Classification Problems Based on Regression Models for Multi-Dimensional Functional Data

Abstract

Data in the form of a continuous vector function on a given interval are referred to as multivariate functional data. These data are treated as realizations of multivariate random processes. We use multivariate functional regression techniques for the classification of multivariate functional data. The approaches discussed are illustrated with an application to two real data sets.

An Application of Functional Multivariate Regression Model to Multiclass Classification

“…The classifiers are constructed based on the scale response functional multivariate regression model and basis functions representation of functional predictors and coefficients. The presented results may be seen as extensions of those given in Górecki et al (2015) from binary to multi-label case.…”

“…In the next Section, this relation is used for multiclass classification for multivariate functional data. Other results of such type and their usage are presented, for instance, in Kayano and Konishi (2009), Matsui and Konishi (2011), Matsui (2014, Górecki et al (2015) and Collazos et al (2016).…”

“…The discrete functional samples in each data set are of different lengths (see Table 1). For this reason, all discrete functional variables in a given data set were extended to the same length of the longest one by the method described and used, for example, in Górecki et al (2015) (see also Rodriguez et al, 2005). To obtain the basis functions representation (3) of the observations, the orthonormal Fourier basis and the least squares method of estimating the coefficients were used (see Krzyśko and Waszak, 2013).…”

“…Some solutions of such problems as analysis of variance, canonical correlation analysis, classification, cluster analysis, linear regression and prediction, or principal component analysis are known in the literature. For example, we refer to the following papers by Górecki and Smaga (2017), Górecki et al (2016), Górecki et al (2015), Jacques and Preda (2014), Collazos et al (2016) and Berrendero et al (2011), respectively, and the references therein. This paper discusses the multiclass classification problem for multivariate functional data.…”

An Extension of the Classical Distance Correlation Coefficient for Multivariate Functional Data with Applications

“…Moreover, the theory of combining classifiers has been extended to functional data (Ferraty and Vieu (2009)). Górecki et al (2015) discussed the problem of classification via regression for multivariate functional data.…”