An evaluation of the bihyperbolic function in the optimization of the backpropagation algorithm
The backpropagation algorithm is one of the most used tools for training artificial neural networks. However, this tool may be very slow in some practical applications. Many techniques have been discussed to speed up the performance of this algorithm and allow its use in an even broader range of app...
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| Veröffentlicht in: | International transactions in operational research Jg. 21; H. 5; S. 835 - 854 |
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| Sprache: | Englisch |
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01.09.2014
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| ISSN: | 0969-6016, 1475-3995 |
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| Abstract | The backpropagation algorithm is one of the most used tools for training artificial neural networks. However, this tool may be very slow in some practical applications. Many techniques have been discussed to speed up the performance of this algorithm and allow its use in an even broader range of applications. Although the backpropagation algorithm has been used for decades, we present here a set of computational results that suggest that by replacing bihyperbolic functions the backpropagation algorithm performs better than the traditional sigmoid functions. To the best of our knowledge, this finding was never previously published in the open literature. The efficiency and discrimination capacity of the proposed methodology are shown through a set of computational experiments, and compared with the traditional problems of the literature. |
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| AbstractList | The backpropagation algorithm is one of the most used tools for training artificial neural networks. However, this tool may be very slow in some practical applications. Many techniques have been discussed to speed up the performance of this algorithm and allow its use in an even broader range of applications. Although the backpropagation algorithm has been used for decades, we present here a set of computational results that suggest that by replacing bihyperbolic functions the backpropagation algorithm performs better than the traditional sigmoid functions. To the best of our knowledge, this finding was never previously published in the open literature. The efficiency and discrimination capacity of the proposed methodology are shown through a set of computational experiments, and compared with the traditional problems of the literature. |
| Author | Miguez, Geraldo Maculan, Nelson Xavier, Adilson Elias |
| Author_xml | – sequence: 1 givenname: Geraldo surname: Miguez fullname: Miguez, Geraldo email: geraldomiguez@gmail.com organization: Federal University of Rio de Janeiro, PESC-COPPE, Rio de Janeiro, Brazil – sequence: 2 givenname: Adilson Elias surname: Xavier fullname: Xavier, Adilson Elias email: adilson@cos.ufrj.br organization: Federal University of Rio de Janeiro, PESC-COPPE, Rio de Janeiro, Brazil – sequence: 3 givenname: Nelson surname: Maculan fullname: Maculan, Nelson email: maculan@cos.ufrj.br organization: Federal University of Rio de Janeiro, PESC-COPPE, Rio de Janeiro, Brazil |
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| Cites_doi | 10.1631/jzus.C1200008 10.1109/TLA.2009.5349049 10.1109/IJCNN.1992.287133 10.1016/0893-6080(89)90020-8 10.1016/S0893-6080(02)00032-1 10.1016/j.neucom.2011.08.026 10.1007/BF02551274 10.2306/scienceasia1513-1874.2013.39.294 10.1109/IJCNN.2002.1005526 10.1109/ICASSP.2013.6638963 10.1016/j.neucom.2004.04.001 10.1073/pnas.81.10.3088 10.3390/jsan1030299 10.1109/IJCNN.1992.227257 10.1080/01431160802549278 10.1109/SHUSER.2012.6268818 10.1073/pnas.87.23.9193 10.1117/12.135110 10.7551/mitpress/5236.001.0001 10.1109/INES.2013.6632792 10.1109/IJCNN.1989.118505 10.1109/TII.2012.2187914 10.1109/34.107014 10.1016/j.procs.2013.05.076 10.1109/IJCNN.1991.155275 10.1109/72.572104 10.1109/PEAM.2012.6612460 10.1016/j.neunet.2013.11.002 |
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| Copyright | 2014 The Authors. International Transactions in Operational Research © 2014 International Federation of Operational Research Societies Published by John Wiley & Sons Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main St, Malden, MA02148, USA. Copyright © 2014 International Federation of Operational Research Societies |
