Morphological analysis (MA) is proposed to determine the local chemical rank of two-way data from hyphenated chromatography in the presence of heteroscedastic noise, based on local least squares regression of each spectrum on its neighboring spectra. The MA method uses an approach different from ordinary analysis of variance to identify the different patterns of the structural and noisy spectra. It employs a morphological factor to distinguish different patterns of the spectral signal and the noise. The morphological factor possesses the property of scale invariance, being unaffected by heteroscedastic noise. A fast algorithm is also proposed based on the Gram-Schmidt orthogonalization technique for the local least squares regression. Both numerical simulation and real analytical data are used to illustrate the feasibility of the proposed method.

The chaotic dynamical system is introduced in g enetic algorithm to train ANN to formulate the CGANN algorithm. Logistic mapping as one of the most important chaotic dynamic mappings provides each new generation a high chance to hold GA's population diversity. This enhances the ability to overcome overfitting in training an ANN. The proposed CGANN has been used for QSAR studies to predict the tetrahedral modes (1(A1) and 2(E)) of halides [MX4]. The frequencies predicted by QSAR were compared with those calculated by quantum chemistry methods including PM3, AM1, and MNDO/d. The possibility of improving the predictive ability of QSAR by including quantum chemistry parameters as feature variables has been investigated using tetrahedral tetrahalide examples.\

In quantitative structure-activity relationship (QSAR) modeling, when compounds in a training set exhibit a significant structural distinction between each other, in particular when chemicals of biological interest interacting on the receptor involve a different mechanism, it might be difficult to construct a single linear model for the whole population of compounds of interest with desired residuals. Developing a piecewise linear local model can be effective to circumvent the aforementioned problem. In this paper, piecewise modeling by the particle swarm optimization (PMPSO) approach is applied to QSAR study. The minimum spanning tree is used for clustering all compounds in the training set to form a tree, and the modified discrete PSO is applied to divide the tree to find satisfactory piecewise linear models. A new objective function is formulated for searching the appropriate piecewise linear models. The proposed PMPSO algorithm was used to predict the antagonism of angiotensin II. The results demonstrated that PMPSO is useful for improvement of the performance of regression models.

The concept of "prepotency" is introduced in evolution algorithm. The logistic mapping as a simple and powerful device in the chaos theory is combined with the newly proposed prepotency evolution (PE) algorithm to formulate a new genetic algorithm. PE with a population initialized by chaotic numbers is applied to the multiple-layer feed-forward ANN training (PECNN). The logistic mapping ensures the PE starts each time from different initial population never used before. The newly designed PE operator partially includes the crossover and mutation operations implicitly. The proposed algorithm has a higher convergence speed comparing to the conventional GA. During the PE operation the distances between members would become smaller and smaller until all members turning to be almost identical with the potential best minimum being found. It does not waste searching time surrounding the testing minima like the conventional GA and not show symptoms of overfitting to the training set samples. The combination of logistic mapping and PE used in ANN training makes PECNN be able to test lots of minima rapidly and effectively. This greatly enlarges the opportunity to find the global minimum. The proposed algorithm has been testified by prediction of the frequency data of tetrahedral vibration modes (

A new second-order calibration procedure, the coupled vectors resolution (COVER) method, has been developed. The objective of the method is to seek a couple of vectors that minimize a least-squares criterion. With the knowledge indispensable for quantitation, the method yields direct solutions to various cases of second-order calibration. Moreover, it allows a statistically plausible way to make use of multisample information. In the case of multiple calibration samples, the method uses the calibration samples to resolve the profiles of the analytes in each order, and then calculates the concentrations of the analytes. This offers the advantage that unknown mixtures newly collected can be predicted in a direct manner. In the case of one calibration sample, the method provides an effective way to utilize the information of spectral profiles of the analytes. Results of simulated experiments and a real analytical example show that the proposed method produces acceptable performance in profile resolution and concentration estimation.