Partial least squares model analysis

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. 

A relatively recent development in QSAR research is molecular reference (MOLREF). This molecular modelling technique is a method that compares the structures of any number of test molecules with a reference molecule, in a quantitative structure-activity relationship study (27). Partial least squares regression analysis was used in molecular reference to analyse the relation between X- and Y-matrices. In this paper, forty-two disubstituted benzene compounds were tested for toxicity to Daphnia... 

Factorial methods - factor analysis (FA) - principal components analysis ( PCA) - partial least squares modeling (PLS) - canonical correlation analysis Finding factors (causal complexes)... 

Schultz TP, Glasser WG (1986) Quantitative structural analysis of lignin by diffuse reflectance Fourier transform infrared spectromety Holzforschung 40 (Suppl) 37-44 Schultz TP, Nicholas DD (1987) Fourier transform infrared spectrometry Detection of incipient brown rot decay in wood Int Analyst 41 35-39 Sjostrom M, Wold, S, Lindberg W, Persson J-A, Martens H (1983) A multivariate calibration problem in analytical chemistry solved by partial least-squares models in latent variables Anal Chim Acta 150 61-70... 

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... 

Near-infrared (NIR) spectroscopy is becoming an important technique for pharmaceutical analysis. This spectroscopy is simple and easy because no sample preparation is required and samples are not destroyed. In the pharmaceutical industry, NIR spectroscopy has been used to determine several pharmaceutical properties, and a growing literature exists in this area. A variety of chemoinfometric and statistical techniques have been used to extract pharmaceutical information from raw spectroscopic data. Calibration models generated by multiple linear regression (MLR) analysis, principal component analysis, and partial least squares regression analysis have been used to evaluate various parameters. 

In the case of many X variables, principal component analysis (PCA) or partial least squares (PLS) analysis (for reviews, see, e.g., Ref. 52) can be used instead of regression analysis, often leading to more stable models. Both methods are discussed in other chapters of this book (see, e.g., Chapters 22 and 25). 

Figure 13.3-5. Partial least-squares discriminant analysis model for the classification of blood plasma samples in terms of coronary artery disease, based on their NMR spectra with visualization of the degree of coronary artery occlusion. Each point is based on data from a NMR spectrum of human blood plasma from subjects with different degrees of coronary artery occlusion. Circles—no stenosis, triangles—stenosis of one artery, inverted triangles—stenosis of two arteries, and squares—stenosis of three arteries. (This figure is available in full color at ftp //ftp.wiley.com/public/sci tech med/pharmaceutical biotech/.)...

The last step in a CoMFA study is a partial least squares (PLS) analysis (chapter 5.3) to determine the minimal set of grid points which is necessary to explain the biological activities of the compounds. Most often good to excellent results are obtained. However, the predictive value of the model must be checked by cross-validation if necessary, the model is refined and the analysis is repeated until a model of high predictive ability is obtained. 

PCA is not only used as a method on its own but also as part of other mathematical techniques such as SIMCA classification (see section on parametric classification methods), principal component regression analysis (PCRA) and partial least-squares modelling with latent variables (PLS). Instead of original descriptor variables (x-variables), PCs extracted from a matrix of x-variables (descriptor matrix X) are used in PCRA and PLS as independent variables in a regression model. These PCs are called latent variables in this context. 

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... 

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). 

IR process control systems have also been used to determine the chemical composition of copolymers and polymer blends (PP/PE, PC/PBT/PET, PC/ABS, EVA) and to control PET, PA6 and EPDM polymerisation processes (end-group determination, etc.) [70, 92]. Partial least squares (PLS) analysis of ATR-FTIR absorbance spectra has provided an accurate, precise, rapid and cost effective method both for off-line and on-line compositional analysis at production sites of EO/FO copolymers in the range of 0-10 wt.% co-polymerised ethylene sites [104]. Proper examination of the statistics underlying the PLS model is essential in providing a robust calibration model. Gotz et al. [80] showed that the composition of ethylene/propylene copolymers could be determined at 200°C by means of an IR sapphire fibre-optic sensor. Similarly, monomer residuals and additives in polymer melts may be determined. 

Two analytical techniques optical absorbance of Safiranin-O-stained cartilage sections and energy dispersive X-ray analysis have been used by Joshua Bowden, Lew Rintoul, Thor Bostrom, James Pope, and Edeline Wentrup-Byme to construct partial least squares models from Fourier transform infra red spectral data which can then be used to predict the constituents in native, degraded or even engineered cartilage. 

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