The critical step of learning the robust regression model from high-dimensional visual data is how to characterize the error term. The existing methods mainly employ the nuclear norm to describe the error term, which are robust against structure noises (e.g., illumination changes and occlusions). Although the nuclear norm can describe the structure property of the error term, global distribution information is ignored in most of these methods. It is known that optimal transport (OT) is a robust distribution metric scheme due to that it can handle correspondences between different elements in the two distributions. Leveraging this property, this article presents a novel robust regression scheme by integrating OT with convex regularization. The OT-based regression with L2L_{2} norm regularization (OTR) is first proposed to perform image classification. The alternating direction method of multipliers is developed to handle the model. To further address the occlusion problem in image classification, the extended OTR (EOTR) model is then presented by integrating the nuclear norm error term with an OTR model. In addition, we apply the alternating direction method of multipliers with Gaussian back substitution to solve EOTR and also provide the complexity and convergence analysis of our algorithms. Experiments were conducted on five benchmark datasets, including illumination changes and various occlusions. The experimental results demonstrate the performance of our robust regression model on biometric image classification against several state-of-the-art regression-based classification methods.

中文翻译：

---

具有凸正则化的联合最优传输用于鲁棒图像分类


从高维视觉数据中学习鲁棒回归模型的关键步骤是如何表征误差项。现有方法主要采用核范数来描述误差项，其对结构噪声（例如光照变化和遮挡）具有鲁棒性。虽然核范数可以描述误差项的结构性质，但大多数这些方法都忽略了全局分布信息。众所周知，最优传输（OT）是一种鲁棒的分布度量方案，因为它可以处理两个分布中不同元素之间的对应关系。利用这一特性，本文通过将 OT 与凸正则化相结合，提出了一种新颖的鲁棒回归方案。首次提出采用 L2L_{2} 范数正则化 (OTR) 的基于 OT 的回归来执行图像分类。开发了乘子交替方向法来处理该模型。为了进一步解决图像分类中的遮挡问题，通过将核范数误差项与 OTR 模型相结合，提出了扩展 OTR (EOTR) 模型。此外，我们应用乘法器交替方向法和高斯反向代入来求解EOTR，并提供了算法的复杂性和收敛性分析。在五个基准数据集上进行了实验，包括光照变化和各种遮挡。实验结果证明了我们的鲁棒回归模型在生物识别图像分类上的性能与几种最先进的基于回归的分类方法相比。