An upper bound of input perturbation for RBFNNS sensitivity analysis

According to the existing definition of sensitivity of radial basis function neural networks (RBFNNs), the sensitivity of each feature of RBFNNs can be numerically calculated. Usually features with small value of sensitivity are regarded as redundant ones that may be removed. By sorting the calculated sensitivity magnitudes, a sequence of features can be obtained. This sequence does depend generally on the input perturbation, which seriously affects the application of RBFNNs sensitivity to redundant feature removal. To overcome this defect, this paper gives an upper bound of input perturbation under which the sequence will be independent of the input perturbation. This upper bound keeps the feature sensitivity order unchanged and leads to a new sensitivity definition of RBFNNs. Simulation has been performed to verify the upper bound and the new sensitivity definition and the simulation result is consistent with the theoretical result.