title: A linear semi-infinite programming strategy for constructing optimal wavelet transforms in multivariate calibration problems.
abstract: A novel strategy for the optimization of wavelet transforms with respect to the statistics of the data set in multivariate calibration problems is proposed. The optimization follows a linear semi-infinite programming formulation, which does not display local maxima problems and can be reproducibly solved with modest computational effort. After the optimization, a variable selection algorithm is employed to choose a subset of wavelet coefficients with minimal collinearity. The selection allows the building of a calibration model by direct multiple linear regression on the wavelet coefficients. In an illustrative application involving the simultaneous determination of Mn, Mo, Cr, Ni, and Fe in steel samples by ICP-AES, the proposed strategy yielded more accurate predictions than PCR, PLS, and nonoptimized wavelet regression.
authors.affiliation: Universidade Federal da Paraíba, Depto de Química, Caixa Postal 5093, 58051-970, João Pessoa, PB, Brazil.
authors.forename: Clarimar José
authors.initials: CJ
authors.lastname: Coelho
authors.forename: Roberto K H
authors.initials: RK
authors.lastname: Galvão
authors.forename: Mário César U
authors.initials: MC
authors.lastname: de Araújo
authors.forename: Maria Fernanda
authors.initials: MF
authors.lastname: Pimentel
authors.forename: Edvan Cirino
authors.initials: EC
authors.lastname: da Silva