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Two different algorithms for time-alignment as a preprocessing step in linear factor models are studied. Correlation optimized warping and dynamic time warping are both presented in the literature as methods that can eliminate shift-related artifacts from measurements by correcting a sample vector towards a reference. In this study both the theoretical properties and the practical implications of using signal warping as preprocessing for chromatographic data are investigated. The connection between the two algorithms is also discussed. The findings are illustrated by means of a case study of principal component analysis on a real data set, including manifest retention time artifacts, of extracts from coffee samples stored under different packaging conditions for varying storage times. We concluded that for the data presented here dynamic time warping with rigid slope constraints and correlation optimized warping are superior to unconstrained dynamic time warping; both considerably simplify interpretation of the factor model results. Unconstrained dynamic time warping was found to be too flexible for this chromatographic data set, resulting in an overcompensation of the observed shifts and suggesting the unsuitability of this preprocessing method for this type of signals.

This paper offers an approach for handling retention time shifts in resolving chromatographic data using the PARAFAC2 model. In Part I of this series an algorithm for PARAFAC2 was developed and extended to N‐way arrays. It was discussed that the PARAFAC2 model has a number of attractive features. It is unique under mild conditions though it puts fewer restrictions on the data than the well‐known PARAFAC1 model. This has important implications for the modeling of chromatographic data in which retention time shifts can be regarded as a violation of the assumption of parallel proportional profiles underlying the PARAFAC1 model. The PARAFAC2 model does not assume parallel proportional elution profiles, but only that the matrix of elution profiles preserve its ‘inner‐product structure’ from sample to sample. This means that the cross‐products of the matrix holding the elution profiles in its columns remain constant. Here an application using chromatographic separation based on the molecular size of thick juice samples from the beet sugar industry illustrates the benefit of using the PARAFAC2 model. Copyright © 1999 John Wiley & Sons, Ltd.

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