Graph-based Semi-Supervised Learning via Maximum Discrimination

TL;DR

This paper introduces AUC-spec, a graph-based semi-supervised learning method that maximizes class separation by optimizing the AUC, achieving competitive results with efficient computation.

Contribution

The paper proposes a novel graph SSL approach that directly maximizes class separation through AUC optimization, improving over traditional label propagation methods.

Findings

AUC-spec balances class separation and graph smoothness.

It achieves competitive accuracy on synthetic and real datasets.

The method maintains computational efficiency comparable to existing techniques.

Abstract

Semi-supervised learning (SSL) addresses the critical challenge of training accurate models when labeled data is scarce but unlabeled data is abundant. Graph-based SSL (GSSL) has emerged as a popular framework that captures data structure through graph representations. Classic graph SSL methods, such as Label Propagation and Label Spreading, aim to compute low-dimensional representations where points with the same labels are close in representation space. Although often effective, these methods can be suboptimal on data with complex label distributions. In our work, we develop AUC-spec, a graph approach that computes a low-dimensional representation that maximizes class separation. We compute this representation by optimizing the Area Under the ROC Curve (AUC) as estimated via the labeled points. We provide a detailed analysis of our approach under a product-of-manifold model, and show that the required number of labeled points for AUC-spec is polynomial in the model parameters. Empirically, we show that AUC-spec balances class separation with graph smoothness. It demonstrates competitive results on synthetic and real-world datasets while maintaining computational efficiency comparable to the field's classic and state-of-the-art methods.