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| References_xml | – reference: Chandra, P., Singh, Y., 2004. An activation function adapting training algorithm for sigmoidal feed forward networks. Neurocomputing 61, 429-437. – reference: Hopfield, J.J., 1984. Neurons with graded response have collective computational properties like those of two-states neurons. Proceedings of the National Academy of Sciences 81, 3088-3092. – reference: Liu, Y., Yang, J., Li, L., Wu, W., 2012. Negative effects of sufficiently small initial weights on back-propagation neural networks. Journal of Zhejiang University Science C 13, 8, 585-592. – reference: Singh, S., Gupta, P.R., 2011. Breast cancer detection and classification using neural network. International Journal of Advanced Engineering Sciences and Technologies 6, 1, 4-9. – reference: Stathakis, D., 2009. How many hidden layers and nodes? International Journal of Remote Sensing 30, 8, 2133-2147. – reference: Mustafa, H.M.H., Abdulhamid, Z.M., 2012. On simulation of brain based learning paradigms (neural networks approach). Elixir Education Technology 52, 11331-11337. – reference: Trucheteta, F., Lénib, P.E., Fougerollea, Y., 2013. New representations for multidimensional functions based on Kolmogorov superposition theorem. Applications on Image Processing Conference Proceedings Saint Petersburg, Russia, Vol. 1, pp. 8-18. – reference: Setiono, R., Liu, H., 1997. Neural-network feature selector. IEEE Transactions on Neural Networks 8, 3, 654-662. – reference: Wolberg, W.H., Mangasarian, O.L., 1990. Multisurface method of pattern separation for medical diagnosis applied to breast cytology. Proceedings of the National Academy of Sciences 87, 9193-9196. – reference: Grossberg, S., 1982. Studies of Mind and Brain, Boston Studies in the Philosophy of Science. D. Reidel Publishing, Boston, MA. – reference: Bache, K., Lichman, M., 2013. UCI Machine Learning Repository. School of Information and Computer Science, University of California, Irvine, CA, USA. Available at http://archive.ics.uci.edu/ml . – reference: Chimieski, B.F., Fagundes, R.D.R., 2013. Association and classification data mining algorithms comparison over medical datasets. Journal of Health Information 5, 2, 44-51. – reference: Yang, S., Ting, T.O., Man, K.L., Guan, S., 2013. Investigation of neural networks for function approximation. First International Conference on Information Technology and Quantitative Management (ITQM2013), Procedia Computer Science 17, 586-594. – reference: Shafie, A.S., Mohtar, S.M., Ahmad, N., 2012. Backpropagation neural network with new improved error function and activation function for classification problem. IEEE Symposium on Humanities, Science and Engineering Research 1, 1359-1364. – reference: Otair, M.A., Salameh, W.A., 2005. Speeding up back-propagation neural networks. Proceedings of the 2005 Informing Science and IT Education Joint Conference, Flagstaff, AZ, Vol. 1, pp. 167-173. – reference: Azmi, M.S.B.M., Cob, Z.C., 2010. Breast cancer prediction based on backpropagation algorithm. Proceedings of 2010 IEEE Student Conference on Research and Development (SCOReD 2010), Putrajaya, Malaysia, Vol. 1, pp. 164-168. – reference: Ng, S.C., Cheung, C.C., Leung, S.H., Luk, A., 2003. Fast convergence for backpropagation network with magnified gradient function. Proceedings of the International Joint Conference Neural Networks 3, 1903-1908. – reference: Xavier, A.E., 2005. Uma Função de Ativação para Redes Neurais Artificiais Mais Flexível e Poderosa e Mais Rápida. Learning and Nonlinear Models-Revista da Sociedade Brasileira de Redes Neurais (SBRN) 1, 5, 276-282. – reference: Haykin, S., 2001. Neural Networks: A Comprehensive Foundation (2nd edn). Prentice-Hall, Englewood Cliffs, NJ. – reference: Rocha Neto, A.R., Barreto, G.A., 2009. On the application of ensembles of classifiers to the diagnosis of pathologies of the vertebral column: a comparative analysis. IEEE Transactions on Latin America 7, 4, 487-496. – reference: Sathyaa, D.J., Geethab, K., 2013. Mass classification in breast DCE-MR images using an artificial neural network trained via a bee colony optimization algorithm. ScienceAsia 39, 294-306. – reference: Draghici, S., 2002. On the capabilities of neural networks using limited precision weights. Neural Networks 15, 395-414. – reference: Rocha Neto, A.R., Barreto, G.A., Cortez, P.C., Mota, H., 2006. SINPATCO: Sistema Inteligente para Diagnóstico de Patologias da Coluna Vertebral. XVI Congresso Brasileiro de Automática Bahia, Brazil, Vol. 1, pp. 929-934. – reference: Rumelhart, D.E., McClelland, J.L., eds, 1986. Parallel Distributed Processing: Explorations, Microstructure of Cognition, Vol. 1: Foundations. MIT Press, Cambridge, MA. – reference: Lin, F., Yu, X.H., Gregor, S., Irons, R., 1995. 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| SubjectTerms | activation function Algorithms Back propagation backpropagation algorithm bihyperbolic function Computation Discrimination machine learning Mathematical analysis Mathematical models Neural networks Operational research Operations research Optimization pattern recognition Studies |
| Title | An evaluation of the bihyperbolic function in the optimization of the backpropagation algorithm |
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