From Spectrum Wavelet to Vertex Propagation: Graph Convolutional Networks Based on Taylor Approximation
This work addresses the need for more adaptable graph convolutional networks for node classification tasks, though it appears incremental as it builds on existing GCN frameworks with alternative approximations.
The paper tackled the problem of graph convolutional networks (GCNs) relying on generic first-order Chebyshev approximations that may not suit diverse datasets, by proposing Taylor-based GCN (TGCN) using vertex propagation to approximate spectral wavelet-kernels. Experiments on citation networks, multimedia datasets, and synthetic graphs showed TGCN outperforms traditional GCN methods in node classification problems.
Graph convolutional networks (GCN) have been recently utilized to extract the underlying structures of datasets with some labeled data and high-dimensional features. Existing GCNs mostly rely on a first-order Chebyshev approximation of graph wavelet-kernels. Such a generic propagation model does not always suit the various datasets and their features. This work revisits the fundamentals of graph wavelet and explores the utility of signal propagation in the vertex domain to approximate the spectral wavelet-kernels. We first derive the conditions for representing the graph wavelet-kernels via vertex propagation. We next propose alternative propagation models for GCN layers based on Taylor expansions. We further analyze the choices of detailed graph representations for TGCNs. Experiments on citation networks, multimedia datasets and synthetic graphs demonstrate the advantage of Taylor-based GCN (TGCN) in the node classification problems over the traditional GCN methods.