The Shift-Dimension of Multipersistence Modules
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866918034407424000 |
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| author | Chachólski, Wojciech Corbet, René Sattelberger, Anna-Laura |
| author_facet | Chachólski, Wojciech Corbet, René Sattelberger, Anna-Laura |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_06509 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The Shift-Dimension of Multipersistence Modules Chachólski, Wojciech Corbet, René Sattelberger, Anna-Laura Commutative Algebra Algebraic Topology 55N31, 16W50 (primary), 16G20, 68W30 (secondary) 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. |
| title | The Shift-Dimension of Multipersistence Modules |
| topic | Commutative Algebra Algebraic Topology 55N31, 16W50 (primary), 16G20, 68W30 (secondary) |
| url | https://arxiv.org/abs/2112.06509 |