This paper presents an approach to semi-supervised learning for the classification of data using the Lipschitz Learning on graphs. We develop a graph-based semi-supervised learning framework that leverages the properties of the infinity Laplacian to propagate labels in a dataset where only a few samples are labeled. By extending the theory of spatial segregation from the Laplace operator to the infinity Laplace operator, both in continuum and discrete settings, our approach provides a robust method for dealing with class imbalance, a common challenge in machine learning. Experimental validation on several benchmark datasets demonstrates that our method not only improves classification accuracy compared to existing methods but also ensures efficient label propagation in scenarios with limited labeled data.

翻译：本文提出了一种利用图上Lipschitz学习的半监督数据分类方法。我们开发了一个基于图的半监督学习框架，该框架利用无穷拉普拉斯算子的特性在仅有少量标注样本的数据集中传播标签。通过将空间隔离理论从拉普拉斯算子扩展到无穷拉普拉斯算子（涵盖连续与离散两种情形），我们的方法为处理机器学习中的常见挑战——类别不平衡问题——提供了一种鲁棒方案。在多个基准数据集上的实验验证表明，与现有方法相比，我们的方法不仅提升了分类准确率，还能在标注数据有限的场景下确保高效的标签传播。