Abstract: Graph data augmentation,as a technique aiming to enhance the performance of graph neural networks,involves transforming and expanding the graph structure and node features to increase the diversity and quantity of training data.The integrity of information structures,the smoothness of feature manifold,the diversity of graph,and local dependencies are difficult to comprehensively considered in graph data augmentation.Additionally,over-smoothing and over-fitting problems exist in the training of graph neural networks,which limit their learning capabilities.To address these issues,a graph data augmentation model(NRGE) based on the entropy theory in thermodynamics is proposed.Firstly,a novel definition of graph entropy is introduced to measure the smoothness of the feature manifold.A new data augmentation strategy,whose main idea is to reduce the loss of graph entropy is proposed to generate more appropriate training data.Secondly, the sampling neighbors of the nodes are augmented to ensure the consistency of data augmentation.To increase the diversity of data augmentation,the first-order neighbors of nodes are randomly replaced with their second-order neighbors.Finally,a neighbor-constrained regularization method is introduced,which improves model performance by enforcing prediction consistency between augmented neighbors.Ablation experiments show that the NRGE model effectively reduces the loss of graph entropy by preserving the information structure of triangles,thereby improving learning effect.Three real datasets are trained by the NRGE model.The obtained low-dimensional representation is applied to node classification.Compared with the baseline methods,the NRGE model achieves a performance improvement of 1.1% on the Cora dataset,0.8% on the Citeseer dataset,and a slight decrease of 0.4% on the Pubmed dataset.The experimental results show that the NRGE model can significantly enhance the performance of graph neural networks and improve the generalization ability.

Key words: Graph entropy, Graph data augmentation, Neighbor replacement, Consistency and diversity, Structural enhancement