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Este artigo propõe uma implementação de regressões seqüenciais para o algoritmo das projeções sucessivas (APS), que é uma técnica de seleção de variáveis para regressão linear múltipla. Para ilustração, apresenta-se um exemplo envolvendo a determinação de proteína em trigo por espectrometria no infravermelho próximo. As previsões do modelo resultante exibiram um coeficiente de correlação de 0.989 e um RMSEP (erro médio quadrático de predição) de 0.2% m/m na faixa de10.2-16.2% m/m. A implementação proposta proporcionou ganhos computacionais de até cinco vezes.This short report proposes a sequential regression implementation for the successive projections algorithm (SPA), which is a variable selection technique for multiple linear regression. An example involving the near-infrared determination of protein in wheat is presented for illustration. The resulting model predictions exhibited a correlation coefficient of 0.989 and an RMSEP (rootmean-square error of prediction) value of 0.2% m/m in the range 10.2-16.2% m/m. The proposed implementation provided computational gains of up to five-fold.Keywords: successive projections algorithm, multivariate calibration, sequential regressions, computational efficiency, near-infrared spectrometry, wheat IntroductionThe successive projections algorithm (SPA) is a variable selection technique designed to minimize multicollinearity problems in multiple linear regression (MLR).1 In several applications concerning UV-Vis, 1,2 ICP-OES, 3 FT-IR 4 and NIR spectrometry, 4-8 SPA was found to provide models with good predictive performance. It has also been successfully employed in other fields such as QSAR (quantitative structure activity relationships) 9 and classification. 10,11A graphic user interface for SPA is freely available at . SPA comprises three main phases. 7,12 Phase 1 consists of projection operations carried out on the matrix of instrumental responses. These projections are used to generate chains of variables with successively more elements. Each element in a chain is selected in order to display the least collinearity with the previous ones. In Phase 2, candidate subsets of variables are extracted from the chains and evaluated according to the predictive performance of the resulting MLR model. Such a performance can be assessed by using cross-validation or a separate validation set. 13 Finally, Phase 3 consists of a variable elimination procedure aimed at improving the parsimony of the model. 7,12 Due to the need of building an MLR model for each subset of variables under consideration, Phase 2 may be considerably more demanding, in computational terms, as compared to Phases 1 and 3. For example, in a problem involving 389 calibration samples, 193 validation samples and 690 variables, Phases 1, 2 and 3 account for 1.9, 98.1 and 0.02% of the total time, respectively. These results were obtained by using the setup described in the Experimental section and may be slightly different if Soares et al. 761 Vol. 21, No. 4, 2010 anothe...

Several variable selection algorithms in multivariate calibration can be accelerated using Graphics Processing Units (GPU). Among these algorithms, the Firefly Algorithm (FA) is a recent proposed metaheuristic that may be used for variable selection. This paper presents a GPU-based FA (FA-MLR) with multiobjective formulation for variable selection in multivariate calibration problems and compares it with some traditional sequential algorithms in the literature. The advantage of the proposed implementation is demonstrated in an example involving a relatively large number of variables. The results showed that the FA-MLR, in comparison with the traditional algorithms is a more suitable choice and a relevant contribution for the variable selection problem. Additionally, the results also demonstrated that the FA-MLR performed in a GPU can be five times faster than its sequential implementation.

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Este artigo estuda o efeito da razão de subamostragem na abordagem subagging para regressão linear múltipla com seleção de variáveis pelo algoritmo das projeções sucessivas. Para isso, apresentam-se investigações envolvendo dados simulados e também determinação de umidade e proteína em trigo e temperaturas de destilação (T10 e T90), massa específica e enxofre em diesel por espectrometria no infravermelho próximo. Em termos de capacidade de predição e sensibilidade a ruído, os melhores resultados foram obtidos para razões de subamostragem em torno de 40%. This paper concerns the effect of the subsampling ratio on the subagging approach for multiple linear regression with variable selection by the successive projections algorithm. Investigations involving simulated data, as well as near-infrared spectrometric determination of moisture and protein in wheat and distillation temperatures (T10 and T90), specific mass and sulphur in diesel, are presented. In terms of prediction ability and sensitivity to noise, the best results were obtained for subsampling ratios around 40%.