Signed Graph Neural Networks: A Frequency Perspective

Abstract

Graph convolutional networks (GCNs) and its variants are designed for unsigned graphs containing only positive links. Many existing GCNs have been derived from the spectral domain analysis of signals lying over (unsigned) graphs and in each convolution layer they perform low-pass filtering of the input features followed by a learnable linear transformation. Their extension to signed graphs with positive as well as negative links imposes multiple issues including computational irregularities and ambiguous frequency interpretation, making the design of computationally efficient low pass filters challenging. In this paper, we address these issues via spectral analysis of signed graphs and propose two different signed graph neural networks, one keeps only low-frequency information and one also retains highfrequency information. We further introduce magnetic signed Laplacian and use its eigendecomposition for spectral analysis of directed signed graphs. We test our methods for node classification and link sign prediction tasks on signed graphs and achieve state-of-the-art performances.

Signed Directed Graph Contrastive Learning with Laplacian Augmentation

“…They have complex eigenvalues and do not satisfy the properties for spectral convolution. Thus, [10,26,41] proposed a novel magnetic Laplacian matrix representing the structure of signed-directed graphs and satisfying positive semidefinite. First of all, we define a complex Hermitian adjacency matrix as follow,…”

“…L 𝑞 𝑈 and L 𝑞 𝑁 are unnormalized and normalized signed-directed magnetic Laplacians. It is well known that the skew-symmetric, complex Hermitian matrix is positive semidefinite [10,26,41]. Thus, the Laplacians are positive semidefinite and diagonalizable by spectral decomposition.…”

“…Magnetic Laplacian was studied in the field of quantum physics [5,35,40]. Thanks to its Hermitian properties, it has been used in graph convolutions for directed and signed-directed [41,54]. Signed magnetic Laplacian encodes graph sturucture, including edge signs and directions.…”