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Computing Multidimensional Persistence

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Author(s): Gunnar Carlsson | Gurjeet Singh | Afra J. Zomorodian

Journal: Journal of Computational Geometry
ISSN 1920-180X

Volume: 1;
Issue: 1;
Start page: 72;
Date: 2010;
Original page

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 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.
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