TITLE:
Functional Analysis of Chemometric Data
AUTHORS:
Ana M. Aguilera, Manuel Escabias, Mariano J. Valderrama, M. Carmen Aguilera-Morillo
KEYWORDS:
Functional Data Analysis; B-Splines; Functional Principal Component Regression; Functional Partial Least Squares; Functional Logit Models; Functional Linear Discriminant Analysis; Spectroscopy; NIR Spectra
JOURNAL NAME:
Open Journal of Statistics,
Vol.3 No.5,
October
9,
2013
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.