Supervised classification of geometrical objects by integrating currents and functional data analysis
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Show full item recordcomunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
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https://doi.org/10.1007/s11749-019-00669-z |
Metadata
Title
Supervised classification of geometrical objects by integrating currents and functional data analysisAuthor (s)
Date
2019Publisher
Springer VerlagISSN
1133-0686; 1863-8260Bibliographic citation
BARAHONA, S., et al. Supervised classification of geometrical objects by integrating currents and functional data analysis. TEST, 2019, p. 1-24.Type
info:eu-repo/semantics/articlePublisher version
https://link.springer.com/article/10.1007/s11749-019-00669-zVersion
info:eu-repo/semantics/publishedVersionSubject
Abstract
This paper focuses on the application of supervised classification techniques to a set of geometrical objects (bodies) characterized by currents, in particular, discriminant analysis and some nonparametric methods. A ... [+]
This paper focuses on the application of supervised classification techniques to a set of geometrical objects (bodies) characterized by currents, in particular, discriminant analysis and some nonparametric methods. A current is a relevant mathematical object to model geometrical data, like hypersurfaces, through integration of vector fields over them. As a consequence of the choice of a vector-valued reproducing kernel Hilbert space (RKHS) as a test space to integrate over hypersurfaces, it is possible to consider that hypersurfaces are embedded in this Hilbert space. This embedding enables us to consider classification algorithms of geometrical objects. We present a method to apply supervised classification techniques in the obtained vector-valued RKHS. This method is based on the eigenfunction decomposition of the kernel. The novelty of this paper is therefore the reformulation of a size and shape supervised classification problem in functional data analysis terms using the theory of currents and vector-valued RKHSs. This approach is applied to a 3D database obtained from an anthropometric survey of the Spanish child population with a potential application to online sales of children’s wear. [-]
Is part of
TEST, 2019, p. 1-24Investigation project
This paper has been partially supported by Projects DPI2017-87333-R and UJI-B2017-13. We would also like to thank the Biomechanics Institute of Valencia for providing us withthe data set.Rights
© Sociedad de Estadística e Investigación Operativa 2019
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- MAT_Articles [765]