Exploring the QSAR's predictive truthfulness of the novel N-tuple discrete derivative indices on benchmark datasets

Choquet integral-based fuzzy molecular characterizations: when global definitions are computed from the dependency among atom/bond contributions (LOVIs/LOEIs)

BACKGROUND

Several topological (2D) and geometric (3D) molecular descriptors (MDs) are calculated from local vertex/edge invariants (LOVIs/LOEIs) by performing an aggregation process. To this end, norm-, mean- and statistic-based (non-fuzzy) operators are used, under the assumption that LOVIs/LOEIs are independent (orthogonal) values of one another. These operators are based on additive and/or linear measures and, consequently, they cannot be used to encode information from interrelated criteria. Thus, as LOVIs/LOEIs are not orthogonal values, then non-additive (fuzzy) measures can be used to encode the interrelation among them.

RESULTS

General approaches to compute fuzzy 2D/3D-MDs from the contribution of each atom (LOVIs) or covalent bond (LOEIs) within a molecule are proposed, by using the Choquet integral as fuzzy aggregation operator. The Choquet integral-based operator is rather different from the other operators often used for the 2D/3D-MDs calculation. It performs a reordering step to fuse the LOVIs/LOEIs according to their magnitudes and, in addition, it considers the interrelation among them through a fuzzy measure. With this operator, fuzzy definitions can be derived from traditional or recent MDs; for instance, fuzzy Randic-like connectivity indices, fuzzy Balaban-like indices, fuzzy Kier-Hall connectivity indices, among others. To demonstrate the feasibility of using this operator, the QuBiLS-MIDAS 3D-MDs were used as study case and, as a result, a module was built into the corresponding software to compute them ( http://tomocomd.com/qubils-midas ). Thus, it is the only software reported in the literature that can be employed to determine Choquet integral-based fuzzy MDs. Moreover, regression models were created on eight chemical datasets. In this way, a comparison between the results achieved by the models based on the non-fuzzy QuBiLS-MIDAS 3D-MDs with regard to the ones achieved by the models based on the fuzzy QuBiLS-MIDAS 3D-MDs was made. As a result, the models built with the fuzzy QuBiLS-MIDAS 3D-MDs achieved the best performance, which was statistically corroborated through the Wilcoxon signed-rank test.

CONCLUSIONS

All in all, it can be concluded that the Choquet integral constitutes a prominent alternative to compute fuzzy 2D/3D-MDs from LOVIs/LOEIs. In this way, better characterizations of the compounds can be obtained, which will be ultimately useful in enhancing the modelling ability of existing traditional 2D/3D-MDs.

GOWAWA Aggregation Operator-based Global Molecular Characterizations: Weighting Atom/bond Contributions (LOVIs/LOEIs) According to their Influence in the Molecular Encoding

A different perspective to compute global weighted definitions of molecular descriptors from the contributions of each atom (LOVIs) or covalent bond (LOEIs) within a molecule is presented, using the generalized ordered weighted averaging - weighted averaging (GOWAWA) aggregation operator. This operator is rather different from the other norm-, mean- and statistic-based operators used up to date for the descriptors calculation from LOVIs/LOEIs. GOWAWA unifies the generalized ordered weighted averaging (GOWA) and the weighted generalized mean (WGM) functions and, in addition, it uses a smoothing parameter to assign different importance values to both functions depending on the problem under study. With the GOWAWA operator, diversity of novel global aggregations of molecular descriptors can be determined, where the influence that each atom (or covalent bond) has on the molecular characterization is taken into account. Therefore, this approach is completely different from the ones reported in the literature, where the values of LOVIs/LOEIs are considered equally important. To demonstrate the feasibility of using this operator, the QuBiLS-MIDAS descriptors (http://tomocomd.com/qubils-midas) were used and, as a result, a module was built into the corresponding software to compute them, being thus the only software reported in the literature that can be employed to determine weighted descriptors. Moreover, several modeling studies were performed on eight chemical datasets, which demonstrated that, with the GOWAWA aggregation operator, weighted QuBiLS-MIDAS descriptors that contribute to develop models with greater predictive power can be computed, if compared to the models based on the non-weighted descriptors calculated from the other operators used up to date. A non-parametric statistical assessment confirmed that the GOWAWA-based predictions are significantly superior to the others obtained. Therefore, all in all, it can be concluded that, from the results achieved, the GOWAWA operator constitutes a prominent alternative to codify relevant chemical information of the molecules, ultimately useful in improving the modeling ability of several old and recent descriptors whose definition is based on the LOVIs/LOEIs calculation.