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Stable Invariants for Multiparameter Persistence
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In this paper we explain how to convert discrete invariants into stable ones via what we call hierarchical stabilization. We illustrate this process by constructing stable invariants for multi-parameter persistence modules with respect to the interleaving distance and so called simple noise systems. For one parameter, we recover the standard barcode information. For more than one parameter we prove that the constructed invariants are in general NP-hard to calculate. A consequence is that computing the feature counting function, proposed by Scolamiero et. al. (2016), is NP-hard.
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Cited by 1 Pith paper
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Path representations in multiparameter persistent homology
A multiparameter persistence distance is defined by taking persistence along monotone piecewise-linear paths instead of straight slices, generalizing the matching distance.
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