Ji-Hong Wang

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.

Clustering data using a modified integer genetic algorithm (IGA)

Abstract This paper developed a modified genetic algorithm with integer representation (IGA) for cluster analysis problem. The IGA method expands the basic concepts of conventional GAs to include fitness scaling, a modified selection operator, and three newly proposed genetic operators, i.e., competition, self-reproduction and diversification. Moreover, a new clustering criterion was introduced and compared with the commonly used square-error criterion. Clustering of simulated and real chemical data showed that IGA consistently outperformed conventional GAs both in search efficiency and in search precision, and the introduced criterion provided better performance than the square-error criterion.

Network training and architecture optimization by a recursive approach and a modified genetic algorithm

A recursive algorithm for optimizing the architecture of feedforward neural networks by the stepwise addition of a reasonable number of hidden nodes is proposed. The recursive algorithm retains the calculation results and approximation precision already obtained in the previous iteration step and uses them in the next step to efficiently lighten the computational burden of network optimization and training. The commonly used genetic algorithm has been modified for network training to circumvent the local optimum problem. Some new genetic operators, competition and self‐reproduction, have been introduced and used together with some substantially modified genetic operators, crossover and mutation, to form a modified genetic algorithm (MGA) which ensures asymptotic convergence to the global optima with relatively high efficiency. The proposed methods have been successfully applied to concentration estimation in chemical analysis and quantitative structure‐activity relationship studies of chemical compounds.

Chemical rank estimation by multiresolution analysis for two-way data in the presence of background

Abstract Resolution methods based on factor analysis are powerful approaches for qualitative and quantitative analysis of unknown multicomponent systems. A reliable assessment of the number of chemical species in the investigated system is of prime importance for a successful resolution. Unfortunately, this is confused very much in practice by instrumental and experimental difficulties. Spectral background and chromatographic drift are two of the most serious problems, which hamper not only the determination of the number of components in the analytical system, but also the final resolution of the mixture. In this paper, multiresolution analysis (MA) based on orthogonal wavelet bases is introduced to remove the influence of complex backgrounds and furthermore to correctly determine the number of components in a system. Making use of properties of backgrounds in two-way chromatographic data, the method needs no special assumption imposed upon the profiles of the baseline and the background spectra. Thus, most kinds of background can be eliminated regardless of their behaviors. Satisfactory results from computer simulation and real analytical systems illustrate the feasibility of the proposed procedure.

Neural network learning to non-linear principal component analysis

Abstract An approach to non-linear principal component analysis (NPCA) has been developed. First, a new formulation of the NPCA problem is proposed by combining the essential properties of linear principal component analysis, least squares approximation property and structure preservation property. This formulation ensures that the proposed approach provides robust results in exploratory data analysis. Second, a new neural network learning algorithm for multi-layer feedforward networks, which allows the network inputs to be updated, is proposed to accomplish NPCA in a flexible and adaptive manner. Experimental investigations with simulated and real chemical data on the behavior of the proposed approach are presented in this paper.

A non-linear mapping-based generalized backpropagation network for unsupervised learning

An unsupervised learning network is developed by incorporating the idea of non‐linear mapping (NLM) into a backpropagation (BP) algorithm. This network performs the learning process by 2iteratively adjusting its network parameters to minimize an appropriate criterion using a generalized BP (GBP) algorithm. This generalization makes the BP learning algorithms more competent for many supervised and unsupervised learning tasks provided that an appropriate criterion has been designed. Results of numerical simulation and real data show that the proposed technique is a promising approach to visualize multidimensional clusters by mapping the multidimensional data to a perceivable low‐dimensional space.

Local chemical rank estimation of two-way data in the presence of heteroscedastic noise: A morphological approach

Abstract 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.

Chemical rank estimation for excitation-emission matrices using a morphological approach

The chemical rank of excitation—emission matrices obtained in fluorescence spectroscopy is determined using a morphological approach. The EEMs are decomposed by the singular value decomposition method. In order to distinguish different patterns of spectral (primary) eigenvectors from noise (secondary) eigenvectors, a morphological function is developed to pick out the spectral eigenvectors, the number of which is the chemical rank of the data matrix. The sample theory and the significance level of the morphological function are also provided. Compared with frequency analysis, the present approach is more convenient and is better at distinguishing the spectral and noise eigenvectors.

Robust back propagation algorithm as a chemometric tool to prevent the overfitting to outliers

Abstract The ordinary back propagation algorithm for the artificial network is non-robust. It has been shown in a straightforward way that the BP algorithm can be robustified by introducing some kind of transform on the residual term r p . Using the proposed robust BP algorithm, the problem of overfitting to outlier points can effectively be circumvented. The feasibility of the proposed method has been testified by treating simulated examples and a real chemical data.

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.