Modification and simplification of chemical spaces

Here dL is the descriptor value of molecule i, dav the average (or mean) value of the entire data set, the a standard deviation, and d( the scaled value of descriptor d for molecule i. This procedure ensures that all chosen descriptors have similar value ranges (i.e., that descriptor axes have comparable length) and thus prevents space distortions. 

Test compounds are shown as white or black dots 

Here the coefficients c reflect the importance of each descriptor (within each compo- 

An alternative to dimension reduction is the use of composite and uncorrelated descriptors that are suitable for the design of information-rich yet low-dimensional chemical spaces. An elegant example is presented by the popular BCUT (Burden-CAS-University of Texas) descriptors (Pearlman and Smith 1998). BCUTs are a set of uncorrelated descriptors that combine information about molecular connectivity, inter-molecular distances, and other molecular properties. BCUT spaces used for many applications are typically only six-dimensional and can frequently be further reduced to 3D representations for visualization purposes by identifying those BCUT axes around which most compounds map. 

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