Research on similarity searching of cheminformatic data sets has been focused on similarity measures using fingerprints. However, nominal scales are the least informative of all metric scales, increasing the tied similarity scores, and decreasing the effectivity of the retrieval engines. Tanimoto's coefficient has been claimed to be the most prominent measure for this task. Nevertheless, this field is far from being exhausted since the computer science no free lunch theorem predicts that "no similarity measure has overall superiority over the population of data sets". We introduce 12 relational agreement (RA) coefficients for seven metric scales, which are integrated within a group fusion-based similarity searching algorithm. These similarity measures are compared to a reference panel of 21 proximity quantifiers over 17 benchmark data sets (MUV), by using informative descriptors, a feature selection stage, a suitable performance metric, and powerful comparison tests. In this stage, RA coefficients perform favourably with repect to the state-of-the-art proximity measures. Afterward, the RA-based method outperform another four nearest neighbor searching algorithms over the same data domains. In a third validation stage, RA measures are successfully applied to the virtual screening of the NCI data set. Finally, we discuss a possible molecular interpretation for these similarity variants.

Cluster tendency assessment is an important stage in cluster analysis. In this sense, a group of promising techniques named visual assessment of tendency (VAT) has emerged in the literature. The presence of clusters can be detected easily through the direct observation of a dark blocks structure along the main diagonal of the intensity image. Alternatively, if the Dunn's index for a single linkage partition is greater than 1, then it is a good indication of the blocklike structure. In this report, the Dunn's index is applied as a novel measure of tendency on 8 pharmacological data sets, represented by machine-learning-selected molecular descriptors. In all cases, observed values are less than 1, thus indicating a weak tendency for data to form compact clusters. Other results suggest that there is an increasing relationship between the Dunn's index as a measure of cluster separability and the classification accuracy of various cluster algorithms tested on the same data sets.

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aWe 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.