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Shape-Based Classification of Partially Observed Curves, With Applications to Anthropology

Matthews, Gregory J.; Bharath, Karthik; Kurtek, Sebastian; Brophy, Juliet; Thiruvanthukal, George; Harel, Ofer

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Authors

Gregory J. Matthews

Sebastian Kurtek

Juliet Brophy

George Thiruvanthukal

Ofer Harel



Abstract

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.

Journal Article Type Article
Acceptance Date Sep 28, 2021
Online Publication Date Oct 26, 2021
Publication Date Oct 26, 2021
Deposit Date Sep 29, 2021
Publicly Available Date Sep 29, 2021
Journal Frontiers in Applied Mathematics and Statistics
Electronic ISSN 2297-4687
Peer Reviewed Peer Reviewed
Volume 7
Article Number 759622
Pages 1-14
DOI https://doi.org/10.3389/fams.2021.759622
Public URL https://nottingham-repository.worktribe.com/output/6347254
Publisher URL https://www.frontiersin.org/articles/10.3389/fams.2021.759622/abstract

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