120 citations · 472 across the 33 of their papers we have counts for
6 papers · 1 filter
Improved Topological Approximations by Digitization
Aruni Choudhary, Michael Kerber, Sharath Raghvendra
Čech complexes are useful simplicial complexes for computing and analyzing topological features of data that lies in Euclidean space. Unfortunately, computing these complexes becom…
Exact computation of the matching distance on 2-parameter persistence modules
Michael Kerber, Michael Lesnick, Steve Oudot
The matching distance is a pseudometric on multi-parameter persistence modules, defined in terms of the weighted bottleneck distance on the restriction of the modules to affine lin…
Chunk Reduction for Multi-Parameter Persistent Homology
Ulderico Fugacci, Michael Kerber
The extension of persistent homology to multi-parameter setups is an algorithmic challenge. Since most computation tasks scale badly with the size of the input complex, an importan…
Topology and Geometry of Gaussian random fields I: on Betti Numbers, Euler characteristic and Minkowski functionals
Pratyush Pranav, Rien van de Weygaert, Gert Vegter +6
This study presents a numerical analysis of the topology of a set of cosmologically interesting three-dimensional Gaussian random fields in terms of their Betti numbers , $β_1…
Computing the interleaving distance is NP-hard
Håvard Bakke Bjerkevik, Magnus Bakke Botnan, Michael Kerber
We show that computing the interleaving distance between two multi-graded persistence modules is NP-hard. More precisely, we show that deciding whether two modules are -interlea…
A Kernel for Multi-Parameter Persistent Homology
René Corbet, Ulderico Fugacci, Michael Kerber +2
Topological data analysis and its main method, persistent homology, provide a toolkit for computing topological information of high-dimensional and noisy data sets. Kernels for one…