使用电流对儿童身体进行无监督分类
Unsupervised classification of children's bodies using currents
摘要：
根据物体的形状和大小对其进行分类在许多科学领域中是非常重要的。这项工作的重点是一个对象的大小和形状的情况下，其特征在于由电流}。电流是一个数学对象，它已经被证明与几何数据（如子流形）的建模有关，通过沿它们积分矢量场。作为选择向量值再生核希尔伯特空间（RKHS）作为积分流形的测试空间的结果，可以认为形状嵌入在这个希尔伯特空间中。向量值RKHS是向量场的希尔伯特空间;因此，可以计算形状的平均值，或计算两个流形之间的距离。这种嵌入使我们能够考虑大小和形状分类算法。这些算法被应用到一个3D数据库，从西班牙儿童人口的人体测量调查与潜在的应用，童装的在线销售。
英文摘要：
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 classification 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.
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