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

TL;DR

This paper introduces Interface Laplace learning, a semi-supervised graph-based method that models non-smooth interfaces between classes, improving performance at low label rates on image datasets.

Contribution

The paper proposes a novel Laplace learning model with an interface term, and a practical algorithm to learn interface positions from data, challenging the smoothness assumption.

Findings

Achieves superior performance at low label rates on MNIST, FashionMNIST, CIFAR-10.

Efficient algorithm for approximating interface positions using k-hop neighborhoods.

Demonstrates the importance of modeling class interfaces in semi-supervised learning.

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.