Hotelling trace criterion as a figure of merit for the optimization of chromatogram alignment

We present a methodology for optimization of chromatogram alignment using a class separability measure called the Hotelling trace criterion (HTC). This metric is a multi‐class distance measure that accounts for within‐class and between‐class variation. We chose the correlation optimized warping algorithm as our alignment method and used the HTC to judge the effectiveness of the alignment based on algorithm parameters called segment length and max warp. Biodiesel feedstock samples representing classes of soy, canola, tallow, waste grease, and hybrid were used in our experiments. Fatty acid methyl esters in each biodiesel were separated using gas chromatography‐mass spectroscopy. The entire data set was baseline corrected, aligned, normalized, and mean‐centered prior to principal components (PCs) analysis. The aligned, baseline corrected data sets were used to compute a figure of merit called warping effect, while the PC‐transformed data sets were used to evaluate the HTC. The segment length and max warp parameters that maximized the warping effect and/or HTC were then determined. Scores plots of pairs of PCs, along with 95% confidence ellipses, were created and analyzed. The results demonstrated that the parameters derived from maximizing the HTC more effectively aligned the data, as evidenced by better clustering of the biodiesels in the scores plots. This behavior was robust to the number of PCs used in the computation of the HTC. We conclude that the HTC is an objective measure of alignment quality that allows for optimal class separability and can be applied to optimize other methods of chromatogram alignment. Copyright © 2015 John Wiley & Sons, Ltd.