Calibration with near-continuous spectral measurements |
Henrik Aalborg Nielsen, Michael Rasmussen, Henrik Madsen
|
| Abstract | In chemometrics traditional calibration in case of spectral
measurements express a quantity of interest (e.g. a concentration) as
a linear combination of the spectral measurements at a number of
wavelengths. Often the spectral measurements are performed at a large
number of wavelengths and in this case the number of coefficients in
the linear combination is magnitudes larger than the number of
observations. Traditional approaches to handling this problem
includes principal components, partial least squares, ridge
regression, LASSO, and other shrinkage methods. As a
continuous-wavelength alternative we suggest replacing the linear
combination by an integral over the range of the wavelength of a
unknown coefficient-function multiplied by the spectral measurements.
We then approximate the unknown function by a linear combination of
some basis functions, e.g. B-splines. The method is illustrated by
an example in which the octane number of gasoline is related to near
infrared spectral measurements. The performance is found to be much
better that for the traditional calibration methods. |
| Keywords | Spectra; spline; PLS; PCR |
| Type | Conference paper [Without referee] |
| Conference | 23. Symposium i Anvendt Statistik |
| Editors | Niels-Erik Jensen og Peter Linde |
| Year | 2001 Month January pp. 255-264 |
| Publisher | |
| ISBN / ISSN | 87-501-1151-5 |
| Electronic version(s) | [pdf] |
| BibTeX data | [bibtex] |
| IMM Group(s) | Mathematical Statistics |