Regularizing Softmax With Graph Similarity for Enhanced Node Classification in Semisupervised Settings

Graph neural networks have emerged as powerful tools for analyzing graph‐structured data, particularly in semisupervised node classification tasks. However, the conventional softmax classifier, widely used in such tasks, fails to leverage the spatial information inherent in graph structures. To address this limitation, we propose a graph similarity regularized softmax for graph neural networks, which incorporates nonlocal total variation regularization into the softmax function to explicitly capture graph structural information. The weights in the nonlocal gradient and divergence operators are determined based on the graph’s adjacency matrix. We implement this regularized softmax in two popular graph neural network architectures, GCN and GraphSAGE, and evaluate its performance on citation (assortative) and webpage linking (disassortative) datasets. Experimental results demonstrate that our method significantly improves node classification accuracy and generalization compared to baseline models. These findings highlight the effectiveness of the proposed regularized softmax in handling both assortative and disassortative graphs, offering a principled way to encode graph spatial information into graph neural network classifiers.