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Functional Analysis of Chemometric Data

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.