A Survey of Vectorization Methods in Topological Data Analysis
Fuente:
arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866913263556493312 |
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| author | Ali, Dashti Asaad, Aras Jimenez, Maria-Jose Nanda, Vidit Paluzo-Hidalgo, Eduardo Soriano-Trigueros, Manuel |
| author_facet | Ali, Dashti Asaad, Aras Jimenez, Maria-Jose Nanda, Vidit Paluzo-Hidalgo, Eduardo Soriano-Trigueros, Manuel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_09703 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A Survey of Vectorization Methods in Topological Data Analysis Ali, Dashti Asaad, Aras Jimenez, Maria-Jose Nanda, Vidit Paluzo-Hidalgo, Eduardo Soriano-Trigueros, Manuel Algebraic Topology 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. |
| title | A Survey of Vectorization Methods in Topological Data Analysis |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2212.09703 |