This paper introduces two generative topographic mapping (GTM) methods that can be used for data visualization, regression analysis, inverse analysis, and the determination of applicability domains (ADs). In GTM-multiple linear regression (GTM-MLR), the prior probability distribution of the descriptors or explanatory variables (X) is calculated with GTM, and the posterior probability distribution of the property/activity or objective variable (y) given X is calculated with MLR; inverse analysis is then performed using the product rule and Bayes’ theorem. In GTM-regression (GTMR), X and y are combined and GTM is performed to obtain the joint probability distribution of X and y; this leads to the posterior probability distributions of y given X and of X given y, which are used for regression and inverse analysis, respectively. Simulations using linear and nonlinear datasets and quantitative structure-activity relationship (QSAR) and quantitative structure-property relationship (QSPR) datasets confirm that GTM-MLR and GTMR enable data visualization, regression analysis, and inverse analysis considering appropriate ADs.

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