Spectral Augmentation for Self-Supervised Learning on Graphs

Graph contrastive learning (GCL), as an emerging self-supervised learning technique on graphs, aims to learn representations via instance discrimination. Its performance heavily relies on graph augmentation to reflect invariant patterns that are robust to small perturbations; yet it still remains unclear about what graph invariance GCL should capture. Recent studies mainly perform topology augmentations in a uniformly random manner in the spatial domain, ignoring its influence on the intrinsic structural properties embedded in the spectral domain. In this work, we aim to find a principled way for topology augmentations by exploring the invariance of graphs from the spectral perspective. We develop spectral augmentation which guides topology augmentations by maximizing the spectral change. Extensive experiments on both graph and node classification tasks demonstrate the effectiveness of our method in unsupervised learning, as well as the generalization capability in transfer learning and the robustness property under adversarial attacks. Graph neural networks (GNNs) (Kipf & Welling, 2017; Veličković et al., 2018; Xu et al., 2019) have advanced graph representation learning in a (semi-)supervised manner, yet it requires supervised labels and may fail to generalize (Rong et al., 2020). To obtain more generalizable and transferable representations, the self-supervised learning (SSL) paradigm emerges which enables GNNs to learn from pretext tasks constructed on unlabeled graph data (Hu et al., 2020c;b; You et al., 2020b; Jin et al., 2020a). As a state-of-the-art SSL technique, graph contrastive learning (GCL) has attracted the most attention due to its remarkable empirical performance (Velickovic et al., 2019; Zhu et al., 2020; Hassani & Khasahmadi, 2020; You et al., 2021; Suresh et al., 2021; Thakoor et al., 2021). A typical GCL method works by creating augmented views of the input graph and learning representations by contrasting related graph objects against unrelated ones. The goal of GCL is to capture graph invariance by maximizing the congruence between node or graph representations in augmented views. This makes graph augmentation one of the most critical designs in GCL, as it determines the effectiveness of the contrastive objective. However, despite that various GCL methods have been proposed, it remains a mystery about what graph invariance GCL should capture. Unlike images, which can be augmented to naturally highlight the main subject from the background, it is less obvious to design the most effective graph augmentation due to the complicated topology structure of diverse nature in different graphs (e.g., citation networks (Sen et al., 2008), social networks (Morris et al., 2020), chemical and biomedical molecules (Li et al., 2021; Hu et al., 2020b)), as discussed in the survey (Ding et al., 2022).