Diffeomorphic Learning

TL;DR

This paper proposes a novel learning paradigm where data is transformed by diffeomorphisms before prediction, optimizing the transformation to improve prediction accuracy while penalizing deviation from the identity.

Contribution

It introduces a new diffeomorphic learning framework inspired by shape analysis, capable of estimating complex transformations in high-dimensional data.

Findings

Demonstrates the approach with synthetic examples showing its potential.

Provides insights on improving diffeomorphic learning methods.

Abstract

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.