Warping methods for spectroscopic and chromatographic signal alignment: A tutorial

• The concepts of warping and alignment are introduced.
• The most important warping methods are critically reviewed and explained.
• Reference selection, evaluation and place of warping in preprocessing are discussed.
• Some pitfalls, especially for LC–MS and similar data, are addressed.
• Examples are provided, together with programming scripts to rework and extend them.

Warping methods are an important class of methods that can correct for misalignments in (a.o.) chemical measurements. Their use in preprocessing of chromatographic, spectroscopic and spectrometric data has grown rapidly over the last decade. This tutorial review aims to give a critical introduction to the most important warping methods, the place of warping in preprocessing and current views on the related matters of reference selection, optimization, and evaluation. Some pitfalls in warping, notably for liquid chromatography–mass spectrometry (LC–MS) data and similar, will be discussed. Examples will be given of the application of a number of freely available warping methods to a nuclear magnetic resonance (NMR) spectroscopic dataset and a chromatographic dataset. As part of the Supporting Information, we provide a number of programming scripts in Matlab and R, allowing the reader to work the extended examples in detail and to reproduce the figures in this paper.

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