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Graph convolutional networks (GCN) have been recently utilized to extract theunderlying structures of datasets with some labeled data and high-dimensionalfeatures. Existing GCNs mostly rely on a first-order Chebyshev approximation ofgraph wavelet-kernels. Such a generic propagation model does not always suitthe various datasets and their features. This work revisits the fundamentals ofgraph wavelet and explores the utility of signal propagation in the vertexdomain to approximate the spectral wavelet-kernels. We first derive theconditions for representing the graph wavelet-kernels via vertex propagation.We next propose alternative propagation models for GCN layers based on Taylorexpansions. We further analyze the choices of detailed graph representationsfor TGCNs. Experiments on citation networks, multimedia datasets and syntheticgraphs demonstrate the advantage of Taylor-based GCN (TGCN) in the nodeclassification problems over the traditional GCN methods.

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