SpeGCL: Self-Supervised Graph Spectrum Contrastive Learning Without Positive Samples

Graph contrastive learning (GCL) has emerged as a powerful method for dealing with noise and fluctuations in graph-structured data, and can be applied to social networks and knowledge graphs. Although various graph augmentation strategies have emerged in the field of GCL, traditional graph convolutional network (GCN) mainly tends to preserve smooth features and has difficulty capturing fine-grained changes between different views. To address the above issue, we first construct Fourier graph neural network (FourierGNN) from the perspective of graph spectrum learning, which captures different frequency components by stacking multiple Fourier graph operations (FGO) layers in Fourier space. Then, we find that the difference between the high-frequency information of two augmented graphs should be larger than the difference between the low-frequency information. Next, we theoretically prove that focusing only on pushing negative pairs farther away can more effectively achieve performance advantages. By leveraging these discoveries, we propose a novel self-supervised graph spectrum contrastive learning framework, i.e., SpeGCL, and design an effective contrastive strategy to optimize this goal. We also provide a theoretical justification for the efficacy of using only negative samples in SpeGCL. Extensive experiments have been conducted on unsupervised, transfer, and semi-supervised learning tasks to show that SpeGCL outperforms existing state-of-the-art (SOTA) GCL methods.