Partial least-squares analysis between different

Chemometric evaluation methods can be applied to the signal from a single sensor by feeding the whole data set into an evaluation program [133,135]. Both principle component analysis (PCA) and partial least square (PLS) models were used to evaluate the data. These are chemometric methods that may be used for extracting information from a multivariate data set (e.g., from sensor arrays) [135]. The PCA analysis shows that the MISiC-FET sensor differentiates very well between different lambda values in both lean gas mixtures (excess air) and rich gas mixtures (excess fuel). The MISiC-FET sensor is seen to behave as a linear lambda sensor [133]. It... 

Table 3 (73) compares the retention coefficients for synthetic peptides from various sources. To ensure comparability, the data has been standardized with respect to lysine and assigned a value of 100. The table shows that there are discrepancies between the results obtained using different chromatographic systems. Predictions of retention times should therefore be made using chromatographic systems similar to those used to calculate the retention coefficients for the amino acids. Casal et al. (75a) have made a comparative study of the prediction of the retention behavior of small peptides in several columns by using partial least squares and multiple linear regression analysis. 

Linear discriminant analysis (LDA) is aimed at finding a linear combination of descriptors that best separate two or more classes of objects [100]. The resulting transformation (combination) may be used as a classifier to separate the classes. LDA is closely related to principal component analysis and partial least square discriminant analysis (PLS-DA) in that all three methods are aimed at identifying linear combinations of variables that best explain the data under investigation. However, LDA and PLS-DA, on one hand, explicitly attempt to model the difference between the classes of data whereas PCA, on the other hand, tries to extract common information for the problem at hand. The difference between LDA and PLS-DA is that LDA is a linear regression-like method whereas PLS-DA is a projection technique... 

Several studies have employed chemometric designs in CZE method development. In most cases, central composite designs were selected with background electrolyte pH and concentration as well as buffer additives such as methanol as experimental factors and separation selectivity or peak resolution of one or more critical analyte pairs as responses. For example, method development and optimization employing a three-factor central composite design was performed for the analysis of related compounds of the tetracychne antibiotics doxycycline (17) and metacychne (18). The separation selectivity between three critical pairs of analytes were selected as responses in the case of doxycycline while four critical pairs served as responses in the case of metacychne. In both studies, the data were htted to a partial least square (PLS) model. The factors buffer pH and methanol concentration proved to affect the separation selectivity of the respective critical pairs differently so that the overall optimized methods represented a compromise for each individual response. Both methods were subsequently validated and applied to commercial samples. 

To establish a correlation between the concentrations of different kinds of nucleosides in a complex metabolic system and normal or abnormal states of human bodies, computer-aided pattern recognition methods are required (15, 16). Different kinds of pattern recognition methods based on multivariate data analysis such as principal component analysis (PCA) (8), partial least squares (16), stepwise discriminant analysis, and canonical discriminant analysis (10, 11) have been reported. Linear discriminant analysis (17, 18) and cluster analysis were also investigated (19,20). Artificial neural network (ANN) is a branch of chemometrics that resolves regression or classification problems. The applications of ANN in separation science and chemistry have been reported widely (21-23). For pattern recognition analysis in clinical study, ANN was also proven to be a promising method (8). 

One difference between a component analysis of an array X and using X in a regression is that the component analysis tries to explain X as well as possible and make the sum of squares of E small while in a regression model the goal is primarily to make the residual ey of y small and not necessarily to use all of X for that purpose. Studies of the residual of X in principal component regression or partial least squares regression should take that into account. 

Mendonca et al. have used an electrospray ionization mass spectrometry (ESI-MS) method to identify the CGA profile, which allowed the discrimination of green Arabica and Robusta coffee beans [22]. This method also allowed discrimination between defective and nondefective coffee beans (ESI-MS positive mode). For this kind of identification and discrimination, they used principal component analysis and hierarchical cluster analysis [22]. Alonso-Salces et al. also used a linear discriminant analysis and a partial least-squares discriminant analysis based on HPLC and UV spectra of phenolic (CGAs) and methykanthine contents for a number of green Robusta and Arabica coffee beans from different geographical origins [9]. 

Partial least squares (PLS) analysis allows the simultaneous investigation of the relationships between a multitude of activity data (F matrix) and a set of chemical descriptors (X matrix) through latent variables (Wold et aL, 1984 Geladi and Kowalski, 1986 Hellberg, 1986 Geladi and Tosato, 1990). The latent variables correspond to the component scores in PCA and the respective coefficients to the PCA loading vectors. The PLS model can also be applied when the number of (collinear) descriptors exceeds the number of compounds in the data set. The main difference between PCA and PLS concerns the criteria for extracting the principal components and the latent variables, respectively PCA is based on the maximum variance criterion, whereas PLS uses covariance with another set of variables (X matrix). 

---