A Survey of Vectorization Methods in Topological Data Analysis
A Survey of Vectorization Methods in Topological Data Analysis
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DOI：
10.1109/tpami.2023.3308391
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发表时间：
2022-12
影响因子：
23.6
通讯作者：
Dashti Ali;Aras T. Asaad;M. Jiménez;Vidit Nanda;Eduardo Paluzo-Hidalgo;M. Soriano-Trigueros
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文献类型：
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作者：
Dashti Ali;Aras T. Asaad;M. Jiménez;Vidit Nanda;Eduardo Paluzo-Hidalgo;M. Soriano-Trigueros
在监督学习任务中结合拓扑信息的尝试已经导致产生了几种用于矢量化持久同源性条形码的技术。在本文中，我们研究了13个这样的方法。除了描述这些方法的组织框架外，我们还将它们与三个著名的分类任务进行了全面的基准测试。令人惊讶的是，我们发现性能最好的方法是一个简单的矢量化，它只包括一些基本的汇总统计。最后，我们提供了一个方便的Web应用程序，该应用程序旨在促进对各种矢量化方法的探索和实验。
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.