2020/06/15 by Kum, S., Duong, M. H., Lim, Y. +1
#FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2006.08743
In this paper, we focus on the analysis of the regularized Wasserstein barycenter problem. We provide uniqueness and a characterization of the barycenter for two important classes of probability measures: (i) Gaussian distributions and (ii) q-Gaussian distributions; each regularized by a particular entropy functional. We propose an algorithm based on gradient projection method in the space of matrices in order to compute these regularized barycenters. We also consider a general class of φ-exponential measures, for which only the non-regularized barycenter is studied. Finally, we numerically show the influence of parameters and stability of the algorithm under small perturbation of data.