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The Generalization Complexity Measure for Continuous Input Data

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 neu...

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Autores principales: Gómez, Iván, Cannas, Sergio A., Osenda, Omar, Jerez, José M., Franco, Leonardo
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4005069/
https://www.ncbi.nlm.nih.gov/pubmed/24983000
http://dx.doi.org/10.1155/2014/815156
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author Gómez, Iván
Cannas, Sergio A.
Osenda, Omar
Jerez, José M.
Franco, Leonardo
author_facet Gómez, Iván
Cannas, Sergio A.
Osenda, Omar
Jerez, José M.
Franco, Leonardo
author_sort Gómez, Iván
collection PubMed
description 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.
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spelling pubmed-40050692014-06-30 The Generalization Complexity Measure for Continuous Input Data Gómez, Iván Cannas, Sergio A. Osenda, Omar Jerez, José M. Franco, Leonardo ScientificWorldJournal Research Article 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. Hindawi Publishing Corporation 2014 2014-04-10 /pmc/articles/PMC4005069/ /pubmed/24983000 http://dx.doi.org/10.1155/2014/815156 Text en Copyright © 2014 Iván Gómez et al. https://creativecommons.org/licenses/by/3.0/ 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.
spellingShingle Research Article
Gómez, Iván
Cannas, Sergio A.
Osenda, Omar
Jerez, José M.
Franco, Leonardo
The Generalization Complexity Measure for Continuous Input Data
title The Generalization Complexity Measure for Continuous Input Data
title_full The Generalization Complexity Measure for Continuous Input Data
title_fullStr The Generalization Complexity Measure for Continuous Input Data
title_full_unstemmed The Generalization Complexity Measure for Continuous Input Data
title_short The Generalization Complexity Measure for Continuous Input Data
title_sort generalization complexity measure for continuous input data
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4005069/
https://www.ncbi.nlm.nih.gov/pubmed/24983000
http://dx.doi.org/10.1155/2014/815156
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