Graph Neural Networks (GNNs) are powerful deep learning models designed for graph-structured data, demonstrating effectiveness across a wide range of applications.The softmax function is the most commonly used classifier for semi-supervised node classification. However, the softmax function lacks spatial information of the graph structure. In this paper, we propose a graph similarity regularized softmax for GNNs in semi-supervised node classification. By incorporating non-local total variation (TV) regularization into the softmax activation function, we can more effectively capture the spatial information inherent in graphs. The weights in the non-local gradient and divergence operators are determined based on the graph's adjacency matrix. We apply the proposed method into the architecture of GCN and GraphSAGE, testing them on citation and webpage linking datasets, respectively. Numerical experiments demonstrate its good performance in node classification and generalization capabilities. These results indicate that the graph similarity regularized softmax is effective on both assortative and disassortative graphs.

本文解决了传统软最大分类器在半监督节点分类中缺乏图结构空间信息的问题。通过将非局部总变差正则化引入软最大激活函数，本文提出了一种新的分类方法，能够更有效地捕捉图中固有的空间信息。实验结果表明，图相似性正则化软最大值在节点分类和泛化能力上表现良好，适用于各种图结构。

图相似性正则化软最大值用于半监督节点分类