Interface Laplace Learning: Nonlocal Interface Model Helps Semi-Supervised Learning
数学专题报告
报告题目(Title)：Interface Laplace Learning: Nonlocal Interface Model Helps Semi-Supervised Learning
报告人(Speaker)：史作强 （清华大学）
地点(Place)：后主楼1124
时间(Time)：2025年6月26日 (周四) 下午16:10-16:50
邀请人(Inviter)：段玉萍
报告摘要
We introduce a novel framework, called Interface Laplace learning, for graph-based semi-supervised learning. Motivated by the nonlocal interface model, 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.
主讲人简介
史作强教授博士毕业于清华大学周培源应用数学研究中心，后赴美国加州理工学院应用与计算数学系做博士后，并曾作为访问学者在美国加州大学洛杉矶分校数学系访问。2012年全职加入清华大学，现任丘成桐数学科学中心副主任、教授、博士生导师。主要从事偏微分方程数值解法、图像处理、机器学习等研究。特别是在点云上偏微分方程的数值方法，高维数据的偏微分方程模型，数据驱动的稀疏时频分析等研究领域中取得了一系列创新研究成果。
