Descriptor validation

Figure 2. Descriptor validation example (a) poor feature set (b) good feature set.

A set of molecules is commonly described with anywhere from 4 to 10,000 descriptors. It is also possible to represent molecules with sparse descriptors numbering up to 2 million. Variable selection, or descriptor subset selection, or descriptor validation, is important, whether the context is supervised or unsupervised learning (Section 6). 

A common practice is to scale each descriptor to have standard deviation of 1. Another is to compute principal components and confine the analysis to the first h components, where h may range from 1 to 20. This is an ad hoc form of dimension reduction that does not remove irrelevant information from the analysis. At Lilly, we prefer a careful descriptor validation to avoid including many irrelevant descriptors into the analysis, combined with a dimension reduction criterion using... 

The authors especially thank W. Guba, K.H. Baringhaus, C. Giegerich, S. Henke, C.Turpin, R. Vaz, E. Chan (Hoechst Marion Roussel),T. Potter (Bayer AG), H. Briem (Boehrin-ger Ingelheim KG), B. Wendt, R.D. Cramer, D.E. Patterson, R.D. Clark, D. Lassen (Tripos) and J.S. Dixon (Metaphorics Inc.) for helpful discussions and collaborations on various issues of molecular similarity and diversity, library design and descriptor validation. 

By all these there was practically proved the reliability of the algebraic approach to explain the eventually statistically paradoxes as well to overcome them in a systematically analytical manner. Still, a more general fundament for the algebraic QSAR approach containing statistical descriptors, validity and predictability effects should be studied at the pure mathematical level regardless of the chemical or biological systems involved. 

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