We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
MiS Preprint
97/2018
Detecting the Coarse Geometry of Networks
Melanie Weber, Jürgen Jost and Emil Saucan
Abstract
Clustering and sampling are key methods for the study of relational data. Learning efficient representations of such data relies on the identification of major geometric and topological features and therefore a characterization of its coarse geometry. Here, we introduce an efficient sampling method for identifying crucial structural features using a discrete notion of Ricci curvature. The introduced approach gives rise to a complexity reduction tools that allows for reducing large relational structures (e.g., networks) to a concise core structure on which to focus further, computationally expensive analysis and hypothesis testing.
