Weighted fuzzy clustering for (fuzzy) constraints in multivariate image analysis–alternating least square of hyperspectral images

In order to investigate hyperspectral images, many techniques such as multivariate image analysis (MIA) or multivariate curve resolution–alternating least squares (MCR–ALS) can be applied. When focusing on the use of MCR–ALS, constraints are of the utmost importance for a correct resolution of the data into its individual contributions. In this article, a fuzzy clustering pattern recognition method (fuzzy C-means) is applied on experimental data in order to improve the results obtained within the MCR–ALS analysis. The big advantage of a fuzzy clustering technique over a hard clustering technique, such as k-means, is that the algorithm determines the probability of a pixel to be assigned to a component, indicating that a pixel can be part of multiple clusters (or components). This is, of course, an important property for dealing with data in which a lot of overlap between the components in the spatial direction occurs. This article deals briefly with the implementation of the constraint into the MCR–ALS algorithm and then shows the application of the constraint on an oil-in-water emulsion obtained by Raman spectroscopy, in which the different components can be decomposed in a clearer way and the interface between the oil and water bubbles becomes more visible