Variable elimination

If a large number of descriptor variables are utilized, reduce the number by variable elimination before modeling. 

In SIMCA, we can determine the modelling power of the variables, i.e. we measure the importance of the variables in modelling the elass. Moreover, it is possible to determine the discriminating power, i.e. which variables are important to discriminate two classes. The variables with both low discriminating and modelling power are deleted. This is more a variable elimination procedure than a selection procedure we do not try to select the minimum number of features that will lead to the best classification (or prediction rate), but rather eliminate those that carry no information at all. 

Unmeasured variable elimination through Q-R orthogonal factorizations... 

The latter variable eliminates a finite range [42] of convergence of series both of X at 2 i e, because of a pole due to intemuclear coulombic repulsion as / 0, and of y at V2 Re, for a similar phenomenon as oo. Expressions for Fy in terms of coefficients cj in the latter series are available in a large consistent collection in Fortran coding [43] up to Cio such expressions, readily calculated, through symbolic computation with efficient procedures [44], first in terms of coefficients and thence converted to bj or Cj as required, are further converted to Fortran or C code for numerical applications. 

Value reported for few-acid Highly variable Elimination phase Apparent eUmination phase Temiinal phase, NR = not reported. 

When the number of noisy (noninformative) variables is too large, PLS models may also supply rather poor predictive performance. In order to overcome such a matter, a number of techniques for the elimination of noisy variables or the selection of useful predictors have been deployed, such as iterative stepwise elimination (ISE), iterative predictor weighting (IPW), uninformative variable elimination (UVE), and Martens uncertainty test (MUT) (Forina et ah, 2007). 

General considerations of renormaiizability are best carried through within the field theoretic formulation. We recall from Sect. 7.2 that a Laplace transform with respect to the chain length variables eliminates the segment summations. In the resulting field theoretic formulation a propagator line of momentum k, being part of the m-th polymer line, yields a factor (cf, Eq. (7.17))... 

Principal component regression and partial least squares are two widely used methods in the factor analysis category. PCR decomposes the matrix of calibration spectra into orthogonal principal components that best capture the variance in the data. These new variables eliminate redundant information and, by using a subset of these principal components, filter noise from the original data. With this compacted and simplified form of the data, equation (12.7) may be inverted to arrive at b. 

Descriptors of chemical structure, the independent variables, or x variables can come from a variety of sources and may be measured, estimated, or calculated as discussed in Chapters 3 to 6. It is quite common these days to use many descriptors in a QSAR study, often many more variables than there are compounds (cases) in the set. This leads to the need for dimension reduction, variable elimination and variable selection. In the early days of QSAR modeling, the 1960s and 1970s, there was little need for any of these methods since the descriptors used were generally tabulated... 

Variable elimination is the name given to the process by which unhelpful or unnecessary variables are removed from a data set. One means by which a variable may be judged is from the information it contains. If the standard deviation of the variable is very small, then it does not contain much information and is thus not likely to be useful in the construction of models. Another common situation is that a variable may contain only a small number of different values, an extreme case being where the values are the same for all compounds in the set except one. If a variable such as this is used in the construction of a model then it may appear to be useful but is usually only serving to identify, and thus explain, the response value for that single compound. An example of this is shown in Table 7.2, which contains values of receptor binding and computed properties for a set of quinuclidine-based muscarinic receptor agonists (Saunders et al., 1990). For some of the compounds (6, 7, 8, and 12) the substitution pattern means that there is not, in fact, an... 

By successive variable elimination we can reduce these p simultaneous equations down to just 1 equation (still with a right-hand side equal to zero) so having eliminated (p - 1) equations during this process leaving us with c+ 2 — (p — 1) = c — p+ 3 unknowns and these can be chosen to be any set from the c + 2 unknowns. 

It is desired to find non-negative values of xu x2, and xa that minimize this function and at the same time satisfy the constraints of the previous example. We shall begin with the basis xa, u1( and u2, which was shown to be feasible in the last example. At the end of the last example these variables were expressed in terms of the nonbasic variables Xi and x2) and so it only remains to express the new cost function in terms of these variables. Eliminating xa with the second line of the final table there gives... 

Gieledak, R. and Polanski, J. (2007) Modeling robust QSAR. 2. Iterative variable elimination schemes for GoMSA application for modeling benzoic add pKa values. J. Chem. Inf. Model., 47, 547—556. 

Polanski, J. and Gieleciak, R. (2003) The comparative molecular surface analysis (CoMSA) withmodified uniformative variable elimination-PLS (UVE-PLS) method application to the steroids binding the aromatase enzyme. J. Chem. Inf. Comput. Sci., 43, 656—666. 

More multivariate methods of variable selection, especially suited for PLS applied to spectral data, are currently available. Among them, we can cite Interactive Variable Selection, Uninformative Variable Elimination, Iterative Predictor Weighting PLS, and Interval PLS. ... 

Problem Definition Selection of Controlled Variables 13.2.1 Engineering Judgment / 13.2.2 Singular Value Decomposition Selection of Manipulated Variables Elimination of Poor Pairings BET Tuning... 

In addition to the similarity indices described above, other similarity indices may be defined and used in QSAR studies. A simple lipophilidty similarity index aij = — log Pi — log PjI (log Pi, logPj = logarithms of the partition coefficients of molecules i and j) can be applied to describe nonlinear lipophilicity-activity relationships of any type by the corresponding lipophilidty similarity matrices [1013]. For different data sets excellent results were obtained (Table 31), not only in homologous series (as in CoMFA studies [1025 — 1027]) but also in heterogeneous sets of compounds, where 3D QSAR approaches must fail. A selection procedure based on genetic algorithms was developed for fast and efficient variable elimination in the PLS analyses [1013]. Also in these examples the similarity matrices produced improved Tpress values in fewer components after elimination of variables which did not contribute to prediction (Table 31). 

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