Graph Size-imbalanced Learning with Energy-guided Structural Smoothing

Graph is a prevalent data structure employed to represent the relationships between entities, frequently serving as a tool to depict and simulate numerous systems, such as molecules and social networks.However, real-world graphs usually suffer from the size-imbalanced problem in the multi-graph classification, i.e., a long-tailed distribution with respect to the number of nodes.Recent studies find that off-the-shelf Graph Neural Networks (GNNs) would compromise model performance under the long-tailed settings.We investigate this phenomenon and discover that the long-tailed graph distribution greatly exacerbates the discrepancies in structural features.To alleviate this problem, we propose a novel energy-based sizeimbalanced learning framework named SIMBA, which smooths the features between head and tail graphs and re-weights them based on the energy propagation.Specifically, we construct a higher-level graph abstraction named Graphs-to-Graph according to the correlations between graphs to link independent graphs and smooths the structural discrepancies.We further devise an energy-based message-passing belief propagation method for re-weighting lower compatible graphs in the training process and further smooth local feature discrepancies.Extensive experimental results over five public size-imbalanced datasets demonstrate the superior effectiveness of the model for size-imbalanced graph classification tasks.