title: Reversible Gap Derivatives and Their Integration.
abstract: Higher-order gap derivatives are sometimes avoided as a preprocessing method for multivariate calibration despite their numerous advantages. One reason that they are avoided is the difficulty in interpreting the complex processed spectra and the regression vectors that arise from common calibration procedures like principal components regression or partial least squares regression. In this report we offer a method of calculating gap derivatives of any order with the aim of retrieving zero-order spectral information via numerical integration. This method is also extended to the integration of the accompanying regression vectors to aid in the interpretation of multivariate calibration models.
authors.affiliation: Department of Chemistry and Biochemistry, University of South Carolina, Columbia, USA.
authors.forename: Stephanie A
authors.initials: SA
authors.lastname: DeJong
authors.affiliation: Department of Chemistry and Biochemistry, University of South Carolina, Columbia, USA.
authors.forename: Zhenyu
authors.initials: Z
authors.lastname: Lu
authors.affiliation: Department of Chemistry and Biochemistry, University of South Carolina, Columbia, USA.
authors.forename: Brianna M
authors.initials: BM
authors.lastname: Cassidy
authors.affiliation: Department of Chemistry and Biochemistry, University of South Carolina, Columbia, USA.
authors.forename: Stephen L
authors.initials: SL
authors.lastname: Morgan
authors.affiliation: Department of Chemistry and Biochemistry, University of South Carolina, Columbia, USA myrick@sc.edu.
authors.forename: Michael L
authors.initials: ML
authors.lastname: Myrick
keywords: IR spectroscopy; Infrared spectroscopy; PLS; derivative; diffuse reflection; integration; multivariate calibration; partial least squares; preprocessing; regression vectors