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Generalized persistence and statistical topology



Datum: 29.06.2010
Uhrzeit: 16 Uhr

Ort: MZH 1090


Vortragende(r): Prof. Dr. Gunnar Carlsson Homepage - Vortragende(r)
[ Department of Mathematics Stanford University, USA ]

Fortsetzung der Bremen Lectures in Mathematics 2010.

In attempting to infer qualitative geometric properties from point cloud data, one is often led to problems involving the choice of a scale parameter. For example, single linkage clustering partitions a point cloud into pieces by connecting all pairs of points whose distance is less than a fixed scale parameter. The choice of this parameter is typically done in ways which do not have good basis in theory, and one should expect that no single choice is "correct" in all situations. Statisticians resolved this problem by studying hierarchical clustering, in which one summarizes all the clusterings which occur for all scale values using a rooted tree called a dendrogram. The idea of summarizing behavior over all parameter values is a very powerful one, and in recent years it has been extended to yield analogous summarizes for higher dimensional Betti numbers. I will discuss this development, as well as generalizations of it which permit, for instance, the study of qualitative properties when one is given a family of samples from a large data set.



Ansprechpartner(in) / Einladende(r):
Prof. Dr. Eva-Maria Feichtner
Prof. Dr. Dmitry Feichtner-Kozlov
Prof. Dr. Rudolf Hoffmann





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