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.

中文翻译：

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通过集成电流和功能数据分析对几何对象进行监督分类

本文着重将监督分类技术应用于以电流为特征的一组几何对象（实体），尤其是判别分析和一些非参数方法。一个电流是一个相关的数学对象，用于通过对矢量数据场进行积分来对几何数据（例如超曲面）进行建模。由于选择了矢量值的再生希尔伯特空间（RKHS）作为测试空间以在超曲面上进行积分，因此可以考虑将超曲面嵌入此希尔伯空间。这种嵌入使我们能够考虑几何对象的分类算法。我们提出一种在获得的向量值RKHS中应用监督分类技术的方法。该方法基于内核的本征函数分解。因此，本文的新颖之处在于使用电流和矢量值RKHS的理论在功能数据分析术语中重新定义了尺寸和形状监督分类问题。