Information theoretic based measures form a fundamental class of similarity measures for comparing clusterings, beside the class of pair-counting based and set-matching based measures. In this paper, we discuss the necessity of correction for chance for information theoretic based measures for clusterings comparison. We observe that the baseline for such measures, i.e. average value between random partitions of a data set, does not take on a constant value, and tends to have larger variation when the ratio between the number of data points and the number of clusters is small. This effect is similar in some other non-information theoretic based measures such as the well-known Rand Index. Assuming a hypergeometric model of randomness, we derive the analytical formula for the expected mutual information value between a pair of clusterings, and then propose the adjusted version for several popular information theoretic based measures. Some examples are given to demonstrate the need and usefulness of the adjusted measures.

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There is an urgent clinical need for antimalarial compounds that target malaria caused by both Plasmodium falciparum and Plasmodium vivax. The M1 and M17 metalloexopeptidases play key roles in Plasmodium hemoglobin digestion and are validated drug targets. We used a multitarget strategy to rationally design inhibitors capable of potent inhibition of the M1 and M17 aminopeptidases from both P. falciparum (Pf-M1 and Pf-M17) and P. vivax (Pv-M1 and Pv-M17). The novel chemical series contains a hydroxamic acid zinc binding group to coordinate catalytic zinc ion/s, and a variety of hydrophobic groups to probe the S1′ pockets of the four target enzymes. Structural characterization by cocrystallization showed that selected compounds utilize new and unexpected binding modes; most notably, compounds substituted with bulky hydrophobic substituents displace the Pf-M17 catalytic zinc ion. Excitingly, key compounds of the series potently inhibit all four molecular targets and show antimalarial activity comparable to current clinical candidates.