Mathematical methods for the processing and analysis of chemometric data

In the field of Chemometrics, methods are constantly being developed for both the pre-processing and analysis of data. Within this thesis, many such methods are explored in the analysis of multiple data sets with real-world applications, and flaws within common methods are discussed. Firstly, one data set exhibits significant issues with alignment, and so a novel approach for pre-processing which uses varying wavelet levels paired with a correlation-based alignment method is presented and applied to this data set, called multi-stage feature extraction (MSFE). This method allows for poor quality NMR data to have usable features extracted accounting for issues within the spectra, and the features are graded to allow for control over the quality of the data used for analysis. Secondly, a method for identifying complementary features over any number of data sets is presented, which allows for common compounds of interest to be identified in each set using data fusion. These methods are shown to improve on existing methods for analysis of data, as well as compound identification. For MSFE this is presented via comparison of the accuracy of models formed from data processed using a range of methods. For the data fusion approach the information gained is used to tentatively identify multiple compounds which were previously difficult to do so. Analysis is also presented on four data sets, with models formed which categorise observations as well as identify potential markers for a variety of parameters. This includes analysis on honey observations from around to world to find how they differ between origins, as well as the floral origin to see which compounds can act as markers for fraud. Three coffee data sets are also analysed with regards to their taste intensities and origin. This analysis makes use of the proposed methods where applicable, including one NMR data set being analysed where existing methods are unable to work. Because of the novel contributions put forward in this thesis, compounds have been identified which have the potential to ask as indicators for both origin and taste intensity.