Shape-Based Classification of Partially Observed Curves, With Applications to Anthropology
We consider the problem of classifying curves when they are observed only partially on their parameter domains. We propose computational methods for (i) completion of partially observed curves; (ii) assessment of completion variability through a nonparametric multiple imputation procedure; (iii) dev...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2021-10-01
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| Series: | Frontiers in Applied Mathematics and Statistics |
| Subjects: | |
| Online Access: | https://www.frontiersin.org/articles/10.3389/fams.2021.759622/full |
| _version_ | 1818361139148357632 |
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| author | Gregory J. Matthews Karthik Bharath Sebastian Kurtek Juliet K. Brophy Juliet K. Brophy George K. Thiruvathukal Ofer Harel |
| author_facet | Gregory J. Matthews Karthik Bharath Sebastian Kurtek Juliet K. Brophy Juliet K. Brophy George K. Thiruvathukal Ofer Harel |
| author_sort | Gregory J. Matthews |
| collection | DOAJ |
| description | We consider the problem of classifying curves when they are observed only partially on their parameter domains. We propose computational methods for (i) completion of partially observed curves; (ii) assessment of completion variability through a nonparametric multiple imputation procedure; (iii) development of nearest neighbor classifiers compatible with the completion techniques. Our contributions are founded on exploiting the geometric notion of shape of a curve, defined as those aspects of a curve that remain unchanged under translations, rotations and reparameterizations. Explicit incorporation of shape information into the computational methods plays the dual role of limiting the set of all possible completions of a curve to those with similar shape while simultaneously enabling more efficient use of training data in the classifier through shape-informed neighborhoods. Our methods are then used for taxonomic classification of partially observed curves arising from images of fossilized Bovidae teeth, obtained from a novel anthropological application concerning paleoenvironmental reconstruction. |
| first_indexed | 2024-12-13T21:11:56Z |
| format | Article |
| id | doaj.art-65624c01bd0942af928af37e7bfb400d |
| institution | Directory Open Access Journal |
| issn | 2297-4687 |
| language | English |
| last_indexed | 2024-12-13T21:11:56Z |
| publishDate | 2021-10-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Applied Mathematics and Statistics |
| spelling | doaj.art-65624c01bd0942af928af37e7bfb400d2022-12-21T23:31:20ZengFrontiers Media S.A.Frontiers in Applied Mathematics and Statistics2297-46872021-10-01710.3389/fams.2021.759622759622Shape-Based Classification of Partially Observed Curves, With Applications to AnthropologyGregory J. Matthews0Karthik Bharath1Sebastian Kurtek2Juliet K. Brophy3Juliet K. Brophy4George K. Thiruvathukal5Ofer Harel6Department of Mathematics and Statistics, Loyola University Chicago, Chicago, IL, United StatesSchool of Mathematical Sciences, University of Nottingham, Nottingham, United KingdomDepartment of Statistics, The Ohio State University, Columbus, OH, United StatesDepartment of Geography and Anthropology, Louisiana State University, Baton Rouge, LA, United StatesCentre for the Exploration of the Deep Human Journey, University of the Witwatersrand, Johannesburg, South AfricaDepartment of Computer Science, Loyola University Chicago, Chicago, IL, United StatesDepartment of Statistics, University of Connecticut, Mansfield, CT, United StatesWe consider the problem of classifying curves when they are observed only partially on their parameter domains. We propose computational methods for (i) completion of partially observed curves; (ii) assessment of completion variability through a nonparametric multiple imputation procedure; (iii) development of nearest neighbor classifiers compatible with the completion techniques. Our contributions are founded on exploiting the geometric notion of shape of a curve, defined as those aspects of a curve that remain unchanged under translations, rotations and reparameterizations. Explicit incorporation of shape information into the computational methods plays the dual role of limiting the set of all possible completions of a curve to those with similar shape while simultaneously enabling more efficient use of training data in the classifier through shape-informed neighborhoods. Our methods are then used for taxonomic classification of partially observed curves arising from images of fossilized Bovidae teeth, obtained from a novel anthropological application concerning paleoenvironmental reconstruction.https://www.frontiersin.org/articles/10.3389/fams.2021.759622/fullshapes of parameterized curvescurve completioninvariancemultiple imputationclassification |
| spellingShingle | Gregory J. Matthews Karthik Bharath Sebastian Kurtek Juliet K. Brophy Juliet K. Brophy George K. Thiruvathukal Ofer Harel Shape-Based Classification of Partially Observed Curves, With Applications to Anthropology Frontiers in Applied Mathematics and Statistics shapes of parameterized curves curve completion invariance multiple imputation classification |
| title | Shape-Based Classification of Partially Observed Curves, With Applications to Anthropology |
| title_full | Shape-Based Classification of Partially Observed Curves, With Applications to Anthropology |
| title_fullStr | Shape-Based Classification of Partially Observed Curves, With Applications to Anthropology |
| title_full_unstemmed | Shape-Based Classification of Partially Observed Curves, With Applications to Anthropology |
| title_short | Shape-Based Classification of Partially Observed Curves, With Applications to Anthropology |
| title_sort | shape based classification of partially observed curves with applications to anthropology |
| topic | shapes of parameterized curves curve completion invariance multiple imputation classification |
| url | https://www.frontiersin.org/articles/10.3389/fams.2021.759622/full |
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