Poisson Learning: Graph Based Semi-Supervised Learning At Very Low Label Rates
Poisson Learning: Graph Based Semi-Supervised Learning At Very Low Label Rates
复制标题
DOI：
--
复制
发表时间：
2020-06
期刊：
影响因子：
--
通讯作者：
J. Calder;Brendan Cook;Matthew Thorpe;D. Slepčev
中科院分区：
文献类型：
--
作者：
J. Calder;Brendan Cook;Matthew Thorpe;D. Slepčev
我们提出了一个称为泊松学习的新框架，用于以非常低的标签率进行基于图的半监督学习。泊松学习的动机是解决该体系中拉普拉斯半监督学习的退化问题。该方法用源和汇的放置代替训练点处标签值的分配，并在图上求解所得的泊松方程。事实证明，其结果比拉普拉斯学习的结果更加稳定且信息丰富。泊松学习高效且易于实现，我们提出的数值实验表明，该方法优于 MNIST、FashionMNIST 和 Cifar-10 上低标签率的其他最新半监督学习方法。我们还提出了泊松学习的图割增强，称为泊松 MBO，它提供了更高的准确性，并且可以结合相对班级规模的先验知识。
We propose a new framework, called Poisson learning, for graph based semi-supervised learning at very low label rates. Poisson learning is motivated by the need to address the degeneracy of Laplacian semi-supervised learning in this regime. The method replaces the assignment of label values at training points with the placement of sources and sinks, and solves the resulting Poisson equation on the graph. The outcomes are provably more stable and informative than those of Laplacian learning. Poisson learning is efficient and simple to implement, and we present numerical experiments showing the method is superior to other recent approaches to semi-supervised learning at low label rates on MNIST, FashionMNIST, and Cifar-10. We also propose a graph-cut enhancement of Poisson learning, called Poisson MBO, that gives higher accuracy and can incorporate prior knowledge of relative class sizes.