Combination of Models Obtained by Regression in the Wavelet Domain

Abstract

Abstract. The wavelet transform is a useful tool to preprocess and compress datasets for linear regression modelling. However, the prediction performance of the resulting model depends on the choice of wavelet filter and number of decomposition levels, which may not be a straightforward task. This paper proposes an alternative approach, which consists of combining models obtained from different wavelet decompositions of the dataset. For this purpose, a method is developed to convert wavelet regression models back to the original domain. The proposed approach is illustrated in a case study involving the determination of density in gasoline samples by using infrared spectroscopy. The results are favourably compared to those obtained by using individual wavelet decompositions.Keywords. Wavelet Transform, Combination of Models, Multiple Linear Regression. IntrodutionThe wavelet transform (WT) has been used in a variety of signal processing applications, such as filtering [10], compression [24] and classification [8]. In particular, the WT has become a popular tool in a field of Analytical Chemistry known as Multivariate Calibration (MC) [7,15]. The MC problem consists of building a mathematical model for estimation of physical or chemical properties of a sample from indirect measurements. Such measurements could be, for instance, emission, absorption or reflection intensities acquired over different wavelengths [20]. Applications of MC include determination of metals in steel alloys [16], analysis of composition of pharmaceutical formulae [5] and prediction of fuel properties [3], among many others.