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arXiv · 2112.06509

The Shift-Dimension of Multipersistence Modules

Wojciech Chachólski·René Corbet·Anna-Laura Sattelberger
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Abstract

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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Wojciech Chachólski, René Corbet, Anna-Laura Sattelberger. 2021-12-13. The Shift-Dimension of Multipersistence Modules. https://doi.org/10.1007/s41468-024-00169-6

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