Partial least squares model chemometrical analysis

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. 

For many applications, quantitative band shape analysis is difficult to apply. Bands may be numerous or may overlap, the optical transmission properties of the film or host matrix may distort features, and features may be indistinct. If one can prepare samples of known properties and collect the FTIR spectra, then it is possible to produce a calibration matrix that can be used to assist in predicting these properties in unknown samples. Statistical, chemometric techniques, such as PLS (partial least-squares) and PCR (principle components of regression), may be applied to this matrix. Chemometric methods permit much larger segments of the spectra to be comprehended in developing an analysis model than is usually the case for simple band shape analyses. 

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 More recently they have been superseded by the successful introduction of partial least squares analysis (PLS) in QSAR.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 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. 

This problem is overcome by the Bio View sensor, which offers the possibility to monitor the whole spectral range simultaneously, and by using suitable data analysis and mathematical methods like chemometric regression models 11061. Real-time fluorescence measurement can be used more effectively comparing time-consuming off-line methods. Partial least squares (PLS) calibration models were developed for simultaneous on-line prediction of the cell dry mass concentration (Fig. 5), product concentration (Fig. 6), and metabolite concentrations (e. g., acetic acid, not shown) from 2D spectra. 

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... 

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. 

The improvement in computer technology associated with spectroscopy has led to the expansion of quantitative infrared spectroscopy. The application of statistical methods to the analysis of experimental data is known as chemometrics [5-9]. A detailed description of this subject is beyond the scope of this present text, although several multivariate data analytical methods which are used for the analysis of FTIR spectroscopic data will be outlined here, without detailing the mathematics associated with these methods. The most conunonly used analytical methods in infrared spectroscopy are classical least-squares (CLS), inverse least-squares (ILS), partial least-squares (PLS), and principal component regression (PCR). CLS (also known as K-matrix methods) and PLS (also known as P-matrix methods) are least-squares methods involving matrix operations. These methods can be limited when very complex mixtures are investigated and factor analysis methods, such as PLS and PCR, can be more useful. The factor analysis methods use functions to model the variance in a data set. 

Acoustic emission power spectra are similar in many respects to optical spectra and are amenable to chemometric processing (multivariate analysis). Principal component analysis, partial least squares (PLS), neural networks, and qualitative techniques such as SIMCA (soft independent modeling of class analogy a pattern recognition technique) have been employed... 

There are a variety of chemometric models for both qualitative and quantitative analysis. A common quantitative model is called partial least squares (PLSs) (or projection to latent structure). PLS condenses the thousands of individual data points across the whole spectrum in all of the standards to a few sources of variation that contrast broad bands of frequencies. These condensed sources of variation are called factors and are selected as part of the model in order of importance in accounting for the variation. The first factor of a good model will account for a large part of the variation and subsequent factors will account for the remaining variation. In practice, only a limited number of factors are required to account for most of the variation. 

Chemometrics is a convenient mathematical tool for developing QSRR or scaling laws that can be embedded in process models. It is somewhat analogous to Wei and Kuo s treatment in that it contracts system dimensions through a projective transformation. Each lump is a linear combination of all original variables. The widely used principal component analysis (PCA) and partial least squares (PLS) are two examples of chemometric modeling. 

An older general review by Stefan et al. [2] considers mathematical modeling for data processing (including a variety of chemometric methods such as linear and nonlinear partial least squares, fuzzy neural networks, and multivariate analysis of variance), designs for electrochemical sensor arrays as well as applications in environmental, food and clinical analysis. Arrays of potentiometric ion-selective electrodes, piezoelectric crystal sensors, and voltammetric biosensors, as well as the electronic nose gas-phase sensor arrays are reviewed. 

Nadler B, Coifman RR. Partial least squares, Beer s law and the net analyte signal statistical modeling and analysis. J Chemometr 2005 19 45-54. 

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