214 citations · 626 across the 16 of their papers we have counts for
14 papers · 1 filter
Fast Queries of Fibered Barcodes
Michael Lesnick, Matthew Wright
The fibered barcode of a bipersistence module is the map sending each non-negatively sloped affine line to the barcode of the restr…
Efficient two-parameter persistence computation via cohomology
Ulrich Bauer, Fabian Lenzen, Michael Lesnick
Clearing is a simple but effective optimization for the standard algorithm of persistent homology (PH), which dramatically improves the speed and scalability of PH computations for…
An Introduction to Multiparameter Persistence
Magnus Bakke Botnan, Michael Lesnick
In topological data analysis (TDA), one often studies the shape of data by constructing a filtered topological space, whose structure is then examined using persistent homology. Ho…
-Distances on Multiparameter Persistence Modules
Håvard Bakke Bjerkevik, Michael Lesnick
Motivated both by theoretical and practical considerations in topological data analysis, we generalize the -Wasserstein distance on barcodes to multiparameter persistence module…
Stability of 2-Parameter Persistent Homology
Andrew J. Blumberg, Michael Lesnick
The Čech and Rips constructions of persistent homology are stable with respect to perturbations of the input data. However, neither is robust to outliers, and both can be insensiti…
Computing Minimal Presentations and Bigraded Betti Numbers of 2-Parameter Persistent Homology
Michael Lesnick, Matthew Wright
Motivated by applications to topological data analysis, we give an efficient algorithm for computing a (minimal) presentation of a bigraded -module , where is a fiel…