Variance-Based Diversity Metrics

For a collection of N compounds, the design matrix is a N X M matrix where the M columns represent a distinct molecular attribute or descriptor. A maximally diverse collection of compounds, therefore, is one that maximizes the value of D. 

Martin and co-workers have adopted the )-optimal criterion in the design of combinatorial libraries (see Section 5). 

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A diversity metric is a function to aid the quantification of the diversity of a set of compounds in some predefined chemical space. Diversity metrics fall into three main classes (1) Distance-based methods, which express diversity as a function of the pairwise molecular dissimilarities defined through measurement. (2) Cell-based methods, which define diversity in terms of occupancy of a finite number of cells that represent disjoint regions of chemical space. (3) Variance-based methods, which quantify diversity based on the degree of correlation between a compound s important features. 

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