Name
Abstract | ||
|---|---|---|
Persistent homology, a central tool of topological data analysis, provides invariants of data called barcodes (also known as persistence diagrams). A barcode is simply a multiset of real intervals. Recent work of Edelsbrunner, Jablonski, and Mrozek suggests an equivalent description of barcodes as functors R -u003e Mch, where R is the poset category of real numbers and Mch is the category whose objects are sets and whose morphisms are matchings (i.e., partial injective functions). Such functors form a category Mch^R whose morphisms are the natural transformations. Thus, this interpretation of barcodes gives us a hitherto unstudied categorical structure on barcodes. The aim of this note is to show that this categorical structure leads to surprisingly simple reformulations of both the well-known stability theorem for persistent homology and a recent generalization called the induced matching theorem. |
Year | Venue | Field |
|---|---|---|
2016 | arXiv: Algebraic Topology | Multiset,Categorification,Persistent homology,Functor category,Topological data analysis,Topology,Combinatorics,Algebra,Pure mathematics,Functor,Partially ordered set,Morphism,Mathematics |
DocType | Volume | Citations |
Journal | abs/1610.10085 | 2 |
PageRank | References | Authors |
0.41 | 7 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ulrich Bauer | 1 | 102 | 10.84 |
| Michael Lesnick | 2 | 53 | 7.67 |