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The Shift-Dimension of Multipersistence Modules

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arxiv 2112.06509 v4 pith:OJW27AA5 submitted 2021-12-13 math.AC math.AT

Wojciech Chachólski , René Corbet , Anna-Laura Sattelberger This is my paper · ORCID
classification math.ACmath.AT
keywords modulesmultipersistenceshift-dimensionmultigradedmultivariatealgebraicalgorithmarising
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We present the shift-dimension of multipersistence modules and investigate its algebraic properties. This gives rise to a new invariant of multigraded modules over the multivariate polynomial ring arising from the hierarchical stabilization of the zeroth total multigraded Betti number. We give a fast algorithm for the computation of the shift-dimension of interval modules in the bivariate case. We construct multipersistence contours that are parameterized by multivariate functions and hence provide a large class of feature maps for machine learning tasks.

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Cited by 1 Pith paper

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  1. Path representations in multiparameter persistent homology

    math.AT 2025-07 conditional novelty 4.0 of 10

    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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