Eppa. Derks et al., ROBUSTNESS ANALYSIS OF RADIAL BASE FUNCTION AND MULTILAYERED FEEDFORWARD NEURAL-NETWORK MODELS, Chemometrics and intelligent laboratory systems, 28(1), 1995, pp. 49-60
In this paper, two popular types of neural network models (radial base
function (RBF) and multi-layered feed-forward (MLF) networks) trained
by the generalized delta rule, are tested on their robustness to rand
om errors in input space. A method is proposed to estimate the sensiti
vity of network outputs to the amplitude of random errors in the input
space, sampled from known normal distributions. An additional paramet
er can be extracted to give a general indication about the bias on the
network predictions. The modelling performances of MLF and RBF neural
networks have been tested on a variety of simulated function approxim
ation problems. Since the results of the proposed validation method st
rongly depend on the configuration of the networks and the data used,
little can be said about robustness as an intrinsic quality of the neu
ral network model. However, given a data set where 'pure' errors from
input and output space are specified, the method can be applied to sel
ect a neural network model which optimally approximates the nonlinear
relations between objects in input and output space. The proposed meth
od has been applied to a nonlinear modelling problem from industrial c
hemical practice. Since MLF and RBF networks are based on different co
ncepts from biological neural processes, a brief theoretical introduct
ion is given.