Three-way Chemometric Methodologies And Quantitative Structure-Activity Relationship (QSAR) Applied In Pharmacology Research

In the field of chemometrics, studying multi-way data analysis and quantitative structure-activity relationship are the most active areas with practical significance. Work in this paper focuses on the methodolodies three-way data analysis and the application of three-way data analysis and quantitative structure-activity relationship in pharmacology. The main results are summarized as follows:1. Three-way data analysis (Chapter 1 to Chapter 5): An alternating asymmetric trilinear decomposition for three-way data arrays analysis (AATLD) method was introduced. The new proposed algorithm combines the merit of PARAFAC-alternating least squares (PARAFAC-ALS) and alternating trilinear decomposition (ATLD). It retains the second-order advantage of quantization for analyte(s) of interest even in the presence of potentially unknown interferents. In contrast with the traditional PARAFAC, ATLD and PARAFAC -ALS, by using simulated and real three-way data arrays of second–order calibration, it was showed that the new proposed algorithm performs better when the data are heavily collinear e.g., the large condition number of the loading matrix A, B and C. Even with heavily collinear simulated data set, it was also found that the AATLD algorithm is faster than others on obtaining solutions with chemical meaning. In the same time, it can obtain satisfactory result with the small samples data arrays.Determining the rank of a trilinear data array is a first step to further the later trilinear component decomposition. Different with estimating the rank of bilinear data, it is more difficult to decide the significant component number to fit exactly the three-way data arrays using trilinear decomposition. A rank-estimating method specifically for trilinear data array was proposed. It utilizes the idea of direct trilinear decomposition (DTLD) to compress the cube matrix into two pseudo samples matrices, and then decompose them by singular value decomposition. Two eigenvectors combining with the projection technique are devised to estimate the rank of trilinear data arrays. Simulated trilinear data arrays with homoscedastic and heteroscedastic noises, different noise level, high collinearity and real three-way data arrays have been used to illustrate the feasibility of the proposed method respectively. Comparing with the other factor-determining methods, it was showed that the new method can give more reliable results in the different conditions. A simple linear transform incorporating Monte Carlo simulation approach (LTMC) to estimating the chemical...