An entropy-based persistence barcode. Issue 2 (February 2015)

• Record Type: Journal Article
• Authors: Chintakunta, Harish; Gentimis, Thanos; Gonzalez-Diaz, Rocio; Jimenez, Maria-Jose; Krim, Hamid
• Is Part Of: Pattern recognition. Volume 48:Issue 2(2015:Feb.)
• Page Start: 391
• Page End: 401
• Publication Date: 2015-02
• Subjects: Pattern perception -- Periodicals; Perception des structures -- Périodiques; Patroonherkenning; 006.4
• DOI: 10.1016/j.patcog.2014.06.023
• Languages: English
• ISSNs: 0031-3203

Abstract

<abstract abstract-type="author" id="ab0005"> <title id="sect0005">Abstract</title> <sec> <p id="sp0055">In persistent homology, the persistence barcode encodes pairs of simplices meaning birth and death of homology classes. Persistence barcodes depend on the ordering of the simplices (called a filter) of the given simplicial complex. In this paper, we define the notion of "minimal" barcodes in terms of entropy. Starting from a given filtration of a simplicial complex <italic>K</italic>, an algorithm for computing a "proper" filter (a total ordering of the simplices preserving the partial ordering imposed by the filtration as well as achieving a persistence barcode with small entropy) is detailed, by way of computation, and subsequent modification, of maximum matchings on subgraphs of the Hasse diagram associated to <italic>K</italic>. Examples demonstrating the utility of computing such a proper ordering on the simplices are given.</p> </sec> </abstract>