Soft modeling

I 1982. Soft Modeling. The Basic Design and Some Extensions. In Joreskog K-G and H Wold litors) Systems under Indirect Observation Volume II. Amsterdam, North-HoUand. 

H. Wold, Soft modelling by latent variables the non-linear iterative partial least squares (NIPALS) algorithm. In Perspectives in Probability and Statistics, J. Gani (Ed.). Academic Press, London, 1975, pp. 117-142. 

A.P. de Weyer, L.M.C. Buydens, G. Kateman and H.M. Heuvel, Neural networks used as a soft modelling technique for quantitative description of the inner relation between physical properties and mechanical properties of poly ethylene terephthalate yams. Chemom. Intell. Lab. Syst., 16(1992) 77-82. 

Wold, H., Soft Modeling The Basic Design and Some Extensions, Systems Under Indirect Observations (K. J. Horeskog and H. Wold, eds.). Elsevier Science, North Holland, Amsterdam, 1982. 

On the other hand, when latent variables instead of the original variables are used in inverse calibration then powerful methods of multivariate calibration arise which are frequently used in multispecies analysis and single species analysis in multispecies systems. These so-called soft modeling methods are based, like the P-matrix, on the inverse calibration model by which the analytical values are regressed on the spectral data ... 

At the same time S. Wold presented the software soft independent modeling of class analogies (SIMCA) and introduced a new way of thinking in data evaluation called soft modeling (Wold and Sjostrom 1977). 

H. Wold, Soft modeling the basic design and some extensions, in Systems Under Indirect Observation, Causality-Structure-Prediction, Part 2, K.G. Joreskog and H. Wold (eds), North-Holland Publishing Co., Amsterdam, 1982, pp 1-54. 

In our original work, we used an ionic-covalent model to interpret the E and C parameters. It has been suggested that our E and C parameters are a quantitative manifestation of the hard-soft model. "Softness (or hardness") can be considered (67) as a measure of the ratio of the tendency of a spedes to undergo covalent interaction to the tendency of the species to undergo electrostatic interaction. The relative "softness or hardness is depicted in the C/E ratio. The ratios for the acids and bases can be calculated from the data in Tables 3 and 4. If the ratio C/E is comparatively large, the add or base would be classified as type B or soft. Inasmuch as the relative ratios of C/E tells the relative importance of the two effects for various donors and acceptors, we agree that the hardness or softness discussed in the HSAB model is given by this ratio. 

H. Wold, Soft modelling the basic design and some extensions, in... 

Model-based nonlinear least-squares fitting is not the only method for the analysis of multiwavelength kinetics. Such data sets can be analyzed by so-called model-free or soft-modeling methods. These methods do not rely on a chemical model, but only on simple physical restrictions such as positiveness for concentrations and molar absorptivities. Soft-modeling methods are discussed in detail in Chapter 11 of this book. They can be a powerful alternative to hard-modeling methods described in this chapter. In particular, this is the case where there is no functional relationship that can describe the data quantitatively. These methods can also be invaluable aids in the development of the correct kinetic model that should be used to analyze the data by hard-modeling techniques. 

De Juan, A., Maeder, M., Martinez, M., and Tauler, R., Combining hard- and soft-modelling to solve kinetic problems, Chemom. Intell. Lab. Syst., 2000, 54, 123-141. 

Biochemical processes are among the most challenging and interesting reaction systems. Due to the nature of the constituents involved, macromolecules such as nucleic acids or proteins, the processes to be analyzed do not follow a simple physicochemical model, and their mechanism cannot be easily predicted. For example, well-known reactions for simple molecules, e.g., protonation equilibria, increase in complexity for macromolecules due to the presence of polyelectrolytic effects or conformational transitions. Because the data analysis cannot be supported in a model-fitting procedure (hard-modeling methods), the analysis of these processes requires soft-modeling methods that can unravel the contributions of the process without the assumption of an a priori model. 

Esteban, M., Anno, C., Dfaz-Cruz, J.M., Dfaz-Cruz, M.S., and Tauler, R., Multivariate curve resolution with alternating least squares optimization a soft-modeling approach to metal complexation studies by voltammetric techniques, Trends Anal. Chem., 19, 49-61, 2000. 

Diewok, J., de Juan, A., Maeder, M., Tauler, R., and Lendl, B., Application of a combination of hard and soft modeling for equilibrium systems to the quantitative analysis of pH-modulated mixture samples, Anal. Chem., 75, 641-647, 2003. 

The SIMCA method, first advocated by the S. Wold in tire early 1970s, is regarded by many as a form of soft modelling used in chemical pattern recognition. Although there are some differences with linear discriminant analysis as employed in traditional statistics, the distinction is not as radical as many would believe. However, SIMCA has an important role in the history of chemometrics so it is important to understand the main steps of the method. 

Wold H. Soft modelling with latent variables The nonlinear iterative partial least squares approach. In Gani J, editor, Perspectives in probability and statistics Papers in honour of M.S. Barlett. London Academic Press, 1975. p. 114-42. 

Quantitative models is a heterogeneous group of models expressed in mathematical language. This includes what can be called hard models of general applicability, e.g. thermodynamic models, quantum mechanical models, absolute rate theory, as well as soft models or local models, usually expressed in terms of analogy and similarity, e.g. linear free energy relationships (LFERs), correlations for spectroscopic structural determination, empirical determined kinetic models, and as we shall see, models obtained by statistical treatment of experimental data from properly designed experiments. 

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