A novel method for examination of the variable contribution to computational neural network models

Computational neural networks (CNNs or, as they are commonly referred to; artificial neural networks, ANNs) have been demonstrated in a large number of applications to be useful for modeling and prediction. They suffer, however, in their conventional use, that is feed forward/back-propagation of the error, from the lack of a simple or straightforward means of interpreting the variable contribution to the models. CNNs are therefore often referred to as black box models. In this study novel algorithmic approaches to the interpretation of CNN models are proposed, examined and compared with the corresponding variable contribution in partial least squares (PLS) regression models. A sensitive analysis of the CNN models is carried out by sequentially setting each input variable to zero. In addition, to evaluate the direction of the variable contribution, the linear regression coefficients for each input variable are generated. The results of these two approaches are then combined to facilitate comparison with PLS models. CNN models for data on chiral separation, 3D-QSRR (quantitative structure–retention relationships) and SIMS (secondary ion mass spectroscopy) are used to demonstrate the feasibility of the method. For the latter two data sets, there is close agreement between the PLS and CNN models with regard to variable contribution. For the nonlinear data set for chiral separation, differences in variable contribution are revealed.