Evaluation of neural network models with generalized sensitivity analysis

Abstract

A sensitivity analysis method for discovering characteristic features of the input data using neural network classification models has been devised. The sensitivity is the gradient of the neural network model response function, and because neural network models are nonlinear, the gradient depends on the point where it is evaluated. Two criteria are used for measuring the sensitivity. The first criterion calculates the sensitivity or gradient of the neural network output with respect to the average of the objects that comprise each class. The second criterion measures the average sensitivity of the class objects. The sensitivity analysis was applied to temperature-constrained cascade correlation network models and evaluated with sets of synthetic data and experimental mobility spectra. The neural network models were built using temperature-constrained cascade correlation networks (TCCCNs). A weight constraint was devised for the output units of the network models. This method implements weight decay with conjugate gradient training and yields more sensitive neural network models. Temperature-constrained hidden units furnish more sensitive network models than networks without constraints. By comparing the sensitivities of the class mean input and the mean sensitivity for all the inputs of a class, the individual input variables may be assessed for linearity. If these two sensitivities for an input variable differ by a constant factor, then that variable is modeled by a simple linear relationship. If the two sensitivities vary by a nonconstant scale factor, then the variable is modeled by higher order functions in the network. The sensitivity method was used to diagnose errors in the training data, and the test for linearity indicated a TCCCN architecture that had better predictability.