Partial least squares PLS regression

Partial least squares regression (PLS). Partial least squares regression applies to the simultaneous analysis of two sets of variables on the same objects. It allows for the modeling of inter- and intra-block relationships from an X-block and Y-block of variables in terms of a lower-dimensional table of latent variables [4]. The main purpose of regression is to build a predictive model enabling the prediction of wanted characteristics (y) from measured spectra (X). In matrix notation we have the linear model with regression coefficients b ... 

This method makes use of a test battery to derive a toxicity index that can be employed to classify effluents as a function of their overall toxicity. A formula is given as an example and a procedure to calculate the index using expert judgements and a PLS (Partial Least Square) regression procedure is described using data on 30 effluents. 

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). 

PCA Principal Component Analysis, PLS Partial Least Square Regression, SIMCA Soft Independent Modeling of Class Analogy... 

After an alignment of a set of molecules known to bind to the same receptor a comparative molecular field analysis CoMFA) makes it possible to determine and visuahze molecular interaction regions involved in hgand-receptor binding [51]. Further on, statistical methods such as partial least squares regression PLS) are applied to search for a correlation between CoMFA descriptors and biological activity. The CoMFA descriptors have been one of the most widely used set of descriptors. However, their apex has been reached. 

Sections 9A.2-9A.6 introduce different multivariate data analysis methods, including Multiple Linear Regression (MLR), Principal Component Analysis (PCA), Principal Component Regression (PCR) and Partial Least Squares regression (PLS). 

Partial Least Squares Regression/Projection to Laterrt Structures (PLS)... 

On the other hand, techniques like Principle Component Analysis (PCA) or Partial Least Squares Regression (PLS) (see Section 9.4.6) are used for transforming the descriptor set into smaller sets with higher information density. The disadvantage of such methods is that the transformed descriptors may not be directly related to single physical effects or structural features, and the derived models are thus less interpretable. 

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. 

Partial least-squares in latent variables (PLS) is sometimes called partial least-squares regression, or PLSR. As we are about to see, PLS is a logical, easy to understand, variation of PCR. 

We will see that CLS and ILS calibration modelling have limited applicability, especially when dealing with complex situations, such as highly correlated predictors (spectra), presence of chemical or physical interferents (uncontrolled and undesired covariates that affect the measurements), less samples than variables, etc. More recently, methods such as principal components regression (PCR, Section 17.8) and partial least squares regression (PLS, Section 35.7) have been... 

A rapid characterization of the viscosity of waterborne automotive paint was reported by Ito et al. [24], FT-Raman spectroscopy in conjunction with partial least squares regression (PLS) was applied and led to a reasonable correlation. 

Multivariate calibration has the aim to develop mathematical models (latent variables) for an optimal prediction of a property y from the variables xi,..., jcm. Most used method in chemometrics is partial least squares regression, PLS (Section 4.7). An important application is for instance the development of quantitative structure—property/activity relationships (QSPR/QSAR). 

Regression can be performed directly with the values of the variables (ordinary least-squares regression, OLS) but in the most powerful methods, such as principal component regression (PCR) and partial least-squares regression (PLS), it is done via a small set of intermediate linear latent variables (the components). This approach has important advantages ... 

PLS (partial least squares) multiple regression technique is used to estimate contributions of various polluting sources in ambient aerosol composition. The characteristics and performance of the PLS method are compared to those of chemical mass balance regression model (CMB) and target transformation factor analysis model (TTFA). Results on the Quail Roost Data, a synthetic data set generated as a basis to compare various receptor models, is reported. PLS proves to be especially useful when the elemental compositions of both the polluting sources and the aerosol samples are measured with noise and there is a high correlation in both blocks. 

The diffusion of correlation methods and related software packages, such as partial-least-squares regression (PLS), canonical correlation on principal components, target factor analysis and non-linear PLS, will open up new horizons to food research. 

Partial least squares regression analysis (PLS) has been used to predict intensity of sweet odour in volatile phenols. This is a relatively new multivariate technique, which has been of particular use in the study of quantitative structure-activity relationships. In recent pharmacological and toxicological studies, PLS has been used to predict activity of molecular structures from a set of physico-chemical molecular descriptors. These techniques will aid understanding of natural flavours and the development of synthetic ones. 

Cd2+ and the Pb2+ and all electrodes display the two peaks but to different extents. Despite the peak overlap, the electrode array can be calibrated for each metal ion using a three-way partial least squares regression (AT-PLS) [53]. The electrode array was employed to analyse three test samples of known concentration of Cu2+, Cd2+ and Pb2+ and the concentrations of each analyte predicted by the calibrated electrode array are shown in Table 10.1. As can be seen from Table 10.1 there is reasonable agreement between the actual and predicted values despite the fact that all electrodes respond to all analytes and that the electrochemical responses to lead and cadmium overlap. Further improvements would be expected if the calibrations were performed with a box experimental design, which encompassed the linear range of all the sensors. 

Partial least squares regression (PLS) [WOLD et al., 1984] is a generalized method of least squares regression. This method uses latent variables i, 2,. .., i.e. matrix U, for separately modeling the objects in the matrix of dependent data Y, and t, t2,. .., i.e. matrix T, for separately modeling the objects in the matrix of independent data X. These latent variables U and T are the basis of the regression model. The starting points are the centered matrices X and Y ... 

This perturbation is used as a probe to estimate the concentration of the N-containing surface species, using Partial Least Squares regression (PLS) and to characterize these different species by infrared curve fitting, combined with 29Si CP MAS NMR. 

Partial Least Squares Regression (PLS) is a multivariate calibration technique, based on the principles of Latent Variable Regression. Originated in a slightly different form in the field of econometrics, PLS has entered the spectroscopic scene.46,47,48 It is mostly employed for quantitative analysis of mixtures with overlapping bands (e.g. mixture of glucose, fructose and sucrose).49,50... 

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