Computing Multidimensional Persistence
Abstract
The theory of multidimensional persistence captures the topology of a multifiltration -- a multiparameter family of increasing spaces. Multifiltrations arise naturally in the topological analysis of scientific data. In this paper, we give a polynomial time algorithm for computing multidimensional persistence. We recast this computation as a problem within computational algebraic geometry and utilize algorithms from this area to solve it. While the resulting problem is Expspace-complete and the standard algorithms take doubly-exponential time, we exploit the structure inherent withing multifiltrations to yield practical algorithms. We implement all algorithms in the paper and provide statistical experiments to demonstrate their feasibility.
Cite
@article{arxiv.0907.2423,
title = {Computing Multidimensional Persistence},
author = {Gunnar Carlsson and Gurjeet Singh and Afra Zomorodian},
journal= {arXiv preprint arXiv:0907.2423},
year = {2010}
}
Comments
This paper has been withdrawn by the authors. Journal of Computational Geometry, 1(1) 2010, pages 72-100. http://jocg.org/index.php/jocg/article/view/19