PARAFAC2×N: Coupled decomposition of multi-modal data with drift in N modes

Michael D Sorochan Armstrong; Jesper Løve Hinrich; A Paulina de la Mata; James J Harynuk

doi:10.1016/j.aca.2023.340909

PARAFAC2×N: Coupled decomposition of multi-modal data with drift in N modes

Anal Chim Acta. 2023 Apr 8:1249:340909. doi: 10.1016/j.aca.2023.340909. Epub 2023 Feb 1.

Authors

Michael D Sorochan Armstrong¹, Jesper Løve Hinrich², A Paulina de la Mata¹, James J Harynuk³

Affiliations

¹ Department of Chemistry, University of Alberta, 11227 Saskatchewan Dr NW, Edmonton, T6G 2G2, Alberta, Canada.
² Department of Food Science, University of Copenhagen, Rolighedsvej 26, Copenhagen, DK-1958, Denmark.
³ Department of Chemistry, University of Alberta, 11227 Saskatchewan Dr NW, Edmonton, T6G 2G2, Alberta, Canada. Electronic address: james.harynuk@ualberta.ca.

PMID: 36868765
DOI: 10.1016/j.aca.2023.340909

Abstract

Analysis of GC×GC-TOFMS data for large numbers of poorly-resolved peaks, and for large numbers of samples remains an enduring problem that hinders the widespread application of the technique. For multiple samples, GC×GC-TOFMS data for specific chromatographic regions manifests as a 4^th order tensor of I mass spectral acquisitions, J mass channels, K modulations, and L samples. Chromatographic drift is common along both the first-dimension (modulations), and along the second-dimension (mass spectral acquisitions), while drift along the mass channel is for all practical purposes nonexistent. A number of solutions to handling GC×GC-TOFMS data have been proposed: these involve reshaping the data to make it amenable to either 2^nd order decomposition techniques based on Multivariate Curve Resolution (MCR), or 3^rd order decomposition techniques such as Parallel Factor Analysis 2 (PARAFAC2). PARAFAC2 has been utilised to model chromatographic drift along one mode, which has enabled its use for robust decomposition of multiple GC-MS experiments. Although extensible, it is not straightforward to implement a PARAFAC2 model that accounts for drift along multiple modes. In this submission, we demonstrate a new approach and a general theory for modelling data with drift along multiple modes, for applications in multidimensional chromatography with multivariate detection. The proposed model captures over 99.9% of variance for a synthetic data set, presenting an extreme example of peak drift and co-elution across two modes of separation.

Keywords: Comprehensive two-dimensional gas chromatography time-of-flight mass spectrometry; Multi-way analysis; PARAFAC2.