Stochastic transformation of quantum similarity matrices and their use in quantum QSAR (QQSAR) models

A stochastic transformation of quantum similarity matrices is described and its role in the field of quantitative structure-activity relationship (QSAR) analyzed. The possible interest to manipulate in such a way a quantum similarity matrix, computed over a quantum object set, is diverse. First, any quantum similarity matrix column or row can easily become a discrete probability distribution, associable to a corresponding quantum object density function. Second, in order to ease its subsequent use, the resulting quantum stochastic matrix can be easily symmetrized, by means of any usual procedure or, as described here, by an inward matrix product algorithm. Third, the final matrix transform can be considered as a new quantum similarity index and can be used as a new quantum object descriptor in QSAR models. Fourth, such symmetric stochastic transform can acquire an interesting role in the approximate solution of the fundamental quantum QSAR (QQSAR) equation under various assumptions. Finally, a new algorithm, based on inward matrix product algebra, to obtain strictly positive constrained solutions of the fundamental QQSAR equation, is described. Some application examples are provided in order to illustrate the previous theoretical development. (C) 2000 John Wiley & Sons, Inc.