Ridge regression in calibration models with symmetric padding extension-daubechies wavelet transform preprocessing

Abstract

Wavelet transformation is commonly used in calibration models as a preprocessing step. This preprocessing does not involve all results of a spectrum discretization; consequently, a lot of information can be missing. To avoid missing information, a symmetric padding extension (SPE) can be used to place all data points into dyadic scales, however, high dimensional discretization points need to be reduced. Dimension reduction can be performed with Daubechies wavelet transformation (DWT). Scale function and Daubechies wavelet are continuous functions, thus they perform a faster approximation. SPE-DWT preprocessing combines SPE and DWT. Multicollinearity often occurs in calibration models; the ridge regression (RR) method can be used to solve multicollinearity problems. This article proposes the RR method with SPE-DWT preprocessing. The proposed method is applied to determine a model for predicting the content of curcumin in turmeric. Selection of the best model is carried out by comparing coefficient of determinations, p-values of the Kolmogorov-Smirnov (KS) error models, and Root Mean Square Error Prediction (RMSEP). Results show that the RR method with SPE-DWT preprocessing gives an accurate prediction.