



@article {2457,
	title = {Neural networks trained with the EEM algorithm: Tuning the smoothing parameter},
	journal = {WSEAS Transactions on SystemsWSEAS Trans. Syst.},
	volume = {4},
	year = {2005},
	note = {Cited By (since 1996): 3Export Date: 21 November 2012Source: ScopusLanguage of Original Document: EnglishCorrespondence Address: Santos, J.M.; Intituto de Engenharia Biom{\'e}dica, Porto, Portugal; email: jms@isep.ipp.ptReferences: Erdogmus, D., Principe, J., "An Error-Entropy Minimization Algorithm for Supervised Training of Nonlinear Adaptive Systems" (2002) Trans. On Signal Processing, 50 (7), pp. 1780-1786;Santos, J.M., Alexandre, L.A., Marques de S{\'a}, J., "The error entropy minimization algorithm for neural network classification" (2004) Proceedings of the 5th International Conference on Recent Advances in Soft Computing, pp. 92-97. , A. Lofti, Ed. Nottingham Trent University; 
Santos, J.M., Marques de S{\'a}, J., Alexandre, L.A., Sereno, F., "Optimization of the error entropy minimization algorithm for neural network classification" (2004) Intelligent Engineering Systems Through Artificial Neural Networks, 14, pp. 81-86. , C.H. Dagli, A.L. Buczak, D.L. Enke, M.J. Embrechts, and O. Ersoy, Eds., ASME Press; 
Erdogmus, D., Principe, J., "Entropy Minimization Algorithm for Neural Networks" (2001) Proceedings of the Intl. Joint Conf. on Neural Networks, pp. 3003-3008; 
Xu, D., Princpe, J., "Training mlps layer-by-layer with the information potential" (1999) Intl. Joint Conf. on Neural Networks, pp. 1716-1720; 
Silverman, B.W., (1986) Density Estimation for Statistics and Data Analisys, 26. , Chapman \& Hall; 
Bowman, A.W., Azzalini, A., (1997) Applied Smooting Techniques for Data Analysis, , London: Oxford University Press; 
Jacobs, R., Jordan, M., Nowlan, S., Hinton, G., "Adaptive mixtures of local experts" (1991) Neural Computation, pp. 79-87
},
	month = {2005///},
	pages = {295 - 299},
	abstract = {The training of Neural Networks and particularly Multi-Layer Perceptrons (MLP{\textquoteright}s) is made by minimizing an error function usually known as "cost function". In our previous works, we apply the Error Entropy Minimization (EEM) algorithm in classification and its optimized version using, as cost function, the entropy of the errors between the outputs and the desired targets of the neural network. One of the difficulties in implementing the EEM algorithm is the choice of the smoothing parameter, also known as window size, in the Parzen Window probability density function estimation for the computation of the entropy and its gradient. We present here a formula yielding the value of the smoothing parameter, depending on the number of data samples and on the neural network output dimension. Several experiments with real data sets were made in order to show the validity of the proposed formula.},
	keywords = {Cost function, entropy, Error entropy minimization (EEM) algorithm, Learning algorithms, Learning systems, Neural networks, Optimization, Parzen, Probability density function, Smoothing parameter},
	isbn = {11092777 (ISSN)},
	url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-21844450579\&partnerID=40\&md5=31c652daee111a68194cd4f006d7ca7b},
	author = {Santos, J.M. and Marques de S{\'a}, J. and Alexandre, L.A.}
}
