Visualization beyond Riemannian Manifolds

Abstract

This dissertation is about dataset visualization methods and recent developments in this field. Techniques like this take a set of high-dimensional points that have many different features and map it into the two-dimensional plane. This has often been achieved with neighbor embedding methods, which require that the data is locally Euclidean, also described as lying on a Riemannian manifold. This assumption has proved limiting in recent times, and methods that can work around this have been developed and are part of this thesis. Dataset visualizations are used in different research disciplines and help practicioners gain insight into complicated relationships that hide in their data. The topics in this thesis will describe how those methods work, the history of these methods, and recent developments that were researched by the author.