Normalize Then Propagate: Efficient Homophilous Regularization for Few-shot Semi-Supervised Node Classification

2025-01-15

AI Summary

To address graph node classification under extremely low label rates, this paper proposes a direction–norm decoupled representation framework. It explicitly disentangles the directional component (encoding class-discriminative information) from the Euclidean norm (reflecting prediction confidence) during message propagation. Leveraging the graph homophily assumption, we design a norm-normalization-guided propagation mechanism and a homophily-aware regularization term to generate reliable pseudo-supervisory signals for unlabeled nodes. We theoretically derive an upper bound on the norm to ensure propagation stability. The method incurs computational complexity comparable to standard GNNs and introduces no additional parameters. Extensive experiments on multiple benchmark datasets demonstrate substantial improvements over existing state-of-the-art methods—achieving an average accuracy gain of 4.2% under only 1% label rate. The approach is computationally efficient, exhibits strong generalization, and offers theoretical interpretability.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text

Abstract

Graph Neural Networks (GNNs) have demonstrated remarkable ability in semi-supervised node classification. However, most existing GNNs rely heavily on a large amount of labeled data for training, which is labor-intensive and requires extensive domain knowledge. In this paper, we first analyze the restrictions of GNNs generalization from the perspective of supervision signals in the context of few-shot semi-supervised node classification. To address these challenges, we propose a novel algorithm named NormProp, which utilizes the homophily assumption of unlabeled nodes to generate additional supervision signals, thereby enhancing the generalization against label scarcity. The key idea is to efficiently capture both the class information and the consistency of aggregation during message passing, via decoupling the direction and Euclidean norm of node representations. Moreover, we conduct a theoretical analysis to determine the upper bound of Euclidean norm, and then propose homophilous regularization to constraint the consistency of unlabeled nodes. Extensive experiments demonstrate that NormProp achieve state-of-the-art performance under low-label rate scenarios with low computational complexity.

Problem

• Graph Neural Networks
• Node Classification
• Limited Labeled Data

Innovation

• NormProp
• Graph Neural Networks (GNNs)
• Label-scarcity Performance Enhancement