The Methods Of Determining The Number Of Principal Factors Based On The Comparison Between The Original Data Matrix And The One Reconstructed

With the widespread application of hyphenated instruments in analytical chemistry, a large number of two dimensional matrices or three dimensional tensor data were generated. These data contain both abundant chemical information of analysis objects and a lot of accumulated noise and background information, e.g., baseline drift and pulsations. Determination of the number of principal factors, which is also known as "chemical rank" in a bi-linear matrix, is helpful to subsequent qualitative and quantitative analysis of data by eliminating noise and redundant and extracting maximum chemical information from the original data. Most methods of determining the number of principal factors are based on principal component analysis, with which eigenvalues and eigenvectors are obtained to distinguish principal factors and secondary ones. However in some cases, only analyzing eigenvalues or eigenvectors of the original data matrix, may not be obtained the desired results. By comparing eigenvalues or eigenvectors obtained from different methods or from the original data matrix and the one reconstructed, that is relative analysis of eigenvalues or eigenvectors, new ideas to estimate the number of principal factors of more complicated data could be developed.Based on the comparison of eigenvectors of the original data matrix and the one reconstructed, the main contents of this thesis are organized as following:1. A novel method OPALS was proposed to determine the number of principle factors of the bi-linear data. At first, key variables were selected by orthogonal projection approach (OPA). Then a new data matrix was constructed from key variables, combined with the method of least squares. Two groups of different eigenvectors were obtained by employing singular value decomposition (SVD) to the original data matrix and the one reconstructed. Finally, the number of principal factors was estimated by congruence coefficient.2. Investigating the performance of OPALS with a simulated GC-IR data that comprises three chemical components. The resistance of the new method to three interfering factors, i.e., elution profile overlapping, minor component and homoscedastic noise, were investigated and results were compared with other four indices, which are NPFPCA、RESO、DRAUG and DRMAD.3. Investigating the performance of OPALS with six different experimental HPLC-DAD data, of which the actual numbers of principal factors were justified by window factor analysis (WFA). The consistency between the estimated results and references were investigated and the accuracy of OPALS was compared with those of other four methods, which are NPFPCA、RESO、 DRAUG and DRMAD.4. Improving OPALS by changing the way of selecting key variables. As the number of key variables involved in OPALS is a variable, which have burdened the operation and made the determination less objective. In order to make estimated results more objective, key variables methods of simple-to-use iterative self-modeling mixture analysis (SIMPLISMA) and needle search (NS) were tested as alternatives to orthogonal projection analysis (OPA), respectively.5. Improving OPALS by changing the discriminant function of principal factors. Since different discriminant functions may have effects on the determined number of principal factors, subspace discrepancy function and subspace projection technique were chosen to replace congruence coefficient function, respectively. After the replacement of discriminant function, the performance of these methods were studied with both simulated data and experiment data.