The aim of this article is to model an ordinal response variable in terms of vector-valued functional data included on a vector-valued reproducing kernel Hilbert space (RKHS). In particular, we focus on the vector-valued RKHS obtained when a geometrical object (body) is characterized by a current and on the ordinal regression model. A common way to solve this problem in functional data analysis is to express the data in the orthonormal basis given by decomposition of the covariance operator. But our data present very important differences with respect to the usual functional data setting. On the one hand, they are vector-valued functions, and on the other, they are functions in an RKHS with a previously defined norm. We propose to use three different bases: the orthonormal basis given by the kernel that defines the RKHS, a basis obtained from decomposition of the integral operator defined using the covariance function and a third basis that combines the previous two. The three approaches are compared and applied to an interesting problem: building a model to predict the fit of children's garment sizes, based on a 3D database of the Spanish child population. Our proposal has been compared with alternative methods that explore the performance of other classifiers (Support Vector Machine and k -NN), and with the result of applying the classification method proposed in this work, from different characterizations of the objects (landmarks and multivariate anthropometric measurements instead of currents), obtaining in all these cases worst results.

中文翻译：

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几何电流预测器的广义线性模型。预测服装合身度的应用程序

本文的目的是根据向量值再现核希尔伯特空间 (RKHS) 中包含的向量值函数数据对有序响应变量进行建模。特别地，我们关注当几何对象（身体）以电流为特征时获得的向量值 RKHS 和序数回归模型。在函数数据分析中解决这个问题的一种常见方法是在协方差算子分解给出的正交基中表达数据。但是我们的数据与通常的功能数据设置存在非常重要的差异。一方面，它们是向量值函数，另一方面，它们是具有先前定义的范数的 RKHS 中的函数。我们建议使用三种不同的基：由定义 RKHS 的内核给出的正交基，从使用协方差函数定义的积分算子的分解获得的基础和结合前两者的第三个基础。将这三种方法进行比较并应用于一个有趣的问题：基于西班牙儿童人口的 3D 数据库，构建一个模型来预测儿童服装尺寸的合身性。我们的提议已经与探索其他分类器（支持向量机和 k-NN）性能的替代方法进行了比较，并且应用了这项工作中提出的分类方法的结果，从对象的不同特征（地标和多变量人体测量学）测量而不是电流），在所有这些情况下获得最差的结果。