Chemical Cluster Analysis And Linear Discriminant Analysis Method

Chapter 1 is an introduction section, which briefly describes the research profile of the area of the chemical pattern recognition, especially the two major branches of the chemical pattern recognition, i.e., linear discriminant analysis and cluster analysis. Furthermore, based on the survey of literature, some problems and some hotspots in the current research is analyzed and discussed, and the research background of this thesis is presented. The research direction of the thesis is focused on the method development and application of linear discriminant analysis and cluster analysis.In chapter 2, the nearest local maximum searching algorithm (NLMSA), an unsupervised clustering algorithm based on kernel density estimation is proposed. It is designed for detecting inherent group structures with arbitrary shape clusters among multidimensional measurement data without any a priori information. The algorithm is named after its clustering mechanism of converging data points to their corresponding nearest local maxima of the data's density estimate along the ascending gradient direction. Two simulated data sets and two real data sets are employed to validate the performance of the method. A comparison between the clustering results obtained from the proposed algorithm and the K-means cluster analysis shows that the NLMSA possesses quite satisfactory performance.In chapter 3, we propose a refined criterion function for the clustering of high-dimensional chemical data. A non-Euclid distance metric of error derived from the latent variable model is introduced to determine the distance of an object to the mean of the class to which it belongs, and the within class error is calculated by summing the error metric of all objects in the class. The proposed criterion function is obtained by summing all the within class error. Based upon the function, a proposed refined clustering method was developed to discover the latent structures of the data in the chemical subspace spanned by the few latent variables. Two simulated data sets and two real data sets are employed to evaluate the performance of the method, and the approach is also compared with the K-means cluster analysis. The study shows that the clustering method based on the refined criterion function would be an effective technique for the clustering of the high-dimensional chemical data.In chapter 4, based on the idea of the "Optimal Hyperplane" introduced by the SVM method (Support Vector Machine), we propose a new criterion for linear discriminant analysis and develop an algorithm named "maximal between-class separation projection linear discriminant analysis" by employing the real number genetic algorithm as the optimization tool. This method separates the projection of the two classes of the data of interests farthest by finding out the proper projection direction to improve the linear discriminant method's classification performance and predication ability. The classfication results of two simulated data sets and two real data sets obtained by using the proposed method show that proposed method has good prediction ability and can effectively cope with the linear-inseparable data.In chapter 5, we use the refined clustering algorithm based on the latent variable modeling, which is proposed in the chapter 3, to recognize the patterns in two metal oxide semiconductor (MOS) gas sensor array data set. The results obtained after the procession of the data show that the algorithm can inerrable identify the samples according to different gas chemical substances in the two data sets.