Unsupervised classification of children’s bodies using currents

• Published in: Advances in data analysis and classification 2018-06, Vol.12 (2), p.365-397
• Main Authors: Barahona, Sonia, Gual-Arnau, Ximo, Ibáñez, Maria Victoria, Simó, Amelia
• Format: Article
• Language: English
• Subjects: Algorithms; Anthropometry; Chemistry and Earth Sciences; Children; Classification; Clustering; Computer Science; Data Mining and Knowledge Discovery; Economics; Embedding; Fields (mathematics); Finance; Health Sciences; Hilbert space; Humanities; Insurance; Law; Management; Manifolds (mathematics); Mathematics and Statistics; Medicine; Physics; Quantum theory; Regular Article; Statistical Theory and Methods; Statistics; Statistics for Business; Statistics for Engineering; Statistics for Life Sciences; Statistics for Social Sciences
• ISSN: 1862-5347; 1862-5355
• DOI: 10.1007/s11634-017-0283-0

Object classification according to their shape and size is of key importance in many scientific fields. This work focuses on the case where the size and shape of an object is characterized by a current . A current is a mathematical object which has been proved relevant to the modeling of geometrical data, like submanifolds, 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 for integrating manifolds, it is possible to consider that shapes are embedded in this Hilbert Space. A vector-valued RKHS is a Hilbert space of vector fields; therefore, it is possible to compute a mean of shapes, or to calculate a distance between two manifolds. This embedding enables us to consider size-and-shape clustering algorithms. These algorithms are 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.