Independent components analysis as a means to have initial estimates for multivariate curve resolution-alternating least squares

Abstract

Multivariate Curve Resolution with Alternating Least Squares (MCR-ALS) is a curve resolution method based on a bilinear model which assumes that the observed spectra are a linear combination of the spectra of the pure components in the system. The algorithm steps include the determination of the number of components by rank analysis methods, initial estimates for the concentrations and/or spectra and an iterative optimization. Sometimes, suitable results may not be achieved when MCR-ALS is applied. One reason for this is the importance of the initial estimates of the spectral profiles. In that case, the MCR-ALS algorithm may reach a local minimum instead of a global minimum and this can result in ineffective curve resolution. The most popular algorithm used to find the initial estimates (PURE derived from SIMPLISMA) suffers from an essential drawback, which is the necessity to have “pure” variables related to a single spectral component, which cannot be expected in all cases because of the strong signal overlapping as in the Ultraviolet–Visible (UV–Vis) spectroscopy. This work summarizes this problem, presenting a case study based on UV–Vis spectroscopy of heated olive oil. To solve the problems of the need for “pure” variables and to avoid local minima with MCR-ALS, Independent Components Analysis (ICA) was used to calculate initial estimates for MCR-ALS. The results from this study suggest that this use of ICA prior to MCR-ALS improves the resolution for UV–Vis data and provides acceptable resolution results when compared to the most used method, PURE.

Keywords

• UV–Vis
• Signal overlapping
• Olive oil
• PURE
• Curve resolution
• Independent Components Analysis