Classification of geometrical objects by integrating currents and functional data analysis. An application to a 3D database of Spanish child population

Sonia Barahona; Pablo Centella; Ximo Gual-Arnau; Maria Victoria Ibáñez; Amelia Simó

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arXiv · 1707.02147

Classification of geometrical objects by integrating currents and functional data analysis. An application to a 3D database of Spanish child population

Sonia Barahona·Pablo Centella·Ximo Gual-Arnau·Maria Victoria Ibáñez·Amelia Simó

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Abstract

This paper focuses on the application of Discriminant Analysis to a set of geometrical objects (bodies) characterized by currents. A current is a relevant mathematical object to model geometrical data, like hypersurfaces, through integration of vector fields along them. As a consequence of the choice of a vector-valued Reproducing Kernel Hilbert Space (RKHS) as a test space to integrate 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. A method to apply Functional Discriminant Analysis in the obtained vector-valued RKHS is given. This method is based on the eigenfunction decomposition of the kernel. So, the novelty of this paper is the reformulation of a size and shape classification problem in Functional Data Analysis terms using the theory of currents and vector-valued RKHS. 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.

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Sonia Barahona, Pablo Centella, Ximo Gual-Arnau, Maria Victoria Ibáñez, Amelia Simó. 2017-07-07. Classification of geometrical objects by integrating currents and functional data analysis. An application to a 3D database of Spanish child population. https://arxiv.org/abs/1707.02147

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