Partial least squares discriminate analysis PLS-DA

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. 

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. 

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... 

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... 

Besides the classical Discriminant Analysis (DA) and the k-Nearest Neighbor (k-NN), other classification methods widely used in QSAR/QSPR studies are SIMCA, Linear Vector Quantization (LVQ), Partial Least Squares-Discriminant Analysis (PLS-DA), Classification and Regression Trees (CART), and Cluster Significance Analysis (CSA), specifically proposed for asymmetric classification in QSAR. 

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... 

Romisch et al. in 2009 presented a study on the characterization and determination of the geographical origin of wines. In this paper, three methods of discrimination and classification of multivariate data were considered and tested the classification and regression trees (CART), the regularized discriminant analysis (RDA) and the partial least squares discriminant analysis (PLS-DA). PLS-DA analysis showed better classification results with percentage of correct classified samples from 88 to 100%. 

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]. 

Classification problems are numerous in food sdenee, for example, classification methods are nsed to determine a food s origin based on chemical fingerprints [9], but can also discriminate among different fig cultivars with sensory attributes, independent of the source and harvest date of the different cultivars [10]. CVA is just one of maity classification techniques, and the reader is referred to specific articles, e.g., partial least squares discriminant analysis (PLS-DA) [11], artificial neural networks (ANNs) [12], and support vector machines (SVMs) [13]. 

B being a matrix of regression coefficients, the PLS approach (see Chapter 4) can be used to calculate the model even in the cases where the matrix X is ill-conditioned (presence of collinearity or low samples/variables ratio). The corresponding classification method is then called partial least squares-discriminant analysis (PLS-DA). 

Supervised and unsupervised classification for example PCA, K-means and fuzzy clustering, linear discriminant analysis (LDA), partial least squares-discriminant analysis (PLS-DA), fisher discriminant analysis (FDA), artificial neural networks (ANN). 

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