  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.
