Theoretical advances on coefficients of relational agreement: application to cheminformatics as k-way biomolecular similarity measures

We provide formal proofs on the partial ordering among chance‐corrected bivariate coefficients of relational agreement. Moreover, we prove that the non‐corrected (chance‐corrected) general formula of multivariate relational agreement is the weighted average of the corresponding non‐corrected (chance‐corrected) general formula of bivariate relational agreement, thus allowing to obtain a specific relationship between each multivariate coefficient and its corresponding bivariate coefficient for seven metric scales of measurements (absolute, difference, ratio, interval, log‐ratio, log‐interval, and ordinal). As a consequence, we report seven newly multivariate coefficients in the literature. Afterwards, eight multivariate coefficients are applied as k‐way biomolecular similarity relations to cheminformatics in order to show their usefulness for discriminating between active and inactive biomolecules. The integration of this type of coefficients into operative virtual screening tools and the generalization to higher‐degree polynomial relationships are discussed in the last part of the paper. Copyright © 2013 John Wiley & Sons, Ltd. We provide formal proofs on the partial ordering among chance‐corrected bivariate coefficients of relational agreement. Moreover, we prove that the non‐corrected (chance‐corrected) general formula of multivariate relational agreement is the weighted average of the corresponding non‐corrected (chance‐corrected) general formula of bivariate relational agreement. As a consequence, we report seven newly multivariate coefficients in the literature. Afterwards, eight multivariate coefficients are applied as k‐way biomolecular similarity relations to cheminformatics in order to show their usefulness for discriminating between active and inactive biomolecules.