INDEX partial least squares

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. 

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. ... 

Seven parameters of physicochemical properties, such as acid number, color, density, refractive index, moisture and volatility, saponification value and PV, were measured for quality and adnlter-ated soybean, as well as quality and rancid rapeseed oils. The chemometric methods were then applied for qualitative and quantitative discrimination and prediction of the oils by methods snch as exploratory principal component analysis (PCA), partial least squares (PLS), radial basis function-artificial neural networks (RBF-ANN), and multi-criteria decision making methods (MCDM), PROMETHEE and GAIA.260... 

In Fig. 23, spectra of two different grades of U.S. gasoline are shown, de Bakker and Fredericks [90] demonstrated that it was possible to perform a variety of petroleum property measurements, including research octane number (RON), motor octane number (MON), density, benzene content, and flexible volatile index (FVI), using fiber-optical FT-Raman spectroscopy coupled with partial least-squares analysis to reduce sample fluorescence. The potential for on-line measurement of these properties was mentioned by both Cooper et al. [89] and de Bakker and Fredericks [90], Cooper et al. [89,92,93] compared Raman spectroscopy to both mid-IR and near-IR for the measurement of several parameters in fuel mixtures including aromatic concentrations, octane number, and vapor pressures. Cooper et al. similarly utilized partial least squares to accomplish the data analysis. In this series of articles. Cooper et al. described their attempts to quantify mid-IR, near-... 

The difference electron density map following the last cycle of least squares refinement did not show evidence for a simple disorder model to explain the anomalously high B for the hydroxyl oxygen. Attempts to refine residual peaks with partial oxygen occupancies did not significantly improve the agreement index. 

Reducing the Number of Partial Derivatives Index-1 Case The effort for the computation of sensitivity matrices can be reduced significantly observing that only directional derivatives in the directions of the degrees of freedom of the system are necessary. This leads to ideas used earlier also in the context of multistage least squares systems see [BES87]. 

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