Variable reduction

J. D. Turner, P. K. Weiner, H. M. Chun, V. Lupi, S. Gallion, and U. C. Singh. Variable reduction techniques applied to molecular dynamics simulations. In W. F. van Gunsteren, P. K. Weiner, and A. J. Wilkinson, editors. Computer Simulation of Biomolecular Systems Theoretical and Experimental Applications, volume 2, chapter 24. ESCOM, Leiden, The Netherlands, 1993. 

The reduction of latent variables is an effective method to reduce the number of possible models, yet in PLS, variable reduction is not needed. The reduction of the number of variables in traditional regression techniques will lead to models with improved predictive ability and, in the case of PLS, a model that is easier to understand. The attempts to reduce the number of variables for PLS have only resulted in simpler models that fit the Training Set better yet do not have the predictive abilities of the complete PLS model (111). The reduction of latent variables with respect to the descriptors is possible with no apparent decrease in the model s ability to predict bioactivities, yet the remaining descriptor-based variables are considered to be more important before reduction and thus introduces bias (111). 

Methyldopa was widely used in the past but is now used primarily for hypertension during pregnancy. It lowers blood pressure chiefly by reducing peripheral vascular resistance, with a variable reduction in heart rate and cardiac output. 

M. L. Griffiths, D. Svozil, P. Worsfold, S. Denham and E. H. Evans, Variable reduction algorithm for atomic emission spectra application to multivariate calibration and quantitative analysis of industrial samples, J. Anal. At. Spectrom., 17, 2002, 800-812. 

Shaw, A. D., Di Camillo, A., Vlahov, G., Jones, A., Bianchi, G., Rowland, J., and Kell, D. B. (1997). Discrimination of the variety and the region of extra virgin olive oils using 13C NMR and multivariate calibration with variable reduction. Anal. Chim. Acta 348,357-374. 

Shaw AD, di Camillo A, Vlahov G, Jones A, Bianchi G, Rowland J, Kell DB (1996) Discrimination of Different Olive Oils using 13C NMR and Variable Reduction, in Food Authenticity 96. Norwich, UK... 

After PCA, die original variables (e.g. absorbances recorded at 28 wavelengths) are reduced to a number of significant principal components (e.g. three). PCA can be used as a form of variable reduction, reducing die large original dataset (recorded at... 

Instead of using raw data, it is possible to use the PCs of the data. This acts as a form of variable reduction, but also simplifies the distance measures, because the variance-covariance matrix will only contain nonzero elements on the diagonals. The expressions for Mahalanobis distance and linear discriminant functions simplify dramatically. 

Chapter 5, we will not give a numerical example in this chapter, but if the number of variables is fairly large, approaches such as Mahalanobis distance are not effective unless there is variable reduction either by first using PCA or simply selecting some of the measurements, so the approach discussed in this section is worth trying. 

The most popular optimization techniques are Newton-Raphson optimization, steepest ascent optimization, steepest descent optimization. Simplex optimization. Genetic Algorithm optimization, simulated annealing. - Variable reduction and - variable selection are also among the optimization techniques. 

With respect to CoMFA, the Compass method effectively reduces the number of descriptors, performing a physicochemically based - variable reduction and overcomes the problem of guessing the best conformation and alignmet of the molecules. 

Connoiiy surface area - molecular surface (O solvent-accessible molecular surface) constant interval reciprocal indices -> distance matrix constant and near-constant variables variable reduction constitutional descriptors... 

K inflation factor variable reduction (O K correlation analysis)... 

The general problem of excluding variables from data, i.e. of estimating the best I vector, can be divided in two main blocks methods for - variable reduction and methods for - variable selection. The first group of methods evaluates the variable exclusion by inner relationships among the p descriptor variables, i.e. 

Variable reduction consists in the selection of a subset of variables able to preserve the essential information contained in the whole -> data set, but eliminating redundancy, too highly intercorrelated variables, etc. 

Variable reduction differs fi om -> variable selection in the fact that the subset of variables is selected independently of the response of interest. 

The most common methods for variable reduction are listed below. 

A preliminary approach to variable reduction consiting in the elimination of all the variables that take the same value for all the objects in the data set. Near-constant variables, i.e. variables that assume the same value except in one or very few cases, would also be excluded. A good measure for evaluating near-constant variables is the -> standardized Shannon s entropy the entropy of a variable with one different value over 10 objects is 0.141, over 20 objects is 0.066, and with two different values over 100 objects is 0.024. 

McCabe techniques of variable reduction [McCabe, 1984] are based on the calculation of the residual correlation (or covariance) matrix Sm of the deleted variables where the effect of the retained variable is removed. TTiis matrix is a square symmetric matrix of order p - k, where k is the number of retained variables, obtained from the correlation (covariance) matrix of the retained variables Sr (of size kxk) and the correlation (or covariance) matrix of the deleted variables Sd (of size qxq). The retained variables by McCabe techniques are called principal variables. This terminology can be extended to all the sets of retciined variables obtained from PCA and correlation analysis. 

A unique advantage of the model-based CD control performance calculations is the two-dimensional information detail for improvement potential. Figure 10.25 shows the process variability reduction for each measuremen-... 

---