Partial least squares models selectivity

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. 

Figure 10. Model selection and assessment diagnostic performance measure S for random forest and partial least squares (PLS) methods applied to the BBB data for various percentages of the data (Ptrain) in the training set.

When compounds are selected according to SMD, this necessitates the adequate description of their structures by means of quantitative variables, "structure descriptors". This description can then be used after the compound selection, synthesis, and biological testing to formulate quantitative models between structural variation and activity variation, so called Quantitative Structure Activity Relationships (QSARs). For extensive reviews, see references 3 and 4. With multiple structure descriptors and multiple biological activity variables (responses), these models are necessarily multivariate (M-QSAR) in their nature, making the Partial Least Squares Projections to Latent Structures (PLS) approach suitable for the data analysis. PLS is a statistical method, which relates a multivariate descriptor data set (X) to a multivariate response data set Y. PLS is well described elsewhere and will not be described any further here [42, 43]. 

PCM modeling aims to find an empirical relation (a PCM equation or model) that describes the interaction activities of the biopolymer-molecule pairs as accurate as possible. To this end, various linear and nonlinear correlation methods can be used. Nonlinear methods have hitherto been used to only a limited extent. The method of prime choice has been partial least-squares projection to latent structures (PLS), which has been found to work very satisfactorily in PCM. PCA is also an important data-preprocessing tool in PCM modeling. Modeling includes statistical model-validation techniques such as cross validation, external prediction, and variable-selection and signal-correction methods to obtain statistically valid models. (For general overviews of modeling methods see [10]). 

Partial Least Squares regression (PLS) is usually performed on a - data matrix to search for a correlation between the thousands of CoMFA descriptors and biological response. However, usually after - variable selection, the PLS model is transformed into and presented as a multiple regression equation to allow comparison with classical QSAR models. 

Intermediate Least Squares regression (ILS) is an extension of the Partial Least Squares (PLS) algorithm where the optimal variable subset model is calculated as intermediate to PLS and stepwise regression, by two parameters whose values are estimated by cross-validation [Frank, 1987]. The first parameter is the number of optimal latent variables and the second is the number of elements in the weight vector w set to zero. This last parameter (ALIM) controls the number of selected variables by acting on the weight vector of each mth latent variable as the following ... 

From the total sample set (48 samples), 45 samples were used as calibration samples. The three samples excluded from the calibration set were selected on the basis of a representative variation of their active ingredient concentrations, and finally used as unknown test samples to predict the content of their active ingredients. Partial least squares (PLS) models for each active ingredient were developed with the Unscrambler Software (version 9.6 CAMO Software AS, Oslo, Norway) from the MSC-pretreated median spectra of all pixels of each of the 45 calibration sample images. Based on these calibration models, the predictions of the active ingredient content for each pixel of the imaging data of the three test samples and their evaluation as histograms, contour plots and RGB plots was performed with Matlab v. 7.0.4 software (see below). 

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