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Jun, 2023
使用有符号条码作为度量标准的多参数持久同调稳定的向量化
Stable Vectorization of Multiparameter Persistent Homology using Signed Barcodes as Measures
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David Loiseaux, Luis Scoccola, Mathieu Carrière, Magnus Bakke Botnan, Steve Oudot
TL;DR
本文旨在通过将符号条形码的解释作为符号测度来显示,将单参数持久性同多参数持久性相结合,从而延伸了从一个参数到多个参数的向量化策略,从而得到了易于定义和计算的特征向量,并且具有可证的稳定性。
Abstract
persistent homology
(PH) provides
topological descriptors
for geometric data, such as weighted graphs, which are interpretable, stable to perturbations, and invariant under, e.g., relabeling. Most applications of
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