Graph Semi-Supervised learning is an important data analysis tool, where given a graph and a set of labeled nodes, the aim is to infer the labels to the remaining unlabeled nodes. In this paper, we start by considering an optimization-based formulation of the problem for an undirected graph, and then we extend this formulation to multilayer hypergraphs. We solve the problem using different coordinate descent approaches and compare the results with the ones obtained by the classic gradient descent method. Experiments on synthetic and real-world datasets show the potential of using coordinate descent methods with suitable selection rules.

翻译：图半监督学习是一种重要的数据分析工具，其目标是在给定图结构和一组标记节点的情况下，推断剩余未标记节点的标签。本文首先针对无向图问题提出基于优化的形式化描述，随后将该形式化扩展到多层超图。我们采用不同的坐标下降方法求解该问题，并将结果与经典梯度下降方法进行对比。在合成数据集和真实世界数据集上的实验表明，结合适当选择规则的坐标下降方法具有应用潜力。