New Algorithms For The Analysis Of Multi-way Data Arrays In Analytical Chemistry

With the emergence of many sophisticated instruments such as HPLC-DAD, GC-IR, GC-MS and the automatization of data collection and transmission, analysts can now obtain data matrixes consisting of hundreds and thousands data points easily. These data matrixes contain plenty of chemical information including the number of chemical components, the pure spectra, chromatograms and contents of these components. However, it is difficult, if not impossible, to extract the above information from the data matrixes composed of vast data points just by conventional analytical techniques. Analysts have to resort to chemometric, the art of extracting meaningful information from chemical data by the combination of mathematics, statistics and computer science. Among the bulk of chemometric methodologies, multi-way data analysis in analytical chemistiy is one of the most active areas with practical significance. It provides promising tools for the analysis of complex chemical systems, which are hard to handle by conventional analytical techniques. An important trend in multi-way data analysis is to incorporate a priori chemical information into chemometric algorithms, with a view to tackle data sets recorded under non-ideal experimental conditions. The present thesis primarily deals with the following aspects of multi-way data analysis in analytical chemistty: 1. Two-way data analysis (Chapter 1 to Chapter 3): the ultra-visible and near infrared spectra of chemical compounds are smooth signals, while the random noises are rough ones. Based on such a priori chemical information, a roughness penalty is defined in Chapter 2 to discriminate the primary eigenvectors or eigenvalues contributed by chemical information and secondary eigenvectors or eigenvalues produced by random noises. It was observed that the roughness penalties of primary eigenvectors are relatively small, and have little influence on the corresponding eigenvalues, while those of secondary eigenvactors are relatively large and greatly affect the secondary eigenvalues. A factor-determining index called RESO (the ratios between the eigenvalues of smoothed PCA and those of ordinary PCA) has been III Abstract established on the above basis. The proposed index possesses excellent performance, and can handle two-way data sets with minor components, heavy collinearity in spectra or heteroscedastic noise. In Chapter 3, a smoothed window factor analysis method for the resolution of two-way data sets has been designed through combining the smoothness feature of spectra with fix-sized moving window factor analysis. The smoothed window factor analysis can suppress random noises, detect minor chemical components or chemical components with veiy similar spectral features. 2. Three-way data analysis (Chapter 4 to Chapter 9): In order to accelerate the optimizing procedure of iterative trilinear decomposition algorithms, self-weighted alternating trilinear decomposition algorithm (SWATLD) has been contrived in Chapter 5. A salient characteristic distinguishing SWATLD from other iterative algorithms with fast convergence rate is that SWATLD tries to avoid being trapped in 搒wamp area* through alternatively minimizing three objective functions with intrinsic relationships. The unique optimizing procedure of SWATLD endows it with the feature of fast convergence. Generally, SV~扐TLD can converge to satisfactory...