Stable Invariants for Multiparameter Persistence

Abstract

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.

References in corpus (1)

• Metrics for generalized persistence modules

Cited by in corpus (2)

• Generalized persistence analysis based on stable rank invariant
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