A Comparative Study of Machine Learning Methods for Persistence Diagrams
Many and varied methods currently exist for featurization, which is the process of mapping persistence diagrams to Euclidean space, with the goal of maximally preserving structure. However, and to our knowledge, there are presently no methodical comparisons of existing approaches, nor a standardized...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2021-07-01
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| Series: | Frontiers in Artificial Intelligence |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/frai.2021.681174/full |
| _version_ | 1818640829746511872 |
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| author | Danielle Barnes Luis Polanco Luis Polanco Jose A. Perea Jose A. Perea |
| author_facet | Danielle Barnes Luis Polanco Luis Polanco Jose A. Perea Jose A. Perea |
| author_sort | Danielle Barnes |
| collection | DOAJ |
| description | Many and varied methods currently exist for featurization, which is the process of mapping persistence diagrams to Euclidean space, with the goal of maximally preserving structure. However, and to our knowledge, there are presently no methodical comparisons of existing approaches, nor a standardized collection of test data sets. This paper provides a comparative study of several such methods. In particular, we review, evaluate, and compare the stable multi-scale kernel, persistence landscapes, persistence images, the ring of algebraic functions, template functions, and adaptive template systems. Using these approaches for feature extraction, we apply and compare popular machine learning methods on five data sets: MNIST, Shape retrieval of non-rigid 3D Human Models (SHREC14), extracts from the Protein Classification Benchmark Collection (Protein), MPEG7 shape matching, and HAM10000 skin lesion data set. These data sets are commonly used in the above methods for featurization, and we use them to evaluate predictive utility in real-world applications. |
| first_indexed | 2024-12-16T23:17:30Z |
| format | Article |
| id | doaj.art-171bedf6bb9f48c3a859ce546d30ea9c |
| institution | Directory Open Access Journal |
| issn | 2624-8212 |
| language | English |
| last_indexed | 2024-12-16T23:17:30Z |
| publishDate | 2021-07-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Artificial Intelligence |
| spelling | doaj.art-171bedf6bb9f48c3a859ce546d30ea9c2022-12-21T22:12:14ZengFrontiers Media S.A.Frontiers in Artificial Intelligence2624-82122021-07-01410.3389/frai.2021.681174681174A Comparative Study of Machine Learning Methods for Persistence DiagramsDanielle Barnes0Luis Polanco1Luis Polanco2Jose A. Perea3Jose A. Perea4Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, MI, United StatesDepartment of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, MI, United StatesDepartment of Mathematics, Michigan State University, East Lansing, MI, United StatesDepartment of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, MI, United StatesDepartment of Mathematics, Michigan State University, East Lansing, MI, United StatesMany and varied methods currently exist for featurization, which is the process of mapping persistence diagrams to Euclidean space, with the goal of maximally preserving structure. However, and to our knowledge, there are presently no methodical comparisons of existing approaches, nor a standardized collection of test data sets. This paper provides a comparative study of several such methods. In particular, we review, evaluate, and compare the stable multi-scale kernel, persistence landscapes, persistence images, the ring of algebraic functions, template functions, and adaptive template systems. Using these approaches for feature extraction, we apply and compare popular machine learning methods on five data sets: MNIST, Shape retrieval of non-rigid 3D Human Models (SHREC14), extracts from the Protein Classification Benchmark Collection (Protein), MPEG7 shape matching, and HAM10000 skin lesion data set. These data sets are commonly used in the above methods for featurization, and we use them to evaluate predictive utility in real-world applications.https://www.frontiersin.org/articles/10.3389/frai.2021.681174/fullpersistent homologymachine learningtopological data analysispersistence diagramsbarcodes |
| spellingShingle | Danielle Barnes Luis Polanco Luis Polanco Jose A. Perea Jose A. Perea A Comparative Study of Machine Learning Methods for Persistence Diagrams Frontiers in Artificial Intelligence persistent homology machine learning topological data analysis persistence diagrams barcodes |
| title | A Comparative Study of Machine Learning Methods for Persistence Diagrams |
| title_full | A Comparative Study of Machine Learning Methods for Persistence Diagrams |
| title_fullStr | A Comparative Study of Machine Learning Methods for Persistence Diagrams |
| title_full_unstemmed | A Comparative Study of Machine Learning Methods for Persistence Diagrams |
| title_short | A Comparative Study of Machine Learning Methods for Persistence Diagrams |
| title_sort | comparative study of machine learning methods for persistence diagrams |
| topic | persistent homology machine learning topological data analysis persistence diagrams barcodes |
| url | https://www.frontiersin.org/articles/10.3389/frai.2021.681174/full |
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