Computing multidimensional persistence
DOI:
https://doi.org/10.20382/jocg.v1i1a6Abstract
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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