The ever-increasing size of modern datasets combined with the difficulty of obtaining label information has made semi-supervised learning of significant practical importance in modern machine learning applications. Compared with supervised learning, the key difficulty in semi-supervised learning is how to make full use of the unlabeled data. In order to utilize manifold information provided by unlabeled data, we propose a novel regularization called the tangent-normal adversarial regularization, which is composed by two parts. The two terms complement with each other and jointly enforce the smoothness along two different directions that are crucial for semi-supervised learning. One is applied along the tangent space of the data manifold, aiming to enforce local invariance of the classifier on the manifold, while the other is performed on the normal space orthogonal to the tangent space, intending to impose robustness on the classifier against the noise causing the observed data deviating from the underlying data manifold. Both of the two regularizers are achieved by the strategy of virtual adversarial training. Our method has achieved state-of-the-art performance on semi-supervised learning tasks on both artificial dataset and FashionMNIST dataset.

本文针对半监督学习问题，提出了一种基于流形的切平面与法线平面对抗正则化方法，称作TNAR。该方法通过在数据流形的切向空间和法向空间上应用虚拟对抗性训练，实现对分类器局部不变性及鲁棒性的提升，在人工和实际数据集测试中取得了优于其他最先进方法的成果。

半监督学习的切线-法向对抗正则化