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We present a novel approach combining unsupervised computation of manifold-valued prototypes and their spatially regularized assignment to given manifold-valued data. Both processes evolve dynamically through coupled flows. The separate representation of prototypes and assignment enables the application to various manifold data models. As a case study, we apply our approach to unsupervised learning on the positive definite matrix manifold. Joint work with Matthias Zisler, Freddie Åström, Stefania Petra and Christoph Schnörr.
This presentation is part of Minisymposium “MS31 - Variational Approaches for Regularizing Nonlinear Geometric Data (3 parts)”
organized by: Martin Storath (Universität Heidelberg) , Martin Holler (École Polytechnique, Université Paris Saclay) , Andreas Weinmann (Hochschule Darmstadt) .