Forward-reflected-backward method with variance reduction

We propose a variance reduced algorithm for solving monotone variational inequalities. Without assuming strong monotonicity, cocoercivity, or boundedness of the domain, we prove almost sure convergence of the iterates generated by the algorithm to a solution. In the monotone case, the ergodic average converges with the optimal O(1/k) rate of convergence. When strong monotonicity is assumed, the algorithm converges linearly, without requiring the knowledge of strong monotonicity constant. We finalize with extensions and applications of our results to monotone inclusions, a class of non-monotone variational inequalities and Bregman projections.

Overrelaxed Sinkhorn–Knopp Algorithm for Regularized Optimal Transport

This article describes a set of methods for quickly computing the solution to the regularized optimal transport problem. It generalizes and improves upon the widely used iterative Bregman projections algorithm (or Sinkhorn–Knopp algorithm). We first proposed to rely on regularized nonlinear acceleration schemes. In practice, such approaches lead to fast algorithms, but their global convergence is not ensured. Hence, we next proposed a new algorithm with convergence guarantees. The idea is to overrelax the Bregman projection operators, allowing for faster convergence. We proposed a simple method for establishing global convergence by ensuring the decrease of a Lyapunov function at each step. An adaptive choice of the overrelaxation parameter based on the Lyapunov function was constructed. We also suggested a heuristic to choose a suitable asymptotic overrelaxation parameter, based on a local convergence analysis. Our numerical experiments showed a gain in convergence speed by an order of magnitude in certain regimes.

Metric Learning with Dynamically Generated Pairwise Constraints for Ear Recognition

The ear recognition task is known as predicting whether two ear images belong to the same person or not. More recently, most ear recognition methods have started based on deep learning features that can achieve a good accuracy, but it requires more resources in the training phase and suffer from time-consuming computational complexity. On the other hand, descriptor features and metric learning play a vital role and also provide excellent performance in many computer vision applications, such as face recognition and image classification. Therefore, in this paper, we adopt the descriptor features and present a novel metric learning method that is efficient in matching real-time for ear recognition system. This method is formulated as a pairwise constrained optimization problem. In each training cycle, this method selects the nearest similar and dissimilar neighbors of each sample to construct the pairwise constraints and then solves the optimization problem by the iterated Bregman projections. Experiments are conducted on Annotated Web Ears (AWE) database, West Pommeranian University of Technology (WPUT), the University of Science and Technology Beijing II (USTB II), and Mathematical Analysis of Images (AMI) databases.. The results show that the proposed approach can achieve promising recognition rates in ear recognition, and its training process is much more efficient than the other competing metric learning methods.