From Spectrum Wavelet to Vertex Propagation: Graph Convolutional Networks Based on Taylor Approximation

Graph convolutional networks (GCN) have been recently applied to semi-supervised classification problems with fewer labeled data and higher-dimensional features. Existing GCNs mostly rely on a first-order Chebyshev approximation of the graph wavelet-kernels. Such a generic propagation model may not always be well suited for the datasets. This work revisits the fundamentals of graph wavelet and explores the utility of spectral wavelet-kernels to signal propagation in the vertex domain. 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 propagation models. We test the proposed Taylor-based GCN (TGCN) in citation networks and 3D point clouds to demonstrate its advantages over traditional GCN methods.