| Chemometrics is well known for extracting more information from instrumental data based on mathematic method with the help of computer. It has been applied to different fields such as medicine, biology and environment. Multivariate analysis, which is one of the most important parts of chemometrics, includes the analysis of matrix, three-way data and high-way data. Generally, multivariate analysis methods are based on hypothesis, e.g. linear model. However, there are always some “unhealthy” structures in the dataset, for instance, outliers, collinearity or noise and they would influence the results of analysis. The estimation of the robustness of multivariate analysis is necessary. We proposed a novel method to estimate the robustness, which can be used to estimate the components number of multivariate analysis, and we extended it to three- and four-way analysis. Apart from this, we did quantification analysis of the medicine with the complex background such as body fluid using the datasets from fluorescence and HPLC-DAD, coupled with three-way analysis. In the high-way analysis, we proposed a new algorithm for four-way analysis which was applied to real-life dataset, and it was proved to be a stable method. The following is the outlines of the thesis:Principal component analysis(PCA) is one of the most important tools in data analysis. However, the result of PCA is easy to be influenced by outliers, as the principal of PCA is to obtain the information of the biggest variance. Thus, it is very important to estimate the robustness of the PCA model. Chapter 2 introduces a new method named angle distribution of loading subspace(ADLS) to estimate the robustness of a PCA model. With the information of the robustness, ADLS is used to estimate the number of principal components and detect outliers. The simulated datasets with different levels of collinearity and noise are constructed to estimate the performance of ADLS of predicting the number of principal components. The results of ADLS were compared with the results of cross-validation, which show that the performance of ADLS is better than cross-validation. Besides, the simulated and real datasets are used to estimate the performance of ADLS of detecting outliers, with the results indicating the satisfactory performance of ADLS.In second-order calibration(three-way analysis), the estimation of the chemical rank is important because the three-way model is built based on the result of chemical rank. The estimation of chemical rank is easily influenced by noise, collinearity and trace component. In Chapter 3, we extended the method of ADLS to three-way analysis, making use of the angle distribution of loading subspace based on bootstrap to estimate the robustness of the three-way analysis model, and select the biggest components number related to a robust model. The method was used for the analysis of the simulated datasets with different levels of collinearity, noise and trace components, with the comparison with the result of core consistency diagnose. The results of the analysis show that the performance of ADLS is more robust, which is also proved in complex real-life datasets.Dextromethorphan(DEX) is an over-the-counter, highly effective and relatively safe antitussive drug. At therapeutic dose, DEX is not an addictive drug, and it is safe. However, addicted people at higher dose than therapeutic would abuse it. Most of the traditional methods for the determination of DEX and its metabolites are based on chromatography. Unfortunately, they are not only expensive, but also demand a painful pretreatment with intensive extraction and clean-up procedures, which affect the recoveries and result in a time-consuming and laborious work. In Chapter 4, second-order calibration, based on the full-rank parallel factor analysis(FRA-PARAFAC) and the parallel factor analysis(PARAFAC) algorithms, was applied coupled with excitation-emission matrix fluorescence. Employing the “second-order advantage”, the proposed methodology utilizes “mathematical separation” instead of “physical or chemical separation” to reduce the pretreatment process and obtain satisfied results and provides a simple, rapid and effective method for the simultaneous determination of DEX and its metabolites dextrorphan(DOR) in plasma samples.Nowadays, traditional Chinese medicine(TCM) plays an important role in the healthcare system and the researches about the process of TCM are more and more popular. However, it is difficult to obtain the perfect parameters for the determination of intricate components with the complex background such as plasma and Chinese patent medicine with HPLC. Except from this, the complex and toxic mobile phase is necessary for the perfect separation of analytes and interferents. In Chapter 5, the problem that chromatographic peaks are heavily overlapped among the analytes and interferents from the background resulting from plasma or TCM can be resolved and the satisfactory quantification results have been gained with the help of the three-way analysis method of alternating trilinear decomposition(ATLD) algorithm which utilized “mathematical separation” to strength “physical or chemical separation”. The result was compared with the result of HPLC-MS/MS, which shows no significant difference between them, and the proposed method is faster and more effective.The concentration determination of 5-Hydroxyindoleacetic acid(5-HIAA) in urine is clinically used to diagnosis disease such as, neuroendocrine tumors. Most of the reported methods of quantifying 5-HIAA in urine are based on time-consuming “physical or chemical separation”. In Chapter 6, a fast fluorescence method was proposed with little experimental preprocessing, combined with “mathematical separation” provided by multivariate calibration. A four-way data(excitation × emission × p H × sample) was constructed by measuring each sample in buffer solution with different p Hs, using fluorescence detector. The four-way dataset was analyzed by multivariate methods of multivariate curve resolution(MCR), PARAFAC and four-way PARAFAC. Angle distribution of loading subspace(ADLS) was extended to estimate the chemical rank of MCR, PARAFAC and four-way PARAFAC with an improved strategy of the calculation of loading subspace. The results show that the result of third-order calibration has a better performance with this highly collinear dataset, compared with first-and second-order calibrations.Self-weighted alternating normalized residue fitting(SWANRF), was extended with new weight factors, for the decomposition of quadrilinear data in Chapter 7. Four-way SWANRF was applied to simulated dataset with the comparison with four-way PARAFAC. The results show that four-way SWANRF is faster and more robust. Both four-way SWANRF and four-way PARAFAC were applied to the quantitative analysis of serotonin contents in plasma samples, using the fluorescence difference with different p Hs. The analysis of this real dataset shows that the introduction of a fourth mode can relieve the serious problem of collinearity, which is one of the “third-order advantages”. |
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