This is Chemometrics in Spectroscopy Column Number 251. In Column Number 250, we left you with a puzzle. We had just shown that a little-known piece of two-hundred-year-old mathematics, Lagrange's method of undetermined multipliers, could force an MLR calibration to ignore one particular, carefully chosen direction of repack-induced spectral change. It worked, but it only handled one direction at a time, and we admitted we had no idea whether the trick could be extended to PCR or PLS. That bothered us. So in this installment we go looking for the more general version of the idea, and we find it sitting in some very good recent work by Neal Gallagher and Nathanial Watson on what they call clutter suppression (a framework built for a completely different problem, target detection in hyperspectral imaging, that turns out to fit ours almost perfectly). Put the two together and you get an algorithm that whitens the calibration spectra with a clutter covariance matrix estimated from repack replicates, then hands the whitened data to the same Lagrangian machine we built last time. The payoff: the correction now generalizes to several, non-proportional directions of diffuse-reflection variability at once, and, because it is just a preprocessing step, it works ahead of PLS and PCR as well as MLR, which finally answers the question we could not answer before. This approach may very well be an answer to repack variation in repeated solid or slurry sample measurements using diffuse reflection. In this column we change gears with our writing tone and format by taking a "chemometry" approach, rather than a strict tutorial one. In future columns we hope to "unpack" this information in our more typical extended and tutorial manner. Let's explore solving this repack variation problem together.
