In real-world machine learning applications, unlabeled training data are readily available, but labeled data are expensive and hard to obtain. Therefore, semi-supervised learning algorithms have gathered much attention. Previous studies in this area mainly focused on a semi-supervised classification problem, whereas semi-supervised regression has received less attention. In this paper, we proposed a novel semi-supervised regression algorithm using heat diffusion with a boundary-condition that guarantees a closed-form solution. Experiments from artificial and real datasets from business, biomedical, physical, and social domain show that the boundary-based heat diffusion method can effectively outperform the top state of the art methods.

在现实世界的机器学习应用程序中，未标记的训练数据很容易获得，但是标记的数据昂贵且难以获得。因此，半监督学习算法备受关注。先前在该领域的研究主要集中在半监督分类问题上，而半监督回归则受到较少的关注。在本文中，我们提出了一种新的半监督回归算法，该算法使用具有边界条件的热扩散来保证封闭形式的解。来自商业，生物医学，物理和社会领域的人工和真实数据集的实验表明，基于边界的热扩散方法可以有效地胜过最先进的方法。