[Topology.beta] Tomorrow lucas slot in ctaaag

[Rot, T.O. (Thomas)]

Dear all,

Tomorrow we have a ctaaag with an external speaker!

Best,
Thomas
AG: 29-04-2025: Lucas Slot:<https://www.lucasslot.com/> Robust persistent features and homological cuts

Persistent homology is a popular method to compute topological features of metric data. Standard approaches based on the \v{C}ech or Vietoris-Rips filtration are stable under small perturbations of the data, but highly sensitive to outliers. Several alternative filtrations have been suggested to address this issue. However, these are only provably robust under relatively tame noise models. In this paper, we take a different perspective and consider the following question: Given metric data $Y = X \cup W$ consisting of uncorrupted data $X$ and a fixed fraction $\alpha \in (0, 1)$ of arbitrary outliers~$W$, which persistent features of~$Y$ can be guaranteed to reflect persistent features of~$X$? We formalize this question by introducing the notion of $\alpha$-robustness, and study the question of deciding whether a given bar in a barcode of $Y$ is $\alpha$-robust.

Join work (in progress) with Pepijn Roos Hoefgeest

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <https://listserver.vu.nl/pipermail/topology.beta/attachments/20250428/080546f7/attachment.html>