Model Kalibrasi dengan Transformasi Wavelet sebagai Metode Pra-Pemrosesan

Abstract

P In the modeling E(y) = f(x1, x2,..., xp) serious problems will be occurred if the number of observations (n) is less than the number of independent variables (p) and between independent variables are correlated. The real applications of this modeling is in multivariate calibration. Reduction of dimension of independent variables (known as a preprocessing method) is useful to solve these problems. In this research we have studied discrete wavelet transformation as a preprocessing method. The study has been done both empirically and theoretically. The exploration of three preprocessing methods, i.e. principal component analysis, Fourier transformation and discrete wavelet transformation (DWT) based on simulated data showed that discrete wavelet transformation resulted in superior goodness of fit when compared with other preprocessing methods, even when using the simplest mother wavelet function such as Haar wavelet. The study showed that the use of any mother wavelet will result in orthogonal matrices. Because the matrix of new variables resulted from DWT which was based on centered matrix X has column sum equal to zero then the statistical properties of the regression of wavelet coefficient are analogous to the statistical properties in the regression model of y on centered independent variables X. If DWT is applied to the original data which are highly correlated, then the resulting variables are generally still correlated. To overcome this problem the regression models are combined with other methods. The combination of DWT and principal component regression has been utilized in this research to predict concentration of gingerol and curcuminoid, and has resulted in better calibration models.