تقرير
Matching distance via the extended Pareto grid
| العنوان: | Matching distance via the extended Pareto grid |
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| المؤلفون: | Frosini, Patrizio, García, Eloy Mósig, Quercioli, Nicola, Tombari, Francesca |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Topology |
| الوصف: | One of the most animated themes of multidimensional persistence is the comparison between invariants. The matching distance between persistent Betti numbers functions (or rank invariants), is among the most studied metrics in this context, particularly in 2-parameter persistence. The main reason for this interest is that, in the 2-parameter case, the foliation method allows for an effective computation of the matching distance, based on filtering the space along lines of positive slope. Our work provides a qualitative analysis, based on a construction called extended Pareto grid, of the filtering lines that actually contribute to the computation of the matching distance. Under certain genericity assumptions, we show that these lines must either be horizontal, vertical, of slope 1 or belong to a finite collection of special lines associated with discontinuity phenomena. Comment: Theorem 5 is now a stronger result and Appendix B has been added |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2312.04201 |
| رقم الأكسشن: | edsarx.2312.04201 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |