21 citations · 21 across the 3 of their papers we have counts for
7 papers
The Degree-Rips Complexes of an Annulus with Outliers
Alexander Rolle
The degree-Rips bifiltration is the most computable of the parameter-free, density-sensitive bifiltrations in topological data analysis. It is known that this construction is stabl…
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…
Compression for 2-Parameter Persistent Homology
Ulderico Fugacci, Michael Kerber, Alexander Rolle
Compression aims to reduce the size of an input, while maintaining its relevant properties. For multi-parameter persistent homology, compression is a necessary step in any computat…
Fast Minimal Presentations of Bi-graded Persistence Modules
Michael Kerber, Alexander Rolle
Multi-parameter persistent homology is a recent branch of topological data analysis. In this area, data sets are investigated through the lens of homology with respect to two or mo…
Stable and consistent density-based clustering via multiparameter persistence
Alexander Rolle, Luis Scoccola
We consider the degree-Rips construction from topological data analysis, which provides a density-sensitive, multiparameter hierarchical clustering algorithm. We analyze its stabil…
Visualization tools for parameter selection in cluster analysis
Alexander Rolle, Luis Scoccola
We propose an algorithm, HPREF (Hierarchical Partitioning by Repeated Features), that produces a hierarchical partition of a set of clusterings of a fixed dataset, such as sets of…
Central extensions and the classifying spaces of projective linear groups
Alexander Rolle
If is a presheaf of groupoids on a small site, and is a sheaf of abelian groups, we prove that the sheaf cohomology group is in bijection with a set of centra…