Partial discriminant analysis

The previously mentioned data set with a total of 115 compounds has already been studied by other statistical methods such as Principal Component Analysis (PCA), Linear Discriminant Analysis, and the Partial Least Squares (PLS) method [39]. Thus, the choice and selection of descriptors has already been accomplished. 

Since that time thousands of QSARs, covering a wide and diverse range of end points, have been published [9] most of these have used MLR, but numerous other statistical techniques have also been used, such as partial least squares, principal component analysis, artificial neural networks, decision trees, and discriminant analysis [f4]. 

While principal components models are used mostly in an unsupervised or exploratory mode, models based on canonical variates are often applied in a supervisory way for the prediction of biological activities from chemical, physicochemical or other biological parameters. In this section we discuss briefly the methods of linear discriminant analysis (LDA) and canonical correlation analysis (CCA). Although there has been an early awareness of these methods in QSAR [7,50], they have not been widely accepted. More recently they have been superseded by the successful introduction of partial least squares analysis (PLS) in QSAR. Nevertheless, the early pattern recognition techniques have prepared the minds for the introduction of modem chemometric approaches. 

A drawback of the method is that highly correlating canonical variables may contribute little to the variance in the data. A similar remark has been made with respect to linear discriminant analysis. Furthermore, CCA does not possess a direction of prediction as it is symmetrical with respect to X and Y. For these reasons it is now replaced by two-block or multi-block partial least squares analysis (PLS), which bears some similarity with CCA without having its shortcomings. 

A total of 185 emission lines for both major and trace elements were attributed from each LIBS broadband spectrum. Then background-corrected, summed, and normalized intensities were calculated for 18 selected emission lines and 153 emission line ratios were generated. Finally, the summed intensities and ratios were used as input variables to multivariate statistical chemometric models. A total of 3100 spectra were used to generate Partial Least Squares Discriminant Analysis (PLS-DA) models and test sets. 

A number of chemometric tools have been employed for these classifications, including partial least squares - hierarchical cluster analysis (PLS-HCA) for Viagra tablets [98] and antimalarial artesunate tablets [99]. de Peinder et al. used partial least squares discriminant analysis (PLS-DA) models to distinguish genuine from counterfeit Lipitor tablets even when the real API was present [100]. The counterfeit samples also were found to have poorer API distribution than the genuine ones based on spectra collected in a cross pattern on the tablet. 

The receptor relevance of BCUT descriptors has inspired several groups to apply them in conjunction with other methods. Beno and Mason reported the use of simulated annealing to optimize library design using BCUT chemistry space and four-point pharmacophores concurrently (33) and the use of chemistry spaces in conjunction with property profiles (52). The application of such composite methods to target class library design is readily apparent. Pirard and Pickett reported the application of the chemometric method, partial least squares discriminant analysis, with BCUT descriptors to successfully classify ATP-site-directed kinase inhibitors active against five different protein kinases... 

Nevertheless, in most of the electronic tongue applications found in the literature, classification techniques like linear discriminant analysis (LDA) and partial least squares discriminant analysis (PLS-DA) have been used in place of more appropriate class-modeling methods. Moreover, in the few cases in which a class-modeling technique such as soft independent modeling of class analogy (SIMCA) is applied, attention is frequently focused only on its classification performance (e.g., correct classification rate). Use of such a restricted focus considerably underutilizes the significant characteristics of the class-modeling approach. 

The data processing of the multivariate output data generated by the gas sensor array signals represents another essential part of the electronic nose concept. The statistical techniques used are based on commercial or specially designed software using pattern recognition routines like principal component analysis (PCA), cluster analysis (CA), partial least squares (PLSs) and linear discriminant analysis (LDA). 

Partial least square (PLS) regression model describes the dependences between two variables blocks, e.g. sensor responses and time variables. Let the X matrix represent the sensor responses and the Y matrix represent time, the X and Y matrices could be approximated to few orthogonal score vectors, respectively. These components are then rotated in order to get as good a prediction of y variables as possible [25], Linear discriminant analysis (LDA) is among the most used classification techniques. The method maximises the variance between... 

It may be possible to use an array of electrodes containing various enzymes in combination with multivariate statistical analyses (principal component analysis, discriminant analysis, partial least-squares regression) to determine which pesticide(s) the SPCE has been exposed to and possibly even how much, provided sufficient training sets of standards have been measured. The construction methods for such arrays would be the same as described in this protocol, with variations in the amounts of enzyme depending on the inhibition constants of other cholinesterases for the various pesticides of interest. 

Multiple Linear Regression Discriminant Analysis Partial Least Squares (PLS)... 

Various classification approaches have been reported to be used successfully in conjunction with fragment descriptors for building classification SAR models the Linear Discriminant Analysis (LDA), the Partial Least Square Discriminant Analysis (PLS-DA), Soft Independent Modeling by Class Analogy (SIMCA), Artificial Neural Networks (ANN), ° Support Vector... 

Using this approach the first multiplexed simultaneous detection of six different DNA sequences, corresponding to different strains of the Escherichia coli bacterium, each labeled with a different commercially available dye label (ROX, HEX, FAM, TET, Cy3, or TAMRA) was reported [52]. In this study, both exploratory discriminant analysis and supervised learning, by partial least squares (PLS) regression, were used and the ability to discriminate whether a particular labeled... 

The methods of data analysis depend on the nature of the final output. If the problem is one of classification, a number of multivariate classifiers are available such as those based on principal components analysis (SIMCA), cluster analysis and discriminant analysis, or non-linear artificial neural networks. If the required output is a continuous variable, such as a concentration, then partial least squares regression or principal component regression are often used [20]. 

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