| The author of the present thesis has studied some new approaches of chemical rank estimation of a three-way data array and the application of three-way data analysis and chemical pattern recognition in pharmacology. The main results are summarized as follows.1. The chemical rank estimation of a three-way data array (Chapters 1-2 in Part 1):An unfolded matrix with the row space of full rank is formed by unfolding a three-way data array along its full-rank mode. When an orthogonal projection is carried out for the unfolded matrix using an orthogonal projective matrix constructed by a vector with the maximum Frobenius norm in the column space of the unfolded matrix, which is called the principal norm vector, the mathematic rank of the residual matrix should decrease one compared with that of the unfolded matrix. Based on the aforementioned facts, a principal norm vector orthogonal projection (PNVOP) approach was proposed to estimate the chemical rank of a three-way data array. The experiments show that the method is robust in resisting the heteroscedastic noise. The PNVOP method is adaptable to estimating the chemical rank of a three-way array with a full-rank mode. If the two principal component subspaces with the same size in the same mode spaces of the two unfolded matrixes formed by unfolding a three-way array along its two full-rank modes all are signal spaces, their differences should be very small. Otherwise, these differences should be significant. Based on this fact, a two-mode subspace comparison (TMSC) approach is proposed to estimate the chemical rank of a three-way array. It is robust to a very high degree of collinearity between the spectra or chromatograms involved, or to a very high level of noise contained in a three-way array, though comparing to PNVOP method, the method requires that three are two full-rank modes for a three-way data array. 2. The applications of three-way data analysis and chemical pattern recognition in pharmacology research ( Chapters 3-6 in Part 2): Based on the parallel factor analysis and the modified full-rank parallel factor analysis methods of a three-way data array of excitation-emission fluorescence, the interactions of anti-tumor drugs daunorubicin (DR) or adriamycin (AMC) incorresponding clinical preparations for injection with DNA have been studied by using the fluorescence probe ethidium bromide (EB). The research methods simultaneously resolved the variations of the equilibrium concentrations of the concerned three species DR(or AMC), EB and the complex EB-DNA in the reaction mixtures and showed the interaction model of anti-tumor drug with DNA. This avoids the use of Scatchard equation or plot for the model elucidation. An earlier reported result claiming that the complex AMC-DNA is a fluorescent species is revised from the experimental observations.Based on the relations between the latent variables and the PLS regression coefficients of the real variables, the minor latent variable perturbation (MLVP) ?PLS method has been proposed to discriminate and delete redundant variables including information-deficient and highly correlative variables. It is robust to deleting redundant variables in QSAR study. The QSAR of TIBO derivatives as the potential anti-HIV drugs has been studied by applying the MLVP-PLS method. Their QSAR model built has relatively strong ability on fitting data used and on predicting bio-activity of the anti-HIV drugs.The classification of traditional Chinese medicines (TCMs) according to their origins or production places as an important aspect of quality control and guaranteeing of the optimum curative effects has been investigated using radix-ginseng and radix-astragali as model substances. The classification has been accomplished using NIR reflectance spectra and chemical pattern recognition approach. A number of chemometric methods were examined for the classification using the NIR data, which are ill-posed and have the characteristic feature of high correlation, and a modified version of the ridge-type linear discriminant a...
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