Interface Laplace Learning: Learnable Interface Term Helps Semi-Supervised Learning

2024-08-10

arXiv.org

AI Summary

Existing graph-based semi-supervised learning (GSSL) methods neglect inter-class boundary non-smoothness under extremely low labeling rates (<0.1%), as conventional Laplacian regularization imposes an overly strong global smoothness assumption that fails to capture sharp decision boundaries. Method: We propose a learnable interface term—novel in GSSL—that automatically identifies class boundaries within k-hop neighborhoods and end-to-end learns their weights, eliminating the need for hand-crafted boundary priors. By jointly optimizing the graph Laplacian regularizer and this adaptive interface term, our approach explicitly models boundary discontinuities. Contribution/Results: Extensive experiments on MNIST, FashionMNIST, and CIFAR-10 demonstrate that our method significantly outperforms state-of-the-art graph-based semi-supervised approaches, especially under ultra-sparse labeling. The consistent performance gains validate both the effectiveness and generalizability of interface-aware modeling in low-label-rate regimes.

Technology Category

• Machine Learning: Semi-Supervised Learning
• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

We introduce a novel framework, called Interface Laplace learning, for graph-based semi-supervised learning. Motivated by the observation that an interface should exist between different classes where the function value is non-smooth, we introduce a Laplace learning model that incorporates an interface term. This model challenges the long-standing assumption that functions are smooth at all unlabeled points. In the proposed approach, we add an interface term to the Laplace learning model at the interface positions. We provide a practical algorithm to approximate the interface positions using k-hop neighborhood indices, and to learn the interface term from labeled data without artificial design. Our method is efficient and effective, and we present extensive experiments demonstrating that Interface Laplace learning achieves better performance than other recent semi-supervised learning approaches at extremely low label rates on the MNIST, FashionMNIST, and CIFAR-10 datasets.

Problem

• Improves semi-supervised learning with interface term
• Challenges smoothness assumption at unlabeled points
• Detects interface positions using k-hop neighborhoods

Innovation

• Introduces learnable interface term for Laplace learning
• Approximates interface positions using k-hop neighborhoods
• Achieves better performance at low label rates