A Survey of Vectorization Methods in Topological Data Analysis

被引：23

作者：

Ali, Dashti ^{[1
]}

Asaad, Aras ^{[1
,2
]}

Jimenez, Maria-Jose ^{[3
,4
]}

Nanda, Vidit ^{[5
]}

Paluzo-Hidalgo, Eduardo ^{[6
]}

Soriano-Trigueros, Manuel ^{[6
,7
]}

机构：

[1] Koya Univ, KO50 1001, Koysinjaq, Kurdistan, Iraq

[2] Univ Buckingham, Sch Comp, Buckingham MK18 1EG, England

[3] Univ Oxford, Mathemat Inst, Oxford OX1 3AZ, England

[4] Univ Seville, Dept Matemat Aplicada 1, Seville 41004, Spain

[5] Univ Oxford, Math Inst, Oxford OX1 3AZ, England

[6] Univ Seville, Dept Matemat Aplicada 1, Seville 41004, Spain

[7] IST Austria, A-3400 Klosterneuburg, Austria

来源：

IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE | 2023年 / 45卷 / 12期

基金：

英国工程与自然科学研究理事会;

关键词：

Barcodes; persistent homology; topological data analysis; vectorization methods; PERSISTENCE; NETWORK;

D O I：

10.1109/TPAMI.2023.3308391

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

Attempts to incorporate topological information in supervised learning tasks have resulted in the creation of several techniques for vectorizing persistent homology barcodes. In this paper, we study thirteen such methods. Besides describing an organizational framework for these methods, we comprehensively benchmark them against three well-known classification tasks. Surprisingly, we discover that the best-performing method is a simple vectorization, which consists only of a few elementary summary statistics. Finally, we provide a convenient web application which has been designed to facilitate exploration and experimentation with various vectorization methods.

引用

页码：14069 / 14080

页数：12

共 63 条

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Adams H, 2017, J MACH LEARN RES, V18

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