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A Survey of Vectorization Methods in Topological Data Analysis

2023; IEEE Computer Society; Volume: 45; Issue: 12 Linguagem: Inglês

10.1109/tpami.2023.3308391

2160-9292

Dashti Ali, Aras Asaad, María-José Jiménez, Vidit Nanda, Eduardo Paluzo-Hidalgo, M. Soriano-Trigueros,

Image Retrieval and Classification Techniques

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.