Weighted Wavelet Packet Domain Regression for Analysis of Near-infrared Spectroscopy at Different Temperatures

Abstract

To efficiently make use of the temperature information in near-infrared (NIR) spectra, a new hybrid algorithm named as WP-WNPLS is proposed to improve the prediction ability of partial least square (PLS) based regression model. In WP-WNPLS, the discrete wavelet packet transform (DWPT) was firstly applied to decompose the 3-D NIR spectra into a series of frequency components. In each frequency component, a sub-model was obtained through using N-way PLS (NPLS) regression. Then, the weighted strategy was employed to take the advantage of multi-scale properties, and all the sub-models were mixed together to build the final weighted-prediction model. To validate the WP-WNPLS algorithm, it was applied to measure the fat concentration of milk using NIR spectra at different temperatures. The experimental results showed that the prediction ability of model obtained was superior to that obtained using conventional PLS algorithm, and the root mean square error of prediction can improve by up to 18.1%, indicating that it is a promising tool for NIR spectra regression model development. Principle and Method N-way Partial Least Squares (NPLS) Algorithm Assume X is a m×n×l data matrix with m samples (first order), n measurements in the second order and l measurements in the third order. In addition, assume Y is the m×p concentration matrix with p calibration properties in m samples. NPLS [5] algorithm is the high dimensional version of PLS. In this paper, the emphasis is on the 3-D space. The method of applying NPLS algorithm to 3-D space can be described as: