Yu-Long Xie

Cluster analysis by simulated annealing

Abstract The present paper tries to apply a new clustering algorithm based on simulated annealing to chemometric research. A new stopping criterion and perturbation method which are more feasible than those proposed in the literature, are proposed. The algorithm is first tested on simulated data, and then used for the classification of Chinese tea samples. The results show that the algorithm which guaranteed obtaining a global optimum compared favourably with the traditional hierarchical technique and K-means algorithm.

Cluster analysis by the K-means algorithm and simulated annealing

Abstract A modified clustering algorithm based on a combination of simulated annealing with the K - m eans algorithm (SAKMC)is put forward and applied to chemometrics research. An empirical stopping criterion and a perturbation method which is more feasible than those proposed in the literature are suggested. The algorithm is tested on simulated data, and then used for the classification of samples of Chinese medicine calculus bovis or bezoar and samples of Chinese tea. The algorithm which guaranteed in obtaining a global optimum with shorter time compared favorably with traditional cluster analysis based on simulated annealing and the K -means algorithm.

Robust Kalman filter as a chemometric method for analytical data processing

Abstract The Kalman filter has been made robust by altering the scheme of the information feedback in the recursive algorithm of the ordinary Kalman filter. A limiting transformation which operates on the innovation term has been defined to eliminate or reduce the influence of outliers on the performance of the Kalman filter. The behaviour of the proposed robust Kalman filter was studied by computer simulation and the robustness to outliers was demonstrated.

Robust regression used for the treatment of partial non-linearity in multivariate calibration

Robust regression is proposed for attacking the problem of partial non-linearity in multivariate calibration in this paper. The non-linear spectral wavelengths were first regarded as outliers deviated from the assumed linear model. In order to reduce or eliminate the influence of the nonlinear spectral wavelengths upon the estimation of the concentration different types of weighting factors used in robust regression were tested. The commonly used Huber-type, Hampel-type and Andrews-type M-estimators were adopted in the robust regression and their performances were compared. The results for numeric simulation and real analytical systems have shown that robust regression may cope with partial non-linearity favourably.

Background bilinearization by the use of generalized standard addition method on two-dimensional data

Abstract The capability of the standard addition method to correct the matrix effects and the advantage of two-dimensional bilinear analytical data were utilized in a hybrid method combining the generalized standard addition method (GSAM) and constrained background bilinearization. The proposed method can effectively compensate for both matrix effects and the influence of unexpected interferents in multivariate calibration. First, GSAM was extended to two-dimensional bilinear data. In the process of standard additions, the background is fixed and the standard responses of the sought-for components in actual samples could be thus acquired even with the existence of unexpected interferents in the sample. The quantification of the sought-for analytes was then completed by use of background bilinearization. In the optimization process of background bilinearization, a global optimization technique, generalized simulated annealing (GSA), was adopted to guarantee the global minimum. The characteristic performance of the proposed method was tested by a series of simulations and experimental fluorescence excitation-emission data with organic dye mixtures.

A nonlinearity tracking analysis algorithm for treatment of non-linearity in multivariate calibration

Abstract In order to locate the nonlinear spectral regions in spectroscopic multivariate calibration an algorithm for nonlinearity tracking analysis is developed. The nonlinear parts detected in the data are then eliminated. The results with such a treatment for both the simulated and real spectral data compared favourably with those obtained by commonly used least square regression without such a procedure.

Chapter 3 Robust principal component analysis and constrained background bilinearization for quantitative analysis

Publisher Summary This chapter focuses on developing robust principal component analysis (PCA) and constrained background bilinearization for quantitative analysis. PCA is an important technique for high-dimensional data reduction and exploratory analysis. It is also the basis and an indispensable part of many multivariate quantitative methods developed in chemometrics, such as most curve resolution procedures, the widely used multivariate calibration methods, such as principal component regression (PCR) and partial least square regression (PLS), and many pattern recognition methods. There are several routines to obtain the robust PCA, which includes M-estimators based on the ellipsoidal distributions and the elementwise robust estimation of the disperse (covariance/correlation) matrix. More recently, a new type method for robust PCA with the use of projection pursuit (PP) has been proposed by Li and Chen. The Monte Carlo simulation has shown that the new procedures compare favorably with other robust methods. They provide results as good as the best of M-estimators in terms of efficiency of robustness and as good as the elementwise approaches with respect to the empirical breakdown point properties

Quantitative calibration of multi-component systems with a known range of possibly co-existing species

Abstract The quantitative calibration of multi-component spectrophotometric systems with a known range of possibly co-existing species was studied. A modified stepwise regression method (MSR) was used for treating such systems. Compared with conventional stepwise regression (CSR), the MSR method does not use an F -test in the variable selection process and the result of selection is an optimum sequence of regression equations with all possible numbers of variables. The Akaike information criterion ( AIC ) was used for the evaluation of a variables contribution in the stepwise process and as a criterion for choosing the best equation from the optimum sequence. A numerical example is treated to show the essential difference between MSR and CSR and how MSR works. Spectrophotometric data for real analytical systems were treated by the proposed method, and the results of simultaneous detection and determination were satisfactory.

Identification of “grey” analytical systems with incomplete information

Abstract For the calibration of “grey” analytical systems with a known range of components, the identification of truly co-existing species in a sample is of primary concern. Variance decomposition proportions (VDP), usually used as an indicator of the collinearities among regressors, were extended as a tool to judge the existence of any species among all possibly existing ones in a specific sample. The effect of the level of noise and the presence of spectral overlap was investigated by computer simulation, and some guidelines were developed. Experimental data for real analytical systems were interpreted by the proposed method with satisfactory results.