Selected statistical methods of data analysis for multivariate 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. The paper is devoted to three statistical dimension reduction techniques for multivariate data. For the first one, principal components analysis, the authors present a review of a recent paper (Jacques and Preda in, Comput Stat Data Anal, 71:92-106, 2014). For two others one, canonical variables and discriminant coordinates, the authors extend existing works for univariate functional data to multivariate. These methods for multivariate functional data are presented, illustrated and discussed in the context of analyzing real data sets. Each of these techniques is applied on real data set.

Independence test and canonical correlation analysis based on the alignment between kernel matrices for multivariate functional data

“…The degree of smoothness of processes X g and Y h depends on the values E g and F h respectively (small values imply more smoothing). The optimum values for E g and F h are selected using Bayesian Information Criterion (BIC) (see Górecki et al 2018). As basis functions we can use e.g.…”

“…Górecki and Smaga (2017) described a multivariate analysis of variance (MANOVA) for functional data. In the paper by Górecki et al (2018), three basic methods of dimension reduction for multidimensional functional data are given: principal component analysis, canonical correlation analysis, and discriminant coordinates.…”

“…Classically the weight functions u u u and v v v are chosen to maximize the sample correlation coefficient (Górecki et al 2018):…”

Discriminant Coordinates Analysis in the Case of Multivariate Repeated Measures Data

“…in modern on-line economy), the alternative may be to use discriminant coordinates for functional data (see e.g. Górecki et al (2018)).…”

An Application of Functional Multivariate Regression Model to Multiclass Classification

“…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.…”