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

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.

References in corpus (11)

• Adam: A Method for Stochastic Optimization
• TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems
• Semi-Supervised Classification with Graph Convolutional Networks
• The Emerging Field of Signal Processing on Graphs: Extending High-Dimensional Data Analysis to Networks and Other Irregular Domains
• Neural Message Passing for Quantum Chemistry
• Spectral Networks and Locally Connected Networks on Graphs
• Molecular Graph Convolutions: Moving Beyond Fingerprints
• Simplifying Graph Convolutional Networks
• Gated Graph Sequence Neural Networks
• Stability Properties of Graph Neural Networks
• Graph Wavelet Neural Network