Ensemble wavelet modelling for determination of wheat and gasoline properties by near and middle infrared spectroscopy

Effect of the subsampling ratio in the application of subagging for multivariate calibration with the successive projections algorithm

“…In fact, by following the demonstration provided by Pinto et al, 20 it can be shown that s ŷ av = s noise ||b av ||, where s noise is the standard deviation of the instrumental noise (assumed to be homoscedastic and uncorrelated across the model variables) and s ŷ av is the standard deviation of the error in the ensemble model predictions resulting from the propagation of the instrumental noise. Ideally, improvements in the ensemble model should provide reductions in both RMSEP and ||b av ||.…”

“…This feature would compromise prediction accuracy if the models were applied to new measurements with lower signal-to-noise ratio, as illustrated elsewhere. 20 In view of the above discussions, by taking into account the results of ||b av || and RMSEP for both properties, the most suitable subsampling ratios would be in the range 40-60%.…”

“…Sensitivity to instrumental noise was taken into account as suggested elsewhere [20][21][22] by calculating the 2-norm of the regression vector (||b av ||), which is defined as: (12) where b k av denotes the regression coefficient associated to variable x k in the ensemble model. In fact, by following the demonstration provided by Pinto et al, 20 it can be shown that s ŷ av = s noise ||b av ||, where s noise is the standard deviation of the instrumental noise (assumed to be homoscedastic and uncorrelated across the model variables) and s ŷ av is the standard deviation of the error in the ensemble model predictions resulting from the propagation of the instrumental noise.…”

Sum of ranking differences (SRD) to ensemble multivariate calibration model merits for tuning parameter selection and comparing calibration methods

“…The minimization expression for the TR variant RR [24,[42][43][44] The L-curve for selecting tuning parameters [3,20,21,[24][25][26][27]29] can be formed by plotting mean RMSEC or RMSECV against a model variance or complexity measure. Models in the corner region of the L-curve represent acceptable compromises for the bias/variance tradeoff,…”

“…Sensitivity refers to the degree of change in signal relative to a change in the quantity of analyte, e.g., in analytical chemistry, a system is sensitive if a small change in analyte concentration generates a large change in signal [13,17]. It follows then that at least two model merits, each trending in opposite directions, should be simultaneously evaluated in order to characterize the balance between under-and over-fitting [20,21,[24][25][26][27][28].…”