Biased random walk based graph neural network

Abstract

Graph neural networks (GNNs) are approaches that extend deep learning neural networks on graph data. Research on graph neural networks has made tremendous progress today. Graph neural networks are usually categorized as spectral-based models and spatial-based models. The spectral-based method has been widely recognized by the academic community due to its solid theoretical foundation. However, the existing spectral-based models induced by the Laplacian matrix usually cannot achieve satisfactory results in experiments due to their insufficient expressive ability. We theoretically derive an unbiased Laplacian matrix based on biased random walks. As a graph shift operator, it is more general than unbiased Laplacian. Based on biased Laplacian, we propose a more powerful spectral-based graph neural network BiGNN. And it achieves better simulation results than traditional spectral-based graph neural networks on Cora, Citeseer and PubMed datasets.