Differential Shannon Entropy

Batista, Godden and Bajorath have developed the MolBlaster method, in which molecular similarity is assessed by Differential Shannon Entropy computed from populations of randomly generated fragments. For the range 0.64 < T < 0.99, this similarity measure provides with the same ranking as the... 

Godden, J.W. and Bajorath, J. (2001) Differential Shannon entropy as a sensitive measure of differences in database variability of molecular descriptors./. Chem. Inf. Comput. Sci., 41, 1060-1066. 

We will describe below the SE formalism in detail and explain how it can be used to estimate chemical information content based on histogram representations of feature value distributions. Examples from our work and studies by others will be used to illustrate key aspects of chemical information content analysis. Although we focus on the Shannon entropy concept, other measures of information content will also be discussed, albeit briefly. We will also explain why it has been useful to extend the Shannon entropy concept by introducing differential Shannon entropy (DSE) to facilitate large-scale analysis and comparison of chemical features. The DSE formalism has ultimately led to the introduction of the SE-DSE metric. 

Differential Shannon Entropy Analysis Identifies Molecular Property Descriptors that Predict Aqueous Solubility of Synthetic Compounds with High Accuracy in Binary QSAR Calculations. 

To identify molecular descriptors that are sensitive to intrinsic differences in two collections of compounds A and B, a differential Shannon s entropy DSE has also been proposed as [Godden and Bajorath, 2001, 2002, 2003 Stahura, Godden et al., 2002]... 

Going beyond statistical analyses, information encoded in molecular descriptor value distributions in databases of natural or synthetic compounds was analyzed in quantitative terms by application of an entropy-based information-theoretic approach. - Descriptor value distributions, represented in histograms, can be reduced to their information content using Shannon entropy (SE) calculations. Differences in information content between databases can be quantified using differential SE (DSE) analysis. " An extension of this approach, SE-DSE analysis," makes it possible to classify molecular descriptors according to their relative information content in diverse databases and to identify those descriptors that are most responsive to systematic differences between compound databases. Figure... 

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