摘要: We present new algorithms to compute the mean of a set empirical probability measures under optimal transport metric. This mean, known as Wasserstein barycenter, is measure that minimizes sum its distances each element in set. propose two original barycenters build upon subgradient method. A direct implementation these is, however, too costly because it would require repeated resolution large primal and dual problems subgradients. Extending work Cuturi (2013), we smooth distance used definition with an entropic regularizer recover doing so strictly convex objective whose gradients can be computed for considerably cheaper computational cost using matrix scaling algorithms. use visualize family images solve constrained clustering problem.