Partial Least Squares examples

Some methods that paitly cope with the above mentioned problem have been proposed in the literature. The subject has been treated in areas like Cheraometrics, Econometrics etc, giving rise for example to the methods Partial Least Squares, PLS, Ridge Regression, RR, and Principal Component Regression, PCR [2]. In this work we have chosen to illustrate the multivariable approach using PCR as our regression tool, mainly because it has a relatively easy interpretation. The basic idea of PCR is described below. 

H. Van der Voet, Pseudo-degrees of freedom for complex predictive models the example of partial least squares, J. Chemom., 13, 1999, 195-208. 

When all of the individual component spectra are not known, implicit calibration methods are often adopted. Among these, factor analysis methods such as principal component regression (PCR)24 and partial least squares (PLS)25 are frequently used because they can function under conditions in which the number of spectra used for calibration is less than the number of wavelengths sampled. For example, a calibration set may include 30 spectra with each spectrum having 500 data points (wavelengths). 

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. 

Geladi, P. and Kowalski, B.R., An example 2-block predictive partial least-squares regression with simulated data, Anal. Chim. Acta, 185, 19-32, 1986. 

Chemometrics is an interdisciplinary field that combines statistics and chemistry. From its earliest days, chemometrics has always been a practically oriented subdiscipline of analytical chemistry aimed at solving problems often overlooked by mainstream statisticians. An important example is solving multivariate calibration problems at reduced rank. The method of partial least-squares (PLS) was quickly recognized and embraced by the chemistry community long before many practitioners in statistics considered it worthy of a second look. ... 

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. ... 

Perhaps the most popular example of 3D-QSARis the comparative molecular field analysis (CoMFA), developed by Cramer et al. (40), which has elegantly combined the power of 3D molecular modeling and partial least-square (PLS) optimization technique (41, 42) and found wide applications in medicinal chemistry and toxicity analysis (see below). Most of... 

An example of a non-covalent MIP sensor array is shown in Fig. 21.14. Xylene imprinted poly(styrenes) (PSt) and poly(methacrylates) (PMA) with 70 and 85% cross-linker have been used for the detection of o- and p-xylene. The detection has been performed in the presence of 20-60% relative humidity to simulate environmental conditions. In contrast to the calixarene/urethane layers mentioned before, p-xylene imprinted PSts still show a better sensitivity to o-xylene. The inversion of the xylene sensitivities can be gathered with PMAs and higher cross-linker ratios. As a consequence of the humidity, multivariate calibration of the array with partial least squares (PLS) and artificial neural networks (ANN) is performed, The evaluated xylene detection limits are in the lower ppm range (Table 21.2), whereas neural networks with back-propagation training and sigmoid transfer functions provide the most accurate data for o- and p-xylene concentrations as compared to PLS analyses. 

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