| Multiway calibration has become an important frontier in chemometric research, which can be classified into zero-order calibration, first-order calibration, second-order calibration, third-order calibration and higher-order calibration. First-order calibration compensates for the lack of total selectivity in the analytical signals with the use of efficient mathematical algorithms to extract selective portions of the overall signal, which is then employed to predict the concentration of component(s) of interest in unknown samples. When there are interferences to the analyte signal due to the presence of other unexpected components in the sample, while such an interferent is not included in the calibration set, the results of first-order calibration are unreliable. Second-order calibration can effectively solve this problem, and it holds the “second-order advantage”, which allows one to directly quantify several components of interest even in the presence of unsuspected interferents. Third-order calibration should have more obvious advantages, i.e. the so-called “third-order advantage”. Up to now, the second- and higher-order calibration methods have widespread applications in several fields, such as biomedical, food, pharmaceutical, environmental sciences. The work in this dissertation focuses on the research on basic multi-way chemometric methodologies and applications1. New advantage of the alternating trilinear decomposition algorithm and new second-order calibration algorithm(Chapter 2 to Chapter 3)Alternating trilinear decomposition(ATLD) is a very useful method for second-order calibration, according to the ideas of alternating least-squares principle, extracting diagonal elements and performing Moor-Penrose generalized inverse calculations based on truncated single value decomposition. ATLD can hold second-order advantage with no need of any constraint condition in computation. The resolution of ATLD is known as a non-strictly least square solution, which is against that of PARAFAC. However, ATLD has many advantages, such as fast convergence, insensitive to the overestimated component number and initial values, and reducing the demand in computational memory. In Chapter 2, the property of ATLD to deal with the problem relating to slight nonlinearity was demonstrated by using experimental data. Moreover, for comparison, PARAFAC was used to analyze this data. The experimental result shows that the ATLD algorithm can overcome slightly nonlinear factors, such as slightly baseline and time drift, which is better than PARAFAC.Second-order calibration as an active domain in chemometric researches has led to the development of algorithms that can adequately extract valid information from multi-way data arrays. In Chapter 3, a novel algorithm, alternating coupled two-unequal residual functions(ACTUF), has been presented to deal with three-way data for second-order calibration and it is able to achieve the important second-order advantage. This new algorithm resolves the parameter matrices by minimizing the two functions of measurement residuals and parameter residuals. The performance of the new algorithm is evaluated by using two simulation and two real data arrays in some aspects, such as noise, collinearity, analysis speed and solution. In addition, two widely-used algorithms, i.e., PARAFAC and SWATLD, were used for comparison. The results reveal that ACTUF can not only remain the second-order advantage, but also be insensitive to excessive component numbers and hold strong anti-noise tolerance. Besides, prior to other two algorithms, ACTUF can successfully deal with the problem due to severe collinearity.2. Dealing with Rayleigh scattering and missing data(Chapter 4 to Chapter 5)Rayleigh scattering, which is often contained in excitation-emission fluorescence data, does not conform to the trilinear structure, and then its existence complicates the decomposition by using second-order calibration methods. In Chapter 4, a novel method, two-direction resection PARAFAC(TDR-PARAFAC) is proposed to deal with three-way fluorescence data including Rayleigh scattering. A simulated data set was employed to demonstrate the reasonability of the new method. Then it was successfully used to analyze one experimental data set in which interferents and significant Rayleigh scattering were present. The performance of the new method was compared with that of inserting missing values PARAFAC(IMV-PARAFAC). The final results suggest that TDR-PARAFAC can not only obtain more stable and satisfactory resolution than IMV-PARAFAC, but also speed up the analysis.Multi-way data arrays contain missing data for several reasons, such as various malfunctions of instruments, responses being outside instrument ranges, irregular measurement intervals between samples and data postprocessing. In Chapter 5, one new algorithm, weighted penalty alternating trilinear decomposition(W-APTD), was given to analyze the three-way data array with missing data based on the weighted trilinear model. In addition, one improved core consistency diagnostic method(W-CORCONDIA) was applied to estimate the chemical rank of the three-way data array containing missing data. The results of one simulation and two real data sets have demonstrated that the new method, W-APTD, can deal with the three-way data array containing missing data and reserves the second-order advantage. What’s more, when the structure of the data array containing missing data is very complex, such as collinear, W-APTD can give more accurate results than Weighted PARAFAC(W-PARAFAC) and PARAFAC with single imputation(PARAFAC-SI).3. New rank-estimation methods for second-order calibration(Chapter 6 to Chapter 7)Determining the chemical rank of multiway data is a key step in many chemometric studies. In Chapter 6, a novel method, self-weighted alternating trilinear decomposition with Monte Carlo simulation(SWATLD-MCS), is developed to determine the chemical rank of three-way data for second-order calibration. The results for two simulated and two real three-way data sets are presented, in comparison with other two factor-determining methods, i.e., ADD-ONE-UP and the core consistency diagnostic(CORCONDIA). The results have demonstrated that this new method can accurately estimate chemical ranks of complex systems even when heavy collinearity and high-intensity noise are present. Also the method has a lower computational burden than competitive methods, which saves overall analysis time.In Chapter 7, a novel method, vector subspace projection with Monte Carlo simulation(VSPMCS), is proposed to esimate the chemical rank of three-way fluorescence data. This new method estimates an appropriate chemical rank by comparing the projection residuals which are obtained from vector subspace projection analysis of two similar pseudo matrices constructed by the technology of Monte Carlo simulation. The influences of noise, collinearity, non-trilinear background, analysis speed and solution on this new method are discussed. Moreover, the new method is compared with other five factor-determining methods, i.e., IND, ADD-ONE-UP, CORCONDIA, LTMC and SPPH, which is present by analyzing two simulation data sets as well as four experimental data sets. The results show a good agreement between simulations and experimentations, suggesting that the new method can accurately and quickly estimate the number of significant components in complicated situations and its precision can be comparable to the other five factor-determining methods. |
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