Name
Abstract | ||
|---|---|---|
We define a simple, explicit map sending a morphism f : M -> N of pointwise finite dimensional persistence modules to a matching between the barcodes of M and N. Our main result is that, in a precise sense, the quality of this matching is tightly controlled by the lengths of the longest intervals in the barcodes of ker f and coker f.As an immediate corollary, we obtain a new proof of the algebraic stability theorem for persistence barcodes [7, 10], a fundamental result in the theory of persistent homology. In contrast to previous proofs, ours shows explicitly how a delta-interleaving morphism between two persistence modules induces a delta-matching between the barcodes of the two modules. Our main result also specializes to a structure theorem for submodules and quotients of persistence modules, and yields a novel "single-morphism" characterization of the interleaving relation on persistence modules. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.20382/JOCG.V6I2A9 | JOURNAL OF COMPUTATIONAL GEOMETRY |
Field | DocType | Volume |
Structured program theorem,Topology,Discrete mathematics,Combinatorics,Quotient,Persistent homology,Mathematical proof,Corollary,Algebraic stability,Mathematics,Morphism,Pointwise | Journal | 6 |
Issue | ISSN | Citations |
2 | 1920-180X | 8 |
PageRank | References | Authors |
1.14 | 12 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ulrich Bauer | 1 | 102 | 10.84 |
| Michael Lesnick | 2 | 53 | 7.67 |