Multi-scale signed graph convolutional network based on framelet.

Abstract

Spectral graph convolutional networks, applying frequency filtering via Fourier transform, have garnered increasing attention and achieved remarkable performance in tasks such as node classification and link prediction. While graph framelets offer a multiresolution analysis for graph signals, most existing research focuses on unsigned (or undirected) graphs. In this paper, we propose an efficient framelet-based GCN for signed (including directed) graphs leveraging the magnetic signed Laplace matrix. Our model constructs a magnetic signed graph framelet system to excavate low-pass and high-pass information from signals and transform them into multi-scale representation for various tasks. The entire architecture performs framelet-based convolution in both real and complex domains because of complex-valued magnetic Laplacian. To mitigate the computational complexity associated with the eigen-decomposition of the Laplacian matrix, we explore Chebyshev polynomial approximation to accelerate framelet transform. The proposed model can be applied in complex graph data, such as signed, directed and weighted graph. Extensive experiments on four real-world datasets and five link prediction tasks demonstrate that the proposed Framelet-MSGCN outperforms state-of-the-art algorithms.