Diffeomorphic Learning

We introduce in this paper a learning paradigm in which the training data is transformed by a diffeomorphic transformation before prediction. The learning algorithm minimizes a cost function evaluating the prediction error on the training set penalized by the distance between the diffeomorphism and the identity. The approach borrows ideas from shape analysis, in the way diffeomorphisms are estimated for shape and image alignment, and brings them in a previously unexplored setting, estimating, in particular diffeomorphisms in much larger dimensions.