Extension of the Generalization Complexity Measure to Real Valued Input Data Sets

This paper studies the extension of the Generalization Complexity (GC) measure to real valued input problems. The GC measure, defined in Boolean space, was proposed as a simple tool to estimate the generalization ability that can be obtained when a data set is learnt by a neural network. Using two different discretization methods, the real valued inputs are transformed into binary values, from which the generalization complexity can be straightforwardly computed. The discretization transformation is carried out both through a very simple method based on equal width intervals (EW) and with a more sophisticated supervised method (the CAIM algorithm) that use much more information about the data. A study of the relationship between data complexity and generalization ability obtained was done together with an analysis of the relationship between best neural architecture size and complexity.