Balanced scaling as a pretreatment step in Multivariate Curve Resolution analysis of noisy data

摘要

Analysis of data sets with heteroscedastic error has been a challenging problem in the chemometrics literature. Different methods have been proposed for analyzing this type of data, in particular, using the Multivariate Curve Resolution Alternating Least Squares (MCR-ALS) method. The present paper introduces the Balanced Scaling (BS) approach as a pretreatment step combined with the Multivariate Curve Resolution Alternating Least Squares (BSMCR-ALS) method as an adequate procedure to analyze data with heteroscedastic noise. In particular, for the analysis of environmental data, the Balanced Scaling (BS) method can be a useful approach to provide an optimal individual data scaling. The performance of the BS-MCR-ALS method is compared with the performance of the Maximum Likelihood Principal Component Analysis Multivariate Curve Resolution Alternating Least Squares (MLPCA-MCR-ALS) method, and also with the performance of the traditional Multivariate Curve Resolution Alternating Least Squares (MCR-ALS) method in the analysis of data sets with different type of error structures. The results obtained in this comparison revealed that the solutions obtained by BS-MCR-ALS and MLPCA-MCR-ALS were very similar.