A definition of partial derivative of random functions and its application to RBFNN sensitivity analysis

Considering the inputs of a feed-forward neural network as random variables, this paper proposes a definition of partial derivative of a function with respect to a random variable in the probability measure space. The mathematical expectation of the mean square or absolute value of the partial derivative is regarded as a type of measure of the network's sensitivity, which extends Zurada's sensitivity definition of networks in Zurada et al, [Perturbation method for deleting redundant inputs of perceptron networks, Neurocomputing 14 (1997) 177-193] from the certain environment to the stochastic environment. Furthermore, for the purpose of network's redundant feature deletion or feature selection, the new sensitivity measure is applied to the sensitivity analysis of Radial Basis Function Neural Networks (RBFNNs). The feasibility and the effectiveness of the sensitivity approach to redundant feature deletion are illustrated.