PARAFAC2×N: Coupled Decomposition of Multi-modal Data with Drift in N Modes

Reliable analysis of comprehensive two-dimensional gas chromatography - time-of-ﬂight mass spectrometry (GC × GC-TOFMS ) data is considered to be a major bot-tleneck for its widespread application. 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 and sample dimensions 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