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Supervised classification of geometrical objects by integrating currents and functional data analysis. (English) Zbl 1460.62209

Summary: 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.

MSC:

62R10 Functional data analysis
62H30 Classification and discrimination; cluster analysis (statistical aspects)
46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
47N30 Applications of operator theory in probability theory and statistics
62P10 Applications of statistics to biology and medical sciences; meta analysis
62P20 Applications of statistics to economics

Software:

R; Matlab; RKHS; fda (R)
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

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