TY - JOUR
T1 - Ripser
T2 - efficient computation of Vietoris–Rips persistence barcodes
AU - Bauer, Ulrich
N1 - Publisher Copyright:
© 2021, The Author(s).
PY - 2021/9
Y1 - 2021/9
N2 - We present an algorithm for the computation of Vietoris–Rips persistence barcodes and describe its implementation in the software Ripser. The method relies on implicit representations of the coboundary operator and the filtration order of the simplices, avoiding the explicit construction and storage of the filtration coboundary matrix. Moreover, it makes use of apparent pairs, a simple but powerful method for constructing a discrete gradient field from a total order on the simplices of a simplicial complex, which is also of independent interest. Our implementation shows substantial improvements over previous software both in time and memory usage.
AB - We present an algorithm for the computation of Vietoris–Rips persistence barcodes and describe its implementation in the software Ripser. The method relies on implicit representations of the coboundary operator and the filtration order of the simplices, avoiding the explicit construction and storage of the filtration coboundary matrix. Moreover, it makes use of apparent pairs, a simple but powerful method for constructing a discrete gradient field from a total order on the simplices of a simplicial complex, which is also of independent interest. Our implementation shows substantial improvements over previous software both in time and memory usage.
KW - Persistent homology. Vietoris-Rips complexes. Topological data analysis. Discrete Morse theory
UR - http://www.scopus.com/inward/record.url?scp=85126325632&partnerID=8YFLogxK
U2 - 10.1007/s41468-021-00071-5
DO - 10.1007/s41468-021-00071-5
M3 - Article
AN - SCOPUS:85126325632
SN - 2367-1726
VL - 5
SP - 391
EP - 423
JO - Journal of Applied and Computational Topology
JF - Journal of Applied and Computational Topology
IS - 3
ER -