  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 where diffeomorphisms
are estimated for shape and image alignment, and brings them in a previously
unexplored setting, estimating, in particular diffeomorphisms in much larger
dimensions. After introducing the concept and describing a learning algorithm,
we present diverse applications, mostly with synthetic examples, demonstrating
the potential of the approach, as well as some insight on how it can be
improved.
