Partial least-squares methods

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  

The latent variables, calculated by means of an iterative process, have the following properties  

In a manner similar to the methods of PCA or FA, PLS extracts linear combinations of essential features which model the original data X and F But, in contrast with the methods above, PLS also models the dependence of the two data sets. This type of model is well suited for modeling and simulating environmental relationships or for multivariate calibration. 

The advance of the PLS method is the nonproblematic handling of multicollinearities. In contrast with the other methods of multivariate data analysis the PLS algorithm is an iterative algorithm which makes it possible to treat data which have more features than objects [GELADI, 1988], 

The goodness of fit of PLS models is calculated as an error of the prediction, in a manner similar to the description in ordinary least squares methods. Using the so-called cross-validation test one can determine the number of significant vectors in U and T and also the error of prediction. 

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Lindberg, W., et al. "Partial Least Squares Method for Spectrofluorimetric Analysis of Mixtures of Humic Acid and Ligninsulfonate , Anal. Chem. 1983, (55)643-648. 

Haaland, D.M., Thomas, E.V., "Partial Least-Squares Methods for Spectral Analysis 1. Relation to Other Quantitative Calibration Methods and the Extraction of Qualitative Information" Anal. Chem. 1988 (60) 1193-1202. 

T. Cserhati, A. Kosa and S. Balogh, Comparison of partial least-square method and canonical correlation analysis in a quantitative structure-retention relationship study. J. Biochem. Biophys. Meth., 36 (1998) 131-141. 

Lindberg, W., Persson, J. A., Wold, S. Anal. Chem. 55, 1983, 643-648. Partial least-squares method for spectrofluorimetric analysis of mixtures of humic acid and lignin-sulfonate. 

Haaland, D. M. and Thomas, E. V. (1988) Partial least-squares methods for spectral analyses. 1. Relation to other quantitative calibration methods and the extraction of qualitative information. Anal. Chem. 60, 1193-1202. 

Madrakian, T., A. Afkhami, R. Moeina, and M. Bahram. 2007. Simultaneous spectrophotometric determination of Sn(II) and Sn(TV) by mean centering of ratio kinetic profiles and partial least squares methods. Talanta 72 1847-1852. 

Very recently, new descriptors have successfully been derived from 3-D molecular fields. These descriptors were correlated with the experimental permeation data by discriminant partial least-squares methods. The training set consisted of 44 compounds. The authors were able to deduce a simple mathematical model that allows external prediction. More than 90% of blood-brain permeation data were correctly predicted [77]. 

Apparatus Use a Fourier transform infrared spectrometer (FTIR), with its associated computer and peripherals, capable of measuring from 4500 to 500 cm-1 and of acquiring data with a resolution of at least 2 cm-1. The optics of the instmment must be sealed and desiccated, or, like the sample chamber, must be under continuous dry air or nitrogen gas purge. The spectrometer is equipped with software capable of multicomponent analysis using the partial least squares method (PLS-1, or equivalent). This software is commercially available as an accessory to the spectrometer or as an external software package. 

Ferraro JR, Basile LJ (1978) Fourier transform infrared application to national problems In Ferraro JR, Basile U (eds) Fourier transform infrared spectroscopy - applications to chemical systems, Vol 4 Academic Press, New York, 275-302 Ferraro JR, Rein AJ (1985) Application of diffuse reflectance spectroscopy in the far-infrared region In Ferraro JR, Basile LJ (eds) Fourier transform infrared spectroscopy -applications to chemical systems, Vol 4 Academic Press, New York, 244-282 Frank IE, Feikema J, Constantine N, Kowalski BR (1984) Prediction of product quality from spectral data using the partial least squares method J Chem Inf Comput Sci 24 20-24 Fuller MP, Griffiths PR (1980) Infrared microsampling by diffuse reflectance Fourier transform spectrometry Appl Spectrosc 34 533-539... 

Multidimensional Skalierung (andere Bezeichnung . .Partial Least Square"-Methode oder kurz PLS bzw. PLSR genannt) [Massart et al. 1988 Martens/Naes 1989]... 

Finally it is important to note that modern analytical equipment frequently offers opportunities for measuring several or many characteristics of a material more or less simultaneously. This has encouraged the development of multivariate statistics methods, which in principle permit the simultaneous analysis of several components of the material. Partial least squares methods and principal component regression are examples of such techniques that are now finding extensive uses in several areas of analytical science. ... 

The partial least squares methods (PLSl, and PLS2) used for analysis of secondary structure have been discussed in detail by Haaland and Thomas (18). The software package PLSPlus version 2.1G for GRAMS/386 was purchased from Galactic Industries. The PLS2 algorithm, because of its speed, was used to determine optimal parameters, after which PLSl was used for prediction of protein secondary structure. 

Kim, K.H. and Martin, Y.C. (1991c). Evaluation of Electrostatic and Steric Descriptors for 3D-QSAR the H and CH3 Probes Using Comparative Molecular Field Analysis (CoMFA) and the Modified Partial Least Squares Method. In QSAR Rational Approaches to the Design of Bioactive Compounds (Silipo, C. and Vittoria, A., eds.), Elsevier, Amsterdam (The Netherlands), pp. 151-154. 

Miyashita, Y, Ohsako, H., Takayama, C. and Sasaki, S. (1992). Multivariate Structure-Activity Relationships Analysis of Fungicidal and Herbicidal Thiocarbamates Using Partial Least Squares Method. Quant.Struct.-Act.Relat, 11,17-22. 

Gao L, Ren S. Simultaneous spectrometric determination of manganese, zinc and cobalt by kernel partial least-squares method. J Automatic Chem 1998 20 179-83. 

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