Frequency-Domain Alignment of Heterogeneous, Multidimensional Separations Data Through Complex Orthogonal Procrustes Analysis

Multidimensional separations data have the capacity to reveal detailed information about complex biological samples. However, data analysis has been an ongoing challenge in the area because the peaks that represent chemical factors may drift over the course of several analytical runs along the first- and second-dimension retention times. This makes higher level analyses of the data difficult, because a 1–1 comparison of samples is seldom possible without sophisticated preprocessing routines. This work offers a very simple solution to the alignment problem through an orthogonal Procrustes analysis of the frequency-domain representation of the data, which for each coefficient relative drift and amplitude are represented as a complex number. Its performance on synthetically generated data presenting nonlinear retention distortions is evaluated, in addition to its applicability to quantitative problems using experimental calibration, and untargeted metabolomics data. This analysis is extremely simple and can be recreated using just a few lines of code, relying only on fast algorithms for matrix multiplication and Fourier transforms.