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.
翻译:图形相联网络(GCNs)及其变体是为那些仅包含正链接的未签名的图形设计的,许多现有的GCNs来自对分布在(未签名)图形上的信号的光谱域分析,在每一个相联层中,它们对输入特征进行低通道过滤,随后进行可学习的线性变换。它们扩展为带有正链接和负链接的签名图形,这带来了多种问题,包括计算异常和模糊的频率解释,使得计算高效的低通过过滤器的设计具有挑战性。在本文中,我们通过对签名的图形进行光谱分析来解决这些问题,并提出两个不同的已签名的图形神经网络,一个只保留低频信息,另一个保留高频信息。我们进一步引入磁性签名 Laplacian,并使用其eigendecomposition来进行定向签名图形的光谱分析。我们测试了我们的节分分类方法,并将签名图表上的预测任务连接在一起,并实现最先进的性能。