Application of maximum likelihood multivariate curve resolution to noisy data sets


Correspondence to: Roma Tauler, IDAEA-CSIC, Jordi Girona 18–24, Barcelona 08034, Spain.



In this work, two different maximum likelihood approaches for multivariate curve resolution based on maximum likelihood principal component analysis (MLPCA) and on weighted alternating least squares (WALS) are compared with the standard multivariate curve resolution alternating least squares (MCR-ALS) method. To illustrate this comparison, three different experimental data sets are used: the first one is an environmental aerosol source apportionment; the second is a time-course DNA microarray, and the third one is an ultrafast absorption spectroscopy. Error structures of the first two data sets were heteroscedastic and uncorrelated, and the difference between them was in the existence of missing values in the second case. In the third data set about ultrafast spectroscopy, error correlation between the values at different wavelengths is present. The obtained results confirmed that the resolved component profiles obtained by MLPCA-MCR-ALS are practically identical to those obtained by MCR-WALS and that they can differ from those resolved by ordinary MCR-ALS, especially in the case of high noise. It is shown that methods that incorporate uncertainty estimations (such as MLPCA-ALS and MCR-WALS) can provide more reliable results and better estimated parameters than unweighted approaches (such as MCR-ALS) in the case of the presence of high amounts of noise. The possible advantage of using MLPCA-MCR-ALS over MCR-WALS is then that the former does not require changing the traditional MCR-ALS algorithm because MLPCA is only used as a preliminary data pretreatment before MCR analysis. Copyright © 2013 John Wiley & Sons, Ltd.