Despite the many demonstrated applications of factor analysis (FA) in analyzing hyperspectral materials images, FA does have inherent mathematical limitations, preventing it from solving certain materials characterization problems. A notable limitation of FA is its parsimony restriction, referring to the fact that in FA the number of components cannot exceed the chemical rank of a dataset. Clustering is a promising alternative to FA for the phase classification of hyperspectral materials images. In contrast with FA, the phases extracted by clustering do not have to be parsimonious. Clustering has an added advantage in its insensitivity to spectral collinearity that can result in phase mixing using FA. For representative energy dispersive X-ray spectroscopy materials images, namely a solder bump dataset and a braze interface dataset, clustering generates phase classification results that are superior to those obtained using representative FA-based methods. For the solder bump dataset, clustering identifies a Cu-Sn intermetallic phase that cannot be isolated using FA alone due to the parsimony restriction. For the braze interface sample that has collinearity among the phase spectra, the clustering results do not exhibit the physically unrealistic phase mixing obtained by multivariate curve resolution, a commonly utilized FA algorithm.
Hyperspectral confocal fluorescence microscopy, when combined with multivariate curve resolution (MCR), provides a powerful new tool for improved quantitative imaging of multi-fluorophore samples. Generally, fully non-negatively constrained models are used in the constrained alternating least squares MCR analyses of hyperspectral images since real emission components are expected to have non-negative pure emission spectra and concentrations. However, in this paper, we demonstrate four separate cases in which partially constrained models are preferred over the fully constrained MCR models. These partially constrained MCR models can sometimes be preferred when system artifacts are present in the data or where small perturbations of the major emission components are present due to environmental effects or small geometric changes in the fluorescing species. Here we demonstrate that in the cases of hyperspectral images obtained from multicomponent spherical beads, autofluorescence from fixed lung epithelial cells, fluorescence of quantum dots in aqueous solutions, and images of mercurochrome-stained endosperm portions of a wild-type corn seed, these alternative, partially constrained MCR analyses provide improved interpretability of the MCR solutions. Often the system artifacts or environmental effects are more readily described as first and/or second derivatives of the main emission components in these alternative MCR solutions since they indicate spectral shifts and/or spectral broadening or narrowing of the emission bands, respectively. Thus, this paper serves to demonstrate the need to test alternative partially constrained models when analyzing hyperspectral images with MCR methods.
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