Alignment using variable penalty dynamic time warping

In this article we highlight a novel variation on dynamic time warping (DTW) for aligning chromatogram signals. We are interested in sets of signals that can be aligned well locally, but not globally, by shifting individual signals in time. This kind of alignment is often sufficient for aligning gas chromatography data. Regular DTW often "over-warps" signals and introduces artificial features into the aligned data. To overcome this we introduce a variable penalty into the DTW process. The penalty is added to the distance metric whenever a nondiagonal step is taken. We select our penalty based on a morphological dilation of the two signals. We showcase our method by aligning GC/MS datafiles from 712 blood plasma samples processed in 23 batches over the course of 6 months. The use of variable penalty DTW significantly reduces the number of nondiagonal moves. In the examples presented here, this reduction is by a factor of 30, with no cost to visual quality of the alignment.