Graph Similarity Regularized Softmax for Semi-Supervised Node Classification

TL;DR

This paper introduces a novel graph similarity regularized softmax function for GNNs that incorporates spatial graph information via non-local total variation regularization, improving semi-supervised node classification.

Contribution

It proposes a new softmax variant that embeds graph structure information, enhancing GNN performance on various graph types.

Findings

Improves node classification accuracy.

Enhances generalization on different graph types.

Effective for both assortative and disassortative graphs.

Abstract

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.