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

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

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.

Citation

Matthews, G. J., Bharath, K., Kurtek, S., Brophy, J., Thiruvanthukal, G., & Harel, O. (2021). Shape-Based Classification of Partially Observed Curves, With Applications to Anthropology. Frontiers in Applied Mathematics and Statistics, 7, 1-14. https://doi.org/10.3389/fams.2021.759622

• 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