Supervised classification of geometrical objects by integrating currents and functional data analysis

S. Barahona (), P. Centella (), X. Gual-Arnau (), M. V. Ibáñez () and A. Simó ()
Additional contact information
S. Barahona: Universitat Jaume I
P. Centella: Universitat Jaume I
X. Gual-Arnau: Universitat Jaume I
M. V. Ibáñez: Universitat Jaume I
A. Simó: Universitat Jaume I

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2020, vol. 29, issue 3, No 2, 637-660

Abstract: 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 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.

Keywords: Currents; Statistical shape and size analysis; Reproducing kernel Hilbert space; Functional data analysis; Supervised classification methods; Discriminant analysis; 58A25; 46E22; 62H30; 47N30 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11749-019-00669-z Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:testjl:v:29:y:2020:i:3:d:10.1007_s11749-019-00669-z

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/11749/PS2

DOI: 10.1007/s11749-019-00669-z

Access Statistics for this article

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research is currently edited by Alfonso Gordaliza and Ana F. Militino

More articles in TEST: An Official Journal of the Spanish Society of Statistics and Operations Research from Springer, Sociedad de Estadística e Investigación Operativa
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().