Diffeomorphic Learning
This work addresses a novel learning paradigm for data transformation, but it is incremental as it adapts existing shape analysis ideas to a new setting with synthetic examples.
The paper tackles the problem of learning with diffeomorphic transformations by introducing a new paradigm that transforms training data before prediction, minimizing a cost function that penalizes deviation from identity. It demonstrates potential through diverse synthetic applications and provides insights for improvement.
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.