Choosing representatives in persistent homology
Vendredi, 15 Décembre, 2023 - 10:30
This talk will center around criteria for choosing representatives in persistent homology, along two main directions.
Firstly, we introduce two algorithms for the computation of an interval basis. An interval basis is a special set of homology generators whose interval modules provide the interval decomposition. One of the algorithms is specialized from a graded version of the Smith normal form, while the other is a scratch-built, parallel one. We compare their complexities and give estimates on when the parallel algorithm has a computational advantage.
Next, we deal with the topic of choosing representative cycles: persistent homology provides a scaffold which has been shown to capture rich mesoscale information in neuroscience, but localizing these representatives is a challenge. We approach the problem via a geometric minimality criterion and present work based on minimal homology bases and related constructions.
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