Two-dimensional semi-parametric alignment of chromatograms

We present a comprehensive alignment algorithm that extends the semi-parametric approach to two dimensions. The algorithm is based on modeling shifts with a two-dimensional “warp function” such that the sample chromatogram – its shifts corrected with the warp function – is adjusted to the reference chromatogram by minimizing the squared intensity difference. A warp function approach has the advantage that overlapping peaks are easily dealt with compared to other proposed two-dimensional algorithms. Another advantage is that missing peaks are allowed if the absence of these peaks has little numerical effect on the warp function computation and if these peaks occur between existing peaks. Performance of the algorithm is demonstrated using GC × GC data from three batches of three diesel oil samples and LC-MS data from a mouse breast cancer data set.