FERNÁNDEZ NAVARRO, FRANCISCO DE ASÍS, CARBONERO RUZ, MARIANO, BECERRA ALONSO, DAVID, TORRES JIMÉNEZ, MERCEDES
No
IEEE Trans. Neural Netw. Learn. Syst.
Article
Científica
7.982
3.406
01/11/2017
000413403900011
2-s2.0-84983050058
Artificial neural networks (ANNs) have traditionally been seen as black-box models, because, although they are able to find "hidden" relations between inputs and outputs with a high approximation capacity, their structure seldom provides any insights on the structure of the functions being approximated. Several research papers have tried to debunk the black-box nature of ANNs, since it limits the potential use of ANNs in many research areas. This paper is framed in this context and proposes a methodology to determine the individual and collective effects of the input variables on the outputs for classification problems based on the ANOVA-functional decomposition. The method is applied after the training phase of the ANN and allows researchers to rank the input variables according to their importance in the variance of the ANN output. The computation of the sensitivity indices for product unit neural networks is straightforward as those indices can be calculated analytically by evaluating the integrals in the ANOVA decomposition. Unfortunately, the sensitivity indices associated with ANNs based on sigmoidal basis functions or radial basis functions cannot be calculated analytically. In this paper, the indices for those kinds of ANNs are proposed to be estimated by the (quasi-) Monte Carlo method.
Feedforward neural networks; functional decomposition; global sensitivity analysis (GSA); multiclassification; product unit neural networks (PUNNs)