Graph contrastive learning (GCL) is a promising direction toward alleviating the label dependence, poor generalization and weak robustness of graph neural networks, learning representations with invariance, and discriminability by solving pretasks. The pretasks are mainly built on mutual information estimation, which requires data augmentation to construct positive samples with similar semantics to learn invariant signals and negative samples with dissimilar semantics to empower representation discriminability. However, an appropriate data augmentation configuration depends heavily on lots of empirical trials such as choosing the compositions of data augmentation techniques and the corresponding hyperparameter settings. We propose an augmentation-free GCL method, invariant-discriminative GCL (iGCL), that does not intrinsically require negative samples. iGCL designs the invariant-discriminative loss (ID loss) to learn invariant and discriminative representations. On the one hand, ID loss learns invariant signals by directly minimizing the mean square error (MSE) between the target samples and positive samples in the representation space. On the other hand, ID loss ensures that the representations are discriminative by an orthonormal constraint forcing the different dimensions of representations to be independent of each other. This prevents representations from collapsing to a point or subspace. Our theoretical analysis explains the effectiveness of ID loss from the perspectives of the redundancy reduction criterion, canonical correlation analysis (CCA), and information bottleneck (IB) principle. The experimental results demonstrate that iGCL outperforms all baselines on five node classification benchmark datasets. iGCL also shows superior performance for different label ratios and is capable of resisting graph attacks, which indicates that iGCL has excellent generalization and robustness. The source code is available at https://github.com/lehaifeng/ T-GCN/tree/master/iGCL.

Traffic flow forecasting is a basic function of intelligent transportation systems, and the accuracy of prediction is of great significance for traffic management and urban planning. The main difficulty of traffic flow predictions is that there is complex underlying spatiotemporal dependence in traffic flow; thus, the existing spatiotemporal graph neural network (STGNN) models need to model both temporal dependence and spatial dependence. Graph neural networks (GNNs) are adopted to capture the spatial dependence in traffic flow, which can model the symmetric or asymmetric spatial relations between nodes in the traffic network. The transmission process of traffic features in GNNs is guided by the node-to-node relationship (e.g., adjacency or spatial distance) between nodes, ignoring the spatial dependence caused by local topological constraints in the road network. To further consider the influence of local topology on the spatial dependence of road networks, in this paper, we introduce Ollivier–Ricci curvature information between connected edges in the road network, which is based on optimal transport theory and makes comprehensive use of the neighborhood-to-neighborhood relationship to guide the transmission process of traffic features between nodes in STGNNs. Experiments on real-world traffic datasets show that the models with Ollivier–Ricci curvature information outperforms those based on only node-to-node relationships between nodes by ten percent on average in the RMSE metric. This study indicates that by utilizing complex topological features in road networks, spatial dependence can be captured more sufficiently, further improving the predictive ability of traffic forecasting models.