Data driven Dirichlet sampling on manifolds

Abstract

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