New algorithms and perspectives for information extraction from gas and liquid chromatography coupled to mass spectrometry data

Chromatographic separation with mass spectrometric detection is one of the most powerful instrumental combination analytical chemistry has to offer. The data acquired from these instruments are information-rich but complex. Therefore, it is still a challenge to convert raw data into actionable, chemical information. Consequently, data analysis often becomes the most time-consuming step in the whole analytical process. This is even more the case for untargeted measurements, in which the goal is to obtain a comprehensive characterization of complex samples. These types of measurements are increasingly popular in environmental science, metabolomics, food science, and the chemical industry.
A lot of research effort has been devoted to developing data analysis capabilities in the form of open-source or commercial data analysis workflows, and software packages. While these efforts have facilitated the conversion from raw data into chemical information, a satisfactory point has thus far not been reached. Existing data analysis workflows require users to define many parameters that have a strong influence on the data analysis, limit the reproducibility of analytical results and may lead to incorrect conclusions. More abstractly, the reason for this overparameterization in existing workflows can be attributed to the reliance on heuristics and a lack of structural assumptions. Furthermore, most open-source data analysis workflows can only process one-dimensional chromatographic data. However, in the field of chemometrics, different methods based on multivariate curve resolution or tensor decomposition have been developed that incorporate a priori knowledge about the chromatographic data. Applications of these methods to one- and two-dimensional chromatography have been demonstrated.
Nevertheless, there are also some drawbacks to these chemometric methods. Specifically, multivariate curve resolution methods suffer from rotational ambiguity, which means that they do not provide a unique solution. Multilinear tensor decomposition methods, on the other hand, provide unique solutions but often have assumptions that are too rigid to match the complexity of the chromatographic data. Additionally, applications of curve resolution or tensor decomposition for the analysis of trace-level compounds can be challenged by low signal-tonoise ratios.
In this PhD thesis, two novel approaches are introduced to address the limitations of existing chemometric methods for chromatographic data analysis. The first set of contributions introduces different versions of shift-invariant models incorporating trilinearity (Paper 1), softtrilinearity (Paper 2), and multi-linearity (Paper 3) to overcome problems with rotational ambiguity. Additionally, they provide a more flexible approach compared to traditional multilinear tensor decomposition methods, better accommodating the complexity of chromatographic data. Applications of these models are demonstrated to one- and twodimensional gas chromatography coupled with mass spectrometry. The second contribution, detailed in Paper 4, presents a signal processing workflow specifically designed for trace-level suspect screening in two-dimensional chromatography coupled with high-resolution mass spectrometry. This workflow includes a mass filtering algorithm that efficiently extracts pure mass spectra, even in complex samples with low signal-to-noise ratios.