Data driven Dirichlet sampling on manifolds

This article presents a new method to sample on manifolds, based the Dirichlet distribution. The proposed strategy allows completely respect underlying manifold around which data are observed, and do massive sampling with low computational effort. can be very helpful, for instance, in neural networks training process, as well uncertainty analysis stochastic optimization. Due its simplicity efficiency, we believe that has great potential. Three manifolds (two dimensional ring, Mobius strip spider geometry) used test methodology, then it is employed an engineering application, related bearing coefficients of rotating machine. In augmented train network.