the-art techniques.
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.