Spectral graph convolutional networks (SGCNs) are one of the leading tools to handle learning tasks with graph structure. SGCNs leverage graph structure to define the graph spectral transformation (i.e., graph Fourier transformation) and pursue a good spectral filter in the spectral domain. For efficiency reasons, the pursued spectral filter is usually approximated by a polynomial of the normalized adjacency matrix in the spatial domain, referred to as the polynomial propagation of SGCNs. In this paper, we present a theoretical analysis on the propagation matrix defined by SGCNs and show that it actually almost always incurs a non-trivial propagation error. We also derive an explicit bound for this error. To mitigate this issue, we propose the Graph Spectral Projection Network (GSPNet) by learning a better spectral transformation, which endows GSPNet with potential to eliminate the error encountered by the polynomial propagation of SGCNs. Experimental results on commonly-used graph datasets suggest that GSPNet can learn a propagation matrix beyond the theoretically optimal polynomial propagation and generate promising results over existing SGCN models.
Geng et al. (Thu,) studied this question.