On the stability of persistent entropy and new summary functions for topological data analysis

被引：47

作者：

Atienza, Nieves ^{[1
]}

Gonzalez-Diaz, Rocio ^{[1
]}

Soriano-Trigueros, Manuel ^{[1
]}

机构：

[1] Univ Seville, Dept Appl Math 1, Seville, Spain

来源：

PATTERN RECOGNITION | 2020年 / 107卷

关键词：

Persistent homology; Persistent entropy; Stability; Dimensionality reduction;

D O I：

10.1016/j.patcog.2020.107509

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

Persistent homology and persistent entropy have recently become useful tools for patter recognition. In this paper, we find requirements under which persistent entropy is stable to small perturbations in the input data and scale invariant. In addition, we describe two new stable summary functions combining persistent entropy and the Betti curve. Finally, we use the previously defined summary functions in a material classification task to show their usefulness in machine learning and pattern recognition. (C) 2020 Elsevier Ltd. All rights reserved.

引用

页数：15

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