Soft modeling methods

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 ... 

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. 

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. 

A disadvantage of this calibration method is the fact that the calibration coefficients (elements of the P matrix) have no physical meaning, since they do not reflect the spectra of the individual components. The usual assumptions about errorless independent variables (here, the absorbances) and error-prone dependent variables (here, concentrations) are not valid. Therefore, if this method of inverse calibration is used in coimection with OLS for estimating the P coefficients, there is only a slight advantage over the classical /C-matrix approach, due to the fact that a second matrix inversion is avoided. However, in coimection with more soft modeling methods, such as PCR or PLS, the inverse calibration approach is one of the most frequently used calibration tools. 

Factor analysis, like in spectrophotometry, can help here to get estimate of the number of species involved in extraction without any a priori suggestions. The ESI method leads to multiple minima problem, but it can speed up the search of chanical model or to prove if the model found is correct. Soft modeling methods like PLS or ANN enable fast determination of stability constants without solving mass balance... 

Wentzell PD. Other topics in soft-modeling maximum likelihood-based soft-modeling methods. In Brown SD, Tauler R, Walczak B, editors. Comprehensive chemometrics chemical and biochemical data analysis. Amsterdam Elsevier Ltd. 2009. 

In the following, we focus on the soft-sphere method since this really is the workhorse of the DPMs. The reason is that it can in principle handle any situation (dense regimes, multiple contacts), and also additional interaction forces—such as van der Waals or electrostatic forces—are easily incorporated. The main drawback is that it can be less efficient than the hard-sphere model. 

Nevertheless, in most of the electronic tongue applications found in the literature, classification techniques like linear discriminant analysis (LDA) and partial least squares discriminant analysis (PLS-DA) have been used in place of more appropriate class-modeling methods. Moreover, in the few cases in which a class-modeling technique such as soft independent modeling of class analogy (SIMCA) is applied, attention is frequently focused only on its classification performance (e.g., correct classification rate). Use of such a restricted focus considerably underutilizes the significant characteristics of the class-modeling approach. 

Examples of nonhierarchical clustering [22] methods include Gaussian mixture models, means, and fuzzy C means. They can be subdivided into hard and soft clustering methods. Hard classification methods such as means assign pixels to membership of only one cluster whereas soft classifications such as fuzzy C means assign degrees of fractional membership in each cluster. 

Cundari, T.R., Deng, J., Pop, H.F. and Sarbu, C. (2000) Structural analysis of transition metal beta-X substituent interactions. Toward the use of soft computing methods for catalyst modelling. J. Chem. Inf. Comp. Sci., 40, 1052. 

Since perfect knowledge of the model is rarely a reasonable assumption, soft computing methods, integrating quantitative and qualitative modeling information, have been developed to improve the performance of observer-based schemes for uncertain systems [36], Major contributions to observer-based approaches can be found in [39, 56] as well, where fault isolation is achieved via a bank of observers, while identification is based on the adoption of online universal interpolators (e.g., ANNs whose weights are updated on line). As for the use of observers in the presence of advanced control techniques, such as MPC or FLC, in [44] an unknown input observer is adopted in conjunction with an MPC scheme. 

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. 

As long as one deals with small clusters, beam analysis is possible by combining spectroscopy with expansion modeling. It is possible to use, for example, the soft ionization methods to obtain a better idea of the relative concentration of different clusters in the beam. Soft ionization can be achieved either by direct photoionization or by applying the multiphoton ionization methods (see Cheshnovsky and Leutwyler as a recent example). This technique does not solve completely the fragmentation problem, since if the positively charged species formed is not stable, it will fall apart. However, combining it with sp>ectroscopy, satisfactory results can be obtained. 

Various attempts have been made to use pattern recognition [24, 25] in QSAR studies and successful applications have been reported. Soft modeling techniques, e.g. the partial least squares (PLS) method [26, 27], now offer better opportunities. With the help of this principal component-like method the explanatory power of many, even hundreds or thousands of variables can be used for a limited number of objects, a task being absolutely impossible in regression analysis in which the number of objects must always be larger than the number of variables. 

The methods of soft modeling are based on the inverse calibration model where concentrations are regressed on spectral data ... 

A wide range of modeling methods are available, from structured to object-oriented methods, and from soft to formal methods. These methods provide different levels of precision and are amenable to different kinds of analysis. Models based on formal methods can be difficult to... 

The soft models defined by the weights of the neural networks are capable of accommodating all types of relationships, being especially useful when the dependence of the retention behavior with the mobile phase variables is unknown. However, neural networks learn the relationships from the data themselves, and hence, more experimental points are needed with respect to hard-modeling methods. The use of neural networks is, therefore, only recommended for those cases where adequate theoretical or empirical models do not exist, such as retention modeling in MLC with four variables (e.g., pH, surfactant, modifier, and temperature). 

Curteanu, S. Nistor, A. Curteanu, N. Airinei, A. Cazacu, M., Applying Soft Computing Methods to Fluorescence Modeling of the Polydimethylsiloxane/Silica Composites Containing Lanthanum. J. Appl. Polym. Sci. 2010,117,3160-3169. 

The counterpart of hard modelling is soft modelling. This theoretical approach is characterized by analytic methods with a minimum of computational efforts (soft theorists consider solved a problem when it has been reduced to quadratures) tailored models obtained by a reduced description of the system (simplification ) generality of the results which hold true usually for a large class of systems, but usually lack of specificity. 

Recently, so-called soft modeling has become more and more important in chemistry, especially related to the partial least squares (PLS) and artificial neural network (ANN) methods. The PLS method has been used to evaluate chemical equilibria in potentiom-etry by Perutka et al. [74]. The other, more advantageous possibility is ANNs. 

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