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The Scientific World Journal
Volume 2014, Article ID 815156, 9 pages
Research Article

The Generalization Complexity Measure for Continuous Input Data

1Departamento de Lenguajes y Ciencias de la Computación, Universidad de Málaga, 29071 Málaga, Spain
2Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, 5000 Córdoba, Argentina

Received 18 December 2013; Accepted 5 March 2014; Published 10 April 2014

Academic Editors: B. Liu and T. Zhao

Copyright © 2014 Iván Gómez et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We introduce in this work an extension for the generalization complexity measure to continuous input data. The measure, originally defined in Boolean space, quantifies the complexity of data in relationship to the prediction accuracy that can be expected when using a supervised classifier like a neural network, SVM, and so forth. We first extend the original measure for its use with continuous functions to later on, using an approach based on the use of the set of Walsh functions, consider the case of having a finite number of data points (inputs/outputs pairs), that is, usually the practical case. Using a set of trigonometric functions a model that gives a relationship between the size of the hidden layer of a neural network and the complexity is constructed. Finally, we demonstrate the application of the introduced complexity measure, by using the generated model, to the problem of estimating an adequate neural network architecture for real-world data sets.