Computing Multidimensional Persistence

Details Computing Multidimensional Persistence Computing Multidimensional Persistence

2009-07-14

arxiv.org/abs/0907.2423v3

Computer Science

Computational Geometry

This paper has been withdrawn by the authors. Journal of Computational Geometry, 1(1) 2010, pages 72-100. http://jocg.org/in

Scientific paper

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.

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