Assessing the importance of features for multi-layer perceptrons

In this paper we establish a mathematical framework in which we develop measures for determining the contribution of individual features to the performance of a classifier. Corresponding to these measures, we design metrics that allow estimation of the importance of features for a specific multi-layer perceptron neural network. It is shown that all measures constitute lower bounds for the correctness that can be obtained when the feature under study is excluded and the classifier rebuilt. We also present a method for pruning input nodes from the network such that most of the knowledge encoded in its weights is retained. The proposed metrics and the pruning method are validated with a number of experiments with artificial classification tasks. The experiments indicate that the metric called replaceability results in the tightest error bounds. Both this metric and the metric called expected influence result in good rankings of the features.