Functional Analysis of Chemometric Data

Abstract

The objective of this paper is to present a review of different calibration and classification methods for functional data in the context of chemometric applications. In chemometric, it is usual to measure certain parameters in terms of a set of spectrometric curves that are observed in a finite set of points (functional data). Although the predictor variable is clearly functional, this problem is usually solved by using multivariate calibration techniques that consider it as a finite set of variables associated with the observed points (wavelengths or times). But these explicative variables are highly correlated and it is therefore more informative to reconstruct first the true functional form of the predictor curves. Although it has been published in several articles related to the implementation of functional data analysis techniques in chemometric, their power to solve real problems is not yet well known. Because of this the extension of multivariate calibration techniques (linear regression, principal component regression and partial least squares) and classification methods (linear discriminant analysis and logistic regression) to the functional domain and some relevant chemometric applications are reviewed in this paper.

Leaf water content estimation by functional linear regression of field spectroscopy data

“…A different approach to tackling the problem of water content estimation from reflectance is based on considering spectral signatures as continuous curves instead of discrete values. A review of potential applications of this kind of functional data analysis to chemometrics is provided by Aguilera, Escabias, Mariano, Valderrama, and Aguilera-Morillo (2013) and by Saeys, Keteleare, and Darius (2008). In exemplifying the use of functional models, Saeys et al (2008) concluded that functional data analysis is comparable to partial least squares regression (PLSR) in terms of predictive ability.…”

A robust functional partial least squares for scalar‐on‐multiple‐function regression

“…Spectral data are the absorbance spectrum of chemicals and can be seen as a function of the wavelength; thus, it is natural to work with functional data in chemometrics. Consult Saeys et al 12 and Aguilera et al 13 for many applications of functional data analysis in chemometrics. Since, Cardot et al 14 the scalar‐on‐function regression model, whose response variable is scalar and predictors consist of random curves, has been well studied in chemometrics analysis of spectral data, see, for example, previous works 15–23 .…”

A Robust Functional Partial Least Squares for Scalar-on-Multiple-Function Regression

“…Spectral data are the absorbance spectrum of chemicals and can be seen as a function of the wavelength; thus, it is natural to work with functional data in chemometrics. Consult Saeys et al (2008) and Aguilera et al (2013) for many applications of functional data analysis in chemometrics. Since Cardot et al (1999), the scalar-on-function regression model, whose response variable is scalar and predictors consist of random curves, has been well studied in chemometrics analysis of spectral data (see e.g., Ferraty and Vieu, 2002;Reiss and Odgen, 2007;Matsui et al, 2008;Jiang and Martin, 2008;Kramer et al, 2008;Aguilera et al, 2010Aguilera et al, , 2016Montesinos-Lopez et al, 2017;Smaga and Matsui, 2018).…”