Computing multidimensional persistence

Computing multidimensional persistence

<p>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 multidime...

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Main Authors: Gunnar Carlsson, Gurjeet Singh, Afra J. Zomorodian
Format: Article
Language:English
Published: Carleton University 2010-11-01
Series:Journal of Computational Geometry
Online Access:http://jocg.org/index.php/jocg/article/view/19
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spelling doaj-42c11cd19726436ba85f6ebcecaa2c522020-11-25T00:09:18ZengCarleton UniversityJournal of Computational Geometry1920-180X2010-11-011110.20382/jocg.v1i1a610Computing multidimensional persistenceGunnar Carlsson0Gurjeet Singh1Afra J. Zomorodian2Stanford UniversityStanford UniversityDartmouth College<p>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 commutative algebra 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.</p>http://jocg.org/index.php/jocg/article/view/19
collection DOAJ
language English
format Article
sources DOAJ
author Gunnar Carlsson
Gurjeet Singh
Afra J. Zomorodian
spellingShingle Gunnar Carlsson
Gurjeet Singh
Afra J. Zomorodian
Computing multidimensional persistence
Journal of Computational Geometry
author_facet Gunnar Carlsson
Gurjeet Singh
Afra J. Zomorodian
author_sort Gunnar Carlsson
title Computing multidimensional persistence
title_short Computing multidimensional persistence
title_full Computing multidimensional persistence
title_fullStr Computing multidimensional persistence
title_full_unstemmed Computing multidimensional persistence
title_sort computing multidimensional persistence
publisher Carleton University
series Journal of Computational Geometry
issn 1920-180X
publishDate 2010-11-01
description <p>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 commutative algebra 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.</p>
url http://jocg.org/index.php/jocg/article/view/19
work_keys_str_mv AT gunnarcarlsson computingmultidimensionalpersistence
AT gurjeetsingh computingmultidimensionalpersistence
AT afrajzomorodian computingmultidimensionalpersistence
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