Opened Access Towards Minimal Barcodes

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Author: González Díaz, Rocío
Jiménez Rodríguez, María José
Krim, Hamid
Department: Universidad de Sevilla. Departamento de Matemática Aplicada I
Date: 2013
Published in: Graph-Based Representations in Pattern Recognition, Lecture Notes in Computer Science, Vol. 7877 p.184-193
Document type: Chapter of Book
Abstract: In the setting of persistent homology computation, a useful tool is the persistence barcode representation in which pairs of birth and death times of homology classes are encoded in the form of intervals. Starting from a polyhedral complex K (an object subdivided into cells which are polytopes) and an initial order of the set of vertices, we are concerned with the general problem of searching for filters (an order of the rest of the cells) that provide a minimal barcode representation in the sense of having minimal number of “k-significant” intervals, which correspond to homology classes with life-times longer than a fixed number k. As a first step, in this paper we provide an algorithm for computing such a filter for k = 1 on the Hasse diagram of the poset of faces of K.
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