Abstract
This work compares the use of a separate validation set and leave-one-out cross-validation to guide the selection of variables in the Successive Projections Algorithm (SPA) for multivariate calibration. Two case studies involving diesel and corn analysis by NIR spectrometry are presented. A graphical interface for SPA is available at www.ele.ita.br/~kawakami/spa/
Highlights
The Successive Projections Algorithm (SPA) is a variable selection technique designed to improve the conditioning of Multiple Linear Regression (MLR) by minimizing collinearity effects in the calibration data set
The present paper presents a comparative study between the use of a separate validation set and leaveone-out cross-validation for the selection of spectral variables by SPA
The prediction set was employed to compare the performance of the resulting models according to the root mean square error of prediction (RMSEP) metric, which is defined by using an equation similar to equation 1
Summary
The Successive Projections Algorithm (SPA) is a variable selection technique designed to improve the conditioning of Multiple Linear Regression (MLR) by minimizing collinearity effects in the calibration data set. It is worth noting that the definition of a representative validation set may not be a trivial task and is a matter of ongoing research.[7,8] This problem is more apparent in analytical applications involving complex matrices, such as fuel and food products, in which the variability of composition cannot be reproduced by optimized experimental designs In this case, the validation set must somehow be extracted from the pool of real samples available for model-building purposes. The validation set must somehow be extracted from the pool of real samples available for model-building purposes In this context, the use of cross-validation techniques may be a valuable alternative, which has never been investigated in previous works concerning SPA.[1,2,3,4,5,6] To address this issue, the present paper presents a comparative study between the use of a separate validation set and leaveone-out cross-validation for the selection of spectral variables by SPA. The GUI files can be downloaded at www.ele.ita.br/~kawakami/spa/
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