22 citations · 32 across the 9 of their papers we have counts for
6 papers · 1 filter
A U-match Algorithm for Persistent Relative Homology
Christian Lentz, Gregory Henselman-Petrusek, Lori Ziegelmeier
A central problem in data-driven scientific inquiry is how to interpret structure in noisy, high-dimensional data. Topological data analysis (TDA) provides a solution via persisten…
Interval Decomposition of Infinite Persistence Modules over a Principal Ideal Domain and Field Choice in Persistent Homology
Jiajie Luo, Gregory Henselman-Petrusek
We study pointwise free and finitely-generated persistence modules over a principal ideal domain, indexed by a (possibly infinite) totally-ordered poset category. We show that such…
Interval Decomposition of Persistence Modules over a Principal Ideal Domain
Jiajie Luo, Gregory Henselman-Petrusek
The study of persistent homology has contributed new insights and perspectives into a variety of interesting problems in science and engineering. Work in this domain relies on the…
Stability for Inference with Persistent Homology Rank Functions
Qiquan Wang, Inés García-Redondo, Pierre Faugère +2
Persistent homology barcodes and diagrams are a cornerstone of topological data analysis that capture the "shape" of a wide range of complex data structures, such as point clouds,…
U-match factorization: sparse homological algebra, lazy cycle representatives, and dualities in persistent (co)homology
Haibin Hang, Chad Giusti, Lori Ziegelmeier +1
Persistent homology is a leading tool in topological data analysis (TDA). Many problems in TDA can be solved via homological -- and indeed, linear -- algebra. However, matrices in…
Minimal Cycle Representatives in Persistent Homology using Linear Programming: an Empirical Study with User's Guide
Lu Li, Connor Thompson, Gregory Henselman-Petrusek +2
Cycle representatives of persistent homology classes can be used to provide descriptions of topological features in data. However, the non-uniqueness of these representatives creat…