



@article {2253,
	title = {The MEE principle in data classification: A perceptron-based analysis},
	journal = {Neural ComputationNeural Comp.},
	volume = {22},
	year = {2010},
	note = {Cited By (since 1996): 3Export Date: 21 November 2012Source: Scopusdoi: 10.1162/NECO_a_00013PubMed ID: 20569178Language of Original Document: EnglishCorrespondence Address: Silva, L.M.; Instituto de Engenharia Biom{\'e}dica, Divis{\~a}o de Sinal e Imagem, Porto 4200-465, Portugal; email: lmsilva@fe.up.ptReferences: Alexandre, L.A., Marques de S{\'a}, J., Error entropy minimization for LSTM training (2006) Proceedings of the 16th International Conference on Artificial Neural Networks, pp. 244-253. , Berlin: Springer;Asuncion, A., Newman, D., (2007) UCI machine learning repository. Irvine University of California, Irvine, , http://www.ics.uci.edu/~mlearn/MLRepository.html, School of Information and Computer Sciences. Available online at; 
Bishop, C., (1995) Neural networks for pattern recognition, , New York: OxfordUniversity Press; 
Erdogmus, D., Hild K., II., Pr{\'\i}ncipe, J.C., Blind source separation using R{\'e}nyi{\textquoteright}s α-marginal entropies (2002) Neurocomputing, 49, pp. 25-38; 
Erdogmus, D., Pr{\'\i}ncipe, J.C., Comparison of entropy and mean square error criteria in adaptive system training using higher order statistics (2000) Proceedings of the Intl. Conf. on ICA and Signal Separation, pp. 75-80. , Berlin: Springer-Verlag; 
Erdogmus, D., Pr{\'\i}ncipe, J.C., An error-entropy minimization algorithm for supervised training of nonlinear adaptive systems (2002) IEEE Transactions on Signal Processing, 50 (7), pp. 1780-1786; 
Erdogmus, D., Pr{\'\i}ncipe, J.C., Convergence properties and data efficiency of the minimum error entropy criterion in adaline training (2003) IEEE Transactions on Signal Processing, 51 (7), pp. 1966-1978; 
Gokcay, E., Pr{\'\i}ncipe, J.C., Information theoretic clustering (2002) IEEE Trans. on Pattern Analysis and Machine Learning, 24 (2), pp. 158-171; 
Han, L., Kernel partial least squares (K-PLS) for scientific data mining. Unpublished doctoral dissertation (2007) Rensselaer Polytechnic Institute; 
Hild, I.I., Erdogmus, K., Pr{\'\i}ncipe D., J.C., Blind source separation using R{\'e}nyi{\textquoteright}s mutual information (2001) IEEE Signal Processing Letters, 8, pp. 174-176; 
Jacobs, R., Jordan, M., Nowlan, S., Hinton, G., Adaptive mixtures of local experts (1991) Neural Computation, 3, pp. 79-87; 
Jenssen, R., Hild, K., Erdogmus, D., Pr{\'\i}ncipe, J.-C., Eltoft, T., Clustering using R{\'e}nyis entropy (2003) Proceedings of the Int. Joint Conference on Neural Networks, pp. 523-528. , Piscataway, NJ: IEEE Press; 
Johnson, N., Kotz, S., (1970) Continuous univariate distributions, , Hoboken, NJ:Wiley; 
Kapur, J., Maximum-entropy models in science and engineering (1993), (rev. ed.). Hoboken, NJ: WileyLagarias, J., Reeds, J.A., Wright, M.H., Wright, P.E., Convergence properties of the nelder-mead simplex method in low dimensions (1998) SIAM Journal of Optimization, 9 (1), pp. 112-147; 
Linsker, R., Self-organization in a perceptual network (1988) IEEE Computer, 21, pp. 105-117; 
Liu, W., Pokharel, P., Pr{\'\i}ncipe, J., Correntropy: Properties and applications in non-gaussian signal processing (2007) IEEE Transactions on Signal Processing, 55 (11), pp. 5286-5298; 
Parzen, E., On the estimation of a probability density function and the mode (1962) Annals of Mathematical Statistics, 33, pp. 1065-1076; 
Pr{\'\i}ncipe, J.C., Xu, D., Fisher, J., Information theoretic learning (2000) Unsupervised adaptive filtering, 1, pp. 265-319. , S. Haykin (Ed.), Blind source separation, Hoboken, NJ: Wiley; 
R{\'e}nyi, A., (1970) Probability theory, , Dordrecht: North-Holland; 
Richard, M., Lippmann, R., Neural network classifiers estimate Bayesian a posteriori probabilities (1991) Neural Computation, 3, pp. 461-483; 
Santos, J., (2007) Data classification with neural networks and entropic criteria, , Unpublished doctoral dissertation, University of Porto; 
Santos, J.M., Marques de S{\'a}, J., Alexandre, L.A., Batch-sequential algorithm for neural networks trained with entropic criteria (2005) Proceedings of the International Conference on Artificial Neural Networks, pp. 91-96. , Berlin: Springer-Verlag; 
Santos, J.M., Marques de S{\'a}, J., Alexandre, L.A., Legclust-a clustering algorithm based on layered entropic subgraphs (2007) IEEE Transactions on Pattern Analysis and Machine Intelligence