In recent years there has been a surprising flow of ideas from the mathematical branch of differential geometry and topology towards applications in the natural sciences. Within an exploratory project of STRUCTURES we started to discuss about recent applications of hyperbolic geometry in machine learning, in particular to reveal underlying hierarchical structures in data sets. The goal of this seminar is to bring together researchers from various Heidelberg institutions interested in these topics from the mathematics side and the application side. We meet bi-weekly on thursdays 12:00 to 13:00 via zoom. Interested people are encouraged to send me (email@example.com) an email to be added to our mailing list and receive the zoom link.
|17/12/2020||Ullrich Koethe||Universitaet Heidelberg||Interpretable Machine Learning and Hyperbolic Geometry||slides, video 1 and video 2 .|
|21/01/2021||Sebastian Damrich||Universitaet Heidelberg||Hyperbolic Machine Learning||Hyperbolic space is better suited at representing hierarchical data than Euclidean space and has therefore found several applications in machine learning in recent years. We will discuss some of the early shallow hyperbolic embedding learning approaches before exploring various deep neural network architectures that use hyperbolic space. Possible use cases are mentioned along the way. slides, video 1 , video 2|
|6/02/2021||Maximilian Schmahl||Universitaet Heidelberg||An Overview of Persistent Homology||Persistent homology is a topological tool of growing popularity for data analysis. We will motivate its use by considering persistent homology as a generalization of hierarchical clustering. Afterwards, we will discuss some results about what persistent homology can tell us about a data set.|