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Workshop

Multidimensional Persistence and Clustering

  • Magnus Botnan (Technical University of Munich)
E1 05 (Leibniz-Saal)

Abstract

It is widely known that multidimensional persistent homology is "hard". But what does this really mean? In the first part of the talk I will discuss this from the point of view of representation theory of quivers. Next I will show how multidimensional clustering gives rise to multidimensional persistence modules of a particularly appealing form. Given their simplicity, it is natural to wonder if we are able to carry out persistence computations like in 1-D in the setting of clustering. I will discuss recent work with Ulrich Bauer, Steffen Oppermann and Johan Steen, which shows that this restriction alleviates the aforementioned "hardness" in only very special cases. The last part of the talk will concern how much of this complexity we see in persistence modules coming from data.

Links

Saskia Gutzschebauch

Max-Planck-Institut für Mathematik in den Naturwissenschaften Contact via Mail

Christiane Görgen

Max-Planck-Institut für Mathematik in den Naturwissenschaften

Sara Kališnik Verovšek

Max-Planck-Institut für Mathematik in den Naturwissenschaften

Vlada Limic

Université de Strasbourg and CNRS, Paris