Researches Of Fundamental Algorithms In Chemometric Methods

As a very developing composite discipline in chemistry, chemometrics uses methods of mathematics and statistics to design or choose optimal measurement process with the help of computer and affords greatly chemical information based on analyzing the measurement data. In the present dissertation, the attentions are paid to the aspects in mathematics and statistics that are with close relationship to chemometrics. These aspects are also the important areas in chemometrics and attract much attention of chemometricians currently. The dissertation is consists of three parts: 1. The modeling and prediction in multivariate calibration and quantitative structure retention relationship research (Part one: Chapter 1-3). Most methods of multivariate calibration in chemometrics are the latent variable methods such as partial least squares regression (PLS) and principal components regression. PLS method seems to be more effective to deal with the collinear problem in the model. In the chapter 1, the simple formula of PLS estimates is obtained. According to this formula, it is simple to see that how each of PLS components works and some of the statistical properties are obtained easily. Then, PLS and ridge regressions are combined together to form a new regression method: generalized PLS regression (GPLS). Comparing to PLS regression, GPLS can give more accuracy estimates and is more stable method. In chemometrics, leave-one-out cross validation are the commonly used method to deal with the problems of model selection and prediction. Unfortunately, it is an asymptotically inconsistent method, it tends to selects a model with unnecessary variables and makes the selected model over-fitted. In chapter 2 and 3, Monte Carlo cross validation, an asymptotically consistent method, is used in the research of multivariate calibration and quantitative structure retention relationship. It successfully selects the correct model and avoids over-fitting. Because the value of Monte Carlo cross validation evaluates the average prediction ability based on the calibration set, which is much smaller than the whole sample set, it is unsuitable for it to estimate the prediction ability for the model. Thus, the corrected Monte Carlo cross validation is proposed. The value of the corrected Monte Carlo cross validation is proven to be more accuracy estimate of the prediction error. 2.The research of the resolution algorithms for the multi-component systems (Part two: Chapter 4-6) The resolution methods for the two-way data, such as data from HPLC-DAD and (3C-MS, are the focus of chemometrics during recent years. The window factor analysis, evolving window factor analysis, heuristic evolving latent 棏Il* projections and orthogonal projection resolution are some of them. In the chapter 4, the two major resolution methods, window factor analysis and orthogonal projection resolution are proven in theory that they are equivalent to each other in algebraic space. For the resolution of embedded peaks of two-way data, a difficult and open problem in the field, the methods mentioned above seem not to be suitable tools for the problem. In chapter 5, an iterative optimal algorithm is developed. This method can solve the common types of embedded peaks and it is successfully used for the resolution of the embedded peaks in a Chinese traditional medicine system. In chapter 6, a procedure that can automatically recognize number of components in the system i...