Minimal Cycle Representatives in Persistent Homology Using Linear Programming: An Empirical Study With User's Guide.

ABSTRACT: Cycle representatives of persistent homology classes can be used to provide descriptions of topological features in data. However, the non-uniqueness of these representatives creates ambiguity and can lead to many different interpretations of the same set of classes. One approach to solving this problem is to optimize the choice of representative against some measure that is meaningful in the context of the data. In this work, we provide a study of the effectiveness and computational cost of several ℓ 1 minimization optimization procedures for constructing homological cycle bases for persistent homology with rational coefficients in dimension one, including uniform-weighted and length-weighted edge-loss algorithms as well as uniform-weighted and area-weighted triangle-loss algorithms. W

SUBMITTER: Li L 

PROVIDER: S-EPMC8544243 | biostudies-literature | 2021

REPOSITORIES: biostudies-literature