Partial least square analysis

L Stable and S. Wold, Partial least square analysis with cross-validation for the two-class problem a Monte Carlo study. J. Chemometrics, 1 (1987) 185-196. 

While principal components models are used mostly in an unsupervised or exploratory mode, models based on canonical variates are often applied in a supervisory way for the prediction of biological activities from chemical, physicochemical or other biological parameters. In this section we discuss briefly the methods of linear discriminant analysis (LDA) and canonical correlation analysis (CCA). Although there has been an early awareness of these methods in QSAR [7,50], they have not been widely accepted. More recently they have been superseded by the successful introduction of partial least squares analysis (PLS) in QSAR. Nevertheless, the early pattern recognition techniques have prepared the minds for the introduction of modem chemometric approaches. 

A drawback of the method is that highly correlating canonical variables may contribute little to the variance in the data. A similar remark has been made with respect to linear discriminant analysis. Furthermore, CCA does not possess a direction of prediction as it is symmetrical with respect to X and Y. For these reasons it is now replaced by two-block or multi-block partial least squares analysis (PLS), which bears some similarity with CCA without having its shortcomings. 

Partial least squares analysis (PLS) has rapidly found applications in QSAR since its introduction by Wold et al. [52]. The reader is referred to Sections 35.7 and 36.2.4 for a thorough discussion of PLS. 

PLS Projection to latent structures by means of a partial least squares analysis... 

Wilkins, C.K., Wolkoff P., Gyntelberg, F., Skov, P. and Valbjum, O. (1993) Characterization of office dust by VOCs and TVOC-release-identification of potential irritant VOCs by partial least squares analysis. Indoor Air, 3, 283-90. 

Optimization of predietions ean be made utilizing linear as well as nonlinear relationships by means of statistieal methods to correlate chemical and physiological descriptors to experimental datasets. These statistical methods inelude multilinear partial least square analysis, principal component analysis, and neural networking. Many of these tools are included in QSPR/QSAR packages through companies sueh as Advanced Chemistry Development, SemiChem, EduSoft, BioByte, TOPKAT, MDL, ChemSilico, Pallas, Pharma Algorithms, and others. 

Figure 4. Partial least squares analysis of twelve glycoside hydrolysates, sensory attribute ratings and volatile compound concentration (normalised) a) component loadings, and b) sample scores. For explanation of codes see Tables II and IV.

This work was supported by a grant from the National Science Foundation, t Abbreviations used are as follows. FTIR Fourier transform infrared spectroscopy, ATR attenuated total reflectance, IRE internal reflection element, SATR solution ATR FTIR, FSD Fourier self-deconvolution, PLS partial least-squares analysis, PRESS prediction residual sum of squares from PLS. SECV standard error of calibration values from PLS, PLSl PLS analysis in which each component is predicted independently, PLS2 PLS analysis in which all components are predicted simultaneously. 

To determine the oil, water, and solids contents simultaneously, sophisticated statistical techniques must usually be applied, such as partial least-squares analysis (PLS) and multivariate analysis (MVA). This approach requires a great deal of preparation and analysis of standards for calibration. Near-infrared peaks can generally be quantified by using Beer s law consequently, NIRA is an excellent analytical tool. In addition, NIRA has a fast spectral acquisition time and can be adapted to fiber optics this adaptability allows the instrument to be placed in a control room somewhat isolated from the plant environment. 

A different approach to mathematical analysis of the solid-state C NMR spectra of celluloses was introduced by the group at the Swedish Forest Products Laboratory (STFI). They took advantage of statistical multivariate data analysis techniques that had been adapted for use with spectroscopic methods. Principal component analyses (PCA) were used to derive a suitable set of subspectra from the CP/MAS spectra of a set of well-characterized cellulosic samples. The relative amounts of the I and I/3 forms and the crystallinity index for these well-characterized samples were defined in terms of the integrals of specific features in the spectra. These were then used to derive the subspectra of the principal components, which in turn were used as the basis for a partial least squares analysis of the experimental spectra. Once the subspectra of the principal components are validated by relating their features to the known measures of variability, they become the basis for analysis of the spectra of other cellulosic samples that were not included in the initial analysis. Here again the interested reader can refer to the original publications or the overview presented earlier. ... 

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