An entropy-based persistence barcode
An entropy-based persistence barcode
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DOI：
10.1016/j.patcog.2014.06.023
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发表时间：
2015-02-01
影响因子：
8
通讯作者：
Krim, Hamid
中科院分区：
文献类型：
--
作者：
Chintakunta, Harish;Gentimis, Thanos;Krim, Hamid
在持久同源性中，持久条形码编码表示同源类的出生和死亡的单形对。持久性条形码取决于给定单纯复形的单纯形（称为过滤器）的排序。在本文中，我们定义的概念，“最小”条码的熵。从单纯复形K的给定过滤开始，通过与K相关联的Hasse图的子图上的最大匹配的计算和随后的修改，详细描述了用于计算“适当”过滤器（保持由过滤施加的偏序的单纯形的总排序以及实现具有小熵的持久性条形码）的算法。给出了示例，演示了在单形上计算这种正确排序的实用性。(C)2014爱思唯尔有限公司版权所有。
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 K, 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 K. Examples demonstrating the utility of computing such a proper ordering on the simplices are given. (C) 2014 Elsevier Ltd. All rights reserved.