120 citations · 472 across the 33 of their papers we have counts for
49 papers
The Localized Union-of-Balls Bifiltration
Michael Kerber, Matthias Söls
We propose an extension of the classical union-of-balls filtration of persistent homology: fixing a point , we focus our attention to a ball centered at whose radius is cont…
Decomposition of zero-dimensional persistence modules via rooted subsets
Ángel Javier Alonso, Michael Kerber
We study the decomposition of zero-dimensional persistence modules, viewed as functors valued in the category of vector spaces factorizing through sets. Instead of working directly…
Sparse Higher Order Čech Filtrations
Mickaël Buchet, Bianca B. Dornelas, Michael Kerber
For a finite set of balls of radius , the -fold cover is the space covered by at least balls. Fixing the ball centers and varying the radius, we obtain a nested sequence…
Filtration-Domination in Bifiltered Graphs
Ángel Javier Alonso, Michael Kerber, Siddharth Pritam
Bifiltered graphs are a versatile tool for modelling relations between data points across multiple grades of a two-dimensional scale. They are especially popular in topological dat…
Keeping it sparse: Computing Persistent Homology revisited
Ulrich Bauer, Talha Bin Masood, Barbara Giunti +3
In this work, we study several variants of matrix reduction via Gaussian elimination that try to keep the reduced matrix sparse. The motivation comes from the growing field of topo…
A Unified View on the Functorial Nerve Theorem and its Variations
Ulrich Bauer, Michael Kerber, Fabian Roll +1
The nerve theorem is a basic result of algebraic topology that plays a central role in computational and applied aspects of the subject. In topological data analysis, one often nee…