Partial least squares-discriminant analysis components

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... 

Two fundamentally different statistical approaches to biomarker selection are possible. With the first, experimental data can be used to construct multivariate statistical models of increasing complexity and predictive power - well-known examples are Partial Least Square Discriminant Analysis (PLS-DA) (Barker Rayens, 2003 Kemsley, 1996 Szymanska et al., 2011) or Principal Component Linear Discriminant Analysis (PC-LDA) (Smit et al., 2007 Werf et al., 2006). Inspection of the model coefficients then should point to those variables that are important for class discrimination. As an alternative, univariate statistical tests can be... 

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]. 

Among the different chemometric methods, exploratory data analysis and pattern recognition are frequently used in the area of food analysis. Exploratory data analysis is focused on the possible relationships between samples and variables, while pattern recognition studies the behavior between samples and variables [95]. Principal component analysis (PCA) and partial least-squares discriminant analysis (PLS-DA) are the methods most commonly used for exploratory analysis and pattern recognition, respectively. The importance of these statistical tools has been demonstrated by the wide number of works in the field of food science where they have been applied. The majority of the applications are related to the characterization and authentication of olive oil, animal fats, marine and vegetable oils [95], wine [97], fruit juice [98], honey [99], cheese [100,101], and so on, although other important use of statistical tools is the detection of adulterants or frauds [96,102]. 

A NMR-based metabonomic study of transgenic maize sets an example of discrimination possible using multivariate techniques (principal component analysis and partial-least squares-discriminant analysis) to NMR data on unfractionated metabolites. Other metabonomics studies are reviewed under... 

Other study was carried out to develop a method based on FTIR spectroscopy combined with chemometrics of multivariate calibrations (partial least square and principal component regression) as well as discriminant analysis for quantification and discrimination of canola oil in virgin coconut oil (Che Man Rohman 2013). 

Linear or nonlinear multiple regression analysis is used as a statistical tool to derive quantitative models, to check the significance of these models and of each individual term in the regression equation. Other statistical methods, such as discriminant analysis, principal component analysis (PCA), or partial least squares (PLS) analysis (see Partial Least Squares Projections to Latent Structures (PLS) in Chemistry) are alternatives to regression analysis (see Che mo me tries Multivariate View on Chemical Problems)Newer approaches compare the similarity of molecules with respect to different physicochemical or other properties with their biological activities. 

Fig. 4 Different chemometric tools used in the development of BioETs clear bars) in comparison with those mostly used for generic ET systems dark bars). PCA principal component analysis, LDA linear discriminant analysis, ANN artificial neural network, PLS partial least squares, PCR. principal component regression, k-NN k-nearest neighbours, MCR multiple component regression. Data obtained from the literature search on the period 1996-2015 using SCOPUS database (Elsevier)...

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. 

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. 

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]. 

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). 

PLS (Partial Least Squares) regression was used for quantification and classification of aristeromycin and neplanocin A (Figure 4). Matlab was used for PCA (Principal Components Analysis) (according to the NIPALS algorithm) to identify correlations amongst the variables from the 882 wavenumbers and reduce the number of inputs for Discriminant Function Analysis (DFA) (first 15 PCA scores used) (Figure 5). 

Kemsley, E. K. (1996). Discriminant analysis of high-dimensional data a comparison of principal components analysis and partial least squares data reduction methods, Chemom. Intell. Lab. Syst. 33 47-61. 

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