Geodesic
The ring of algebraic functions on persistence bar codes
Homology, homotopy, and applications, Tome 18 (2016) no. 1, pp. 381-402.

Voir la notice de l'article provenant de la source International Press of Boston

Persistent homology is a rapidly developing field in the study of numerous kinds of data sets. It is a functor which assigns to geometric objects so-called persistence bar codes, which are finite collections of intervals. These bar codes can be used to infer topological aspects of the geometric object. The set of all persistence bar codes, suitably defined, is known to possess metrics that are quite useful both theoretically and in practice. In this paper, we explore the possibility of coordinatizing, in a suitable sense, this same set of persistence bar codes. We derive a set of coordinates using results about multi-symmetric functions, study the property of the corresponding ring of functions, and demonstrate in an example how they work.
DOI : 10.4310/HHA.2016.v18.n1.a21
Classification : 55N99, 62-07
Keywords: persistent homology, point cloud, metric space, data analysis 
@article{HHA_2016_18_1_a20,
     author = {Aaron Adcock and Erik Carlsson and Gunnar Carlsson},
     title = {The ring of algebraic functions on persistence bar codes},
     journal = {Homology, homotopy, and applications},
     pages = {381--402},
     publisher = {mathdoc},
     volume = {18},
     number = {1},
     year = {2016},
     doi = {10.4310/HHA.2016.v18.n1.a21},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2016.v18.n1.a21/}
}
TY  - JOUR
AU  - Aaron Adcock
AU  - Erik Carlsson
AU  - Gunnar Carlsson
TI  - The ring of algebraic functions on persistence bar codes
JO  - Homology, homotopy, and applications
PY  - 2016
SP  - 381
EP  - 402
VL  - 18
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4310/HHA.2016.v18.n1.a21/
DO  - 10.4310/HHA.2016.v18.n1.a21
LA  - en
ID  - HHA_2016_18_1_a20
ER  - 
%0 Journal Article
%A Aaron Adcock
%A Erik Carlsson
%A Gunnar Carlsson
%T The ring of algebraic functions on persistence bar codes
%J Homology, homotopy, and applications
%D 2016
%P 381-402
%V 18
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4310/HHA.2016.v18.n1.a21/
%R 10.4310/HHA.2016.v18.n1.a21
%G en
%F HHA_2016_18_1_a20
Aaron Adcock; Erik Carlsson; Gunnar Carlsson. The ring of algebraic functions on persistence bar codes. Homology, homotopy, and applications, Tome 18 (2016) no. 1, pp. 381-402. doi : 10.4310/HHA.2016.v18.n1.a21. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2016.v18.n1.a21/

Cité par Sources :