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 [5, 9], a fundamental result in the theory of persistent homology. In contrast to previous proofs, ours shows explicitly how a δ-interleaving morphism between two persistence modules induces a δ-matching between the barcodes of the two modules. Our main result also specializes to a structure theorem for submodules and quotients of persistence modules. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1145/2582112.2582168 | symposium on computational geometry |
Keywords | DocType | Volume |
main result,explicit map,immediate corollary,pointwise finite dimensional persistence,structure theorem,persistence module,persistence barcodes,induced matchings,algebraic stability theorem,fundamental result,algebraic stability,interleaving morphism | Conference | abs/1311.3681 |
Citations | PageRank | References |
12 | 0.93 | 14 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ulrich Bauer | 1 | 102 | 10.84 |
| Michael Lesnick | 2 | 53 | 7.67 |