Signed Graph Neural Networks: A Frequency Perspective
This work addresses the problem of handling signed graphs for machine learning practitioners, offering a novel spectral analysis approach that improves performance in graph-based tasks.
The paper tackled the problem of extending graph convolutional networks to signed graphs with positive and negative links, which posed computational and frequency interpretation challenges, and achieved state-of-the-art performances in node classification and link sign prediction tasks.
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 high-frequency 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.