Joint Optimal Transport With Convex Regularization for Robust Image Classification.

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 L₂ 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.