The successive projections algorithm for variable selection in spectroscopic multicomponent analysis

The “Successive Projections Algorithm”, a forward selection method which uses simple operations in a vector space to minimize variable collinearity, is proposed as a novel variable selection strategy for multivariate calibration. The algorithm was applied to UV–VIS spectrophotometric data for simultaneous analysis of complexes of Co2+, Cu2+, Mn2+, Ni2+ e Zn2+ with 4-(2-piridilazo)resorcinol in samples containing the analytes in the 0.02–0.5 mg l−1 concentration range. A convenient spectral window was first chosen by a procedure also proposed here and applying Successive Projections Algorithm to this range allowed an improvement of the predictive capabilities of Principal Component Regression, Partial Least Squares and Multiple Linear Regression models using only 20% of the number of wavelengths. Successive Projections Algorithm selection resulted in a root mean square error of prediction at the test set of 0.02 mg l−1, while the best and worst realizations of a genetic algorithm used for comparison yielded 0.01 and 0.03 mg l−1. However, genetic algorithm took 200 times longer than Successive Projections Algorithm, and this ratio tends to increase dramatically with the number of wavelengths employed. Finally, unlike genetic algorithm, Successive Projections Algorithm is a deterministic search technique whose results are reproducible and it is more robust with respect to the choice of the validation set.