The two main topics of this article are the introduction of the "optimally tuned robust improper maximum likelihood estimator"(OTRIMLE) for robust clustering based on the multivariate Gaussian model for clusters, and a comprehensive simulation study comparing the OTRIMLE to maximum likelihood in Gaussian mixtures with and without noise component, mixtures of t-distributions, and the TCLUST approach for trimmed clustering. The OTRIMLE uses an improper constant density for modeling outliers and noise. This can be chosen optimally so that the nonnoise part of the data looks as close to a Gaussian mixture as possible. Some deviation from Gaussianity can be traded in for lowering the estimated noise proportion. Covariance matrix constraints and computation of the OTRIMLE are also treated. In the simulation study, all methods are confronted with setups in which their model assumptions are not exactly fulfilled, and to evaluate the experiments in a standardized way by misclassification rates, a new model-based definition of "true clusters" is introduced that deviates from the usual identification of mixture components with clusters. In the study, every method turns out to be superior for one or more setups, but the OTRIMLE achieves the most satisfactory overall performance. The methods are also applied to two real datasets, one without and one with known "true" clusters. Supplementary materials for this article are available online.

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Background Traditional quantitative structure-activity relationship models usually neglect the molecular alterations happening in the exposed systems (the mechanism of action, MOA), that mediate between structural properties of compounds and phenotypic effects of an exposure. Results Here, we propose a computational strategy that integrates molecular descriptors and MOA information to better explain the mechanisms underlying biological endpoints of interest. By applying our methodology, we obtained a statistically robust and validated model to predict the binding affinity to human serum albumin. Our model is also able to provide new venues for the interpretation of the chemical-biological interactions. Conclusion Our observations suggest that integrated quantitative models of structural and MOA-activity relationships are promising complementary tools in the arsenal of strategies aiming at developing new safe- and useful-by-design compounds. Electronic supplementary material The online version of this article (10.1186/s13321-019-0359-2) contains supplementary material, which is available to authorized users.

Abstract. The so-called noise-component has been introduced by Banfield and Raftery (1993) to improve the robustness of cluster analysis based on the normal mixture model. The idea is to add a uniform distribution over the convex hull of the data as an additional mixture component. While this yields good results in many practical applications, there are some problems with the original proposal: 1) As shown by Hennig (2004), the method is not breakdown-robust.2) The original approach doesn't define a proper ML estimator, and doesn't have satisfactory asymptotic properties.We discuss two alternatives. The first one consists of replacing the uniform distribution by a fixed constant, modelling an improper uniform distribution that doesn't depend on the data. This can be proven to be more robust, though the choice of the involved tuning constant is tricky. The second alternative is to approximate the ML-estimator of a mixture of normals with a uniform distribution more precisely than it is done by the "convex hull" approach. The approaches are compared by simulations and for a real data example.

Supplementary data are available at Bioinformatics online.