The Generalization Complexity measure for continuous input data

IVAN GOMEZ; SERGIO A. CANNAS; OMAR OSENDA; JOSE JEREZ; LEONARDO FRANCO

SCIENTIFIC WORLD JOURNAL, THE

THESCIENTIFICWORLD LTD

Lugar: New York; Año: 2014 vol. 2014 p. 1 - 9

1537-744X

We introduce in this work an extension for the Generalization Com- plexity measure to continuous input data. The measure, originally dened in Boolean space, quanties the complexity of data in relation- ship to the prediction accuracy that can be expected when using a supervised classier like a neural network, SVM, etc. We rst 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, con- sider the case of having a nite number of data points (inputs/outputs pairs) that is usually the practical case. Using a set of trigonomet- ric 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.