Scaling of the descriptor variables

There are certain situations where scaling to unit variance is not the preferred procedure and where no scaling at all is better. If all descriptor variables are of the same kind and measured in the same unit, e.g. intensities of spectral absorbtion at different frequencies or peak heights in chromatographic profiles, it is sometimes unnecessary to scale the variables. Autoscaling such variables would exaggerate minor variations. Another case, when scaling may be unnecessary is when a variable 

The principal component score is a linear combination of the descriptors. 

Chemical phenomena are rarely purely linear. In a limited domain of variation we can regard a principal components model as a local linearization by a Taylor expansion. As such it is likely to apply for classes of similar compounds. 

If the values of some descriptor vary in magnitudes over the set of compounds it is difficult to assume that a linear model will be a good approximation to account for such large variations. In these cases, a better model can often be obtained after a logarithmic transformation of this variable prior to scaling to unit variance. 

Another situation where transformation of a descriptor, x is indicated is when it is known by some physical model how this descriptor is linked to more fundamental properties of the molecule. This may indicate some kind of mathematical transformation of the descriptor prior to autoscaling, e.g. In Xj, expfxj, l/ti- One example is spectral data, for which the wavelength, Xj, of an absorption by the reciprocal transformation l/Vj is transformed into a frequency measure which is proportional to the energy of excitation. 

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