A linear semi-infinite programming strategy for constructing optimal wavelet transforms in multivariate calibration problems.
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.
Coelho
Clarimar José
CJ
Universidade Federal da Paraíba, Depto de Química, Caixa Postal 5093, 58051-970, João Pessoa, PB, Brazil.
Galvão
Roberto K H
RK
de Araújo
Mário César U
MC
Pimentel
Maria Fernanda
MF
da Silva
Edvan Cirino
EC