A Survey of Vectorization Methods in Topological Data Analysis

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 comprehen...

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Bibliographic Details
Published in:IEEE transactions on pattern analysis and machine intelligence 2023-12, Vol.45 (12), p.1-14
Main Authors: Ali, Dashti, Asaad, Aras, Jimenez, Maria-Jose, Nanda, Vidit, Paluzo-Hidalgo, Eduardo, Soriano-Trigueros, Manuel
Format: Article
Language:English
Subjects:
Applications programs
barcodes
Cognitive tasks
Data analysis
Homology
persistent homology
Supervised learning
Topological data analysis
Topology
vectorization methods
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Summary: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.
ISSN:0162-8828
2160-9292
1939-3539
DOI:10.1109/TPAMI.2023.3308391