Orthogonalize the variables

Since, as we shall see, we do not need to deal with the general case, we can use a simpler method to orthogonalize the variables, based on Daniel and Wood, who showed how a variable can be transformed so that the square of that variable is uncorrelated with the variable. This is a matter of creating a new variable by simply calculating a quantity Z and subtracting that from each of the original values of X. A symmetric distribution of the data is not required since that is taken into account in the formula. Z is calculated using the expression (see p. 121 in [9]). In Appendix A, we present the derivation of this formula ... 

Euclidian distances can, from a strict perspective, only be used for determining the distance between orthogonal variables. This is most often not the case for chemical descriptors. The problem of orthogonality can be handled in two ways either compensate for the nonorthogonal behavior within the distance calculation, for example, use Mahalanobis distance instead [98] of an Euclidian distance or orthogonalize the variables, for example, by principal component analysis, prior to the Euclidian distance calculation. 

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See also in sourсe #XX -- [ ]

See also in sourсe #XX -- [ ]

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