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Divisive cover. (English) Zbl 1469.55004

The main contribution of the paper is to present a method for computing persistent homology that performs well at large filtration values. For this purpose the authors introduce the notion of filtered nerve of a filtered cover and construct a new approximation to the Čech complex computing persistent homology down to a predefined threshold that can be chosen arbitrarily. The top-down approach proposed is fundamentally different from existing algorithms which are fundamentally bottom-up.

MSC:

55N31 Persistent homology and applications, topological data analysis
55U99 Applied homological algebra and category theory in algebraic topology
68Q32 Computational learning theory

Software:

SimBa
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Full Text: DOI arXiv

References:

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