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.

本研究解决了图基半监督学习中的一个问题，即函数在未标记点处的光滑性假设。我们提出的界面拉普拉斯学习模型引入了界面项，通过k-hop邻域索引来近似界面位置，并从标记数据中学习界面项。实验结果表明，该方法在极低标记率下在多个数据集上优于现有的半监督学习方法。

界面拉普拉斯学习：可学习的界面项助力半监督学习