Generalized Linear Models for Geometrical Current predictors. An application to predict garment fit

TL;DR

This paper develops a generalized linear model using vector-valued RKHS to predict garment fit from 3D body data, addressing unique challenges of vector-valued functional data in an application to children's clothing sizing.

Contribution

It introduces a novel approach to modeling ordinal responses with vector-valued RKHS and compares three basis methods for functional data analysis in garment fit prediction.

Findings

The proposed models effectively predict children's garment sizes.

Comparison of three basis methods shows differences in predictive performance.

Application demonstrates the utility of vector-valued RKHS in practical sizing problems.

Abstract

The aim of this paper is to model an ordinal response variable in terms of vector-valued functional data included on a vector-valued 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.