Partial least squares models dimensionality

Factor The result of a transformation of a data matrix where the goal is to reduce the dimensionality of the data set. Estimating factors is necessary to construct principal component regression and partial least-squares models, as discussed in Section 5.3.2. (See also Principal Component.)... 

Nord, L.I., Fransson, D. and Jacobsson, S.P. (1998). Prediction of Liquid Chromatographic Retention Times of Steroids by Three-Dimensional Structiure Descriptors and Partial Least Squares Modeling. Chemom.InteliLab.Syst, 44,257-269. 

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 ... 

Fig. 3.12. Discriminant partial-least-squares score plot for the global model of blood-brain barrier (BBB) permeability prediction. The model offers a good discrimination and evaluation of a compound s ability to cross the BBB good permeability, BBB+ (black circles) poor permeability, BBB- (open circles). The model assigned a correct BBB profile to more than 90% of the compounds. A confidence interval is built in the t1-t2 space, where BBB prediction can be borderline and doubtful. (From Crivori P, Crucian G, Carrupt PA, et al. Predicting blood-brain barrier permeation from three-dimensional molecular structure. J Med Chem 2000 43 2204-2216 with permission.)...

In the case of multivariate modeling, several independent as well as several dependent variables may operate. Out of the many regression methods, we will learn about the conventional method of ordinary least squares (OLS) as well as methods that are based on biased parameter estimations reducing simultaneously the dimensionality of the regression problem, that is, principal component regression (PCR) and the partial least squares (PLS) method. 

Partial least squares and principal components regression can be used to reduce the dimensionality of the input space, in this case attempting to reduce the degrees of freedom of the models to 14 or less without losing the most important information in the input data. 

Infrared, near-infrared, and Raman spectroscopy were used to study high density, linear low density (LLDPE), and low density polyethylene. Overlapping spectral bands were separated using the second derivative, principal component analysis, and two-dimensional correlation analysis. A model was developed, using partial least squares regression, to calculate the density of LLDPE. 1 ref. 

Although colorimetric methods were the earliest to be used for pesticide analysis [203], competitive spectroscopic methodologies for the determination of these pollutants were not developed until the last decade. The spectroscopic determination of several pesticides in mixtures has been the major hindrance, especially when their analytical characteristics are similar and their signals overlap as a result. Multivariate calibration has proved effective with a view to developing models for qualitative and quantitative prediction from spectroscopic data. Thus, partial least squares (PLS) and principal component regression (PCR) have been used as calibration models for the spectrofluorimetric determination of three pesticides (carbendazim, fuberidazole, and thiabendazole) [204]. A three-dimensional excitation-emission matrix fluorescence method has also been used for this purpose (Table 18.3) [205]. 

We have applied kNN (Zheng and Tropsha 2000) and simulated annealing - partial least squares (SA-PLS) (Cho et al. 1998) QSAR approaches to a dataset of 48 chemically diverse functionalized amino acids (FAAs) with anticonvulsant activity that were synthesized previously, and successful QSAR models of FAA anticonvulsants have been developed (Shen et al. 2002). Both methods utilized multiple descriptors such as molecular connectivity indices or atom-pair descriptors, which are derived from two-dimensional molecular topology. QSAR models with high internal accuracy were generated, with leave-one-out cross-validated (q ) values rang-... 

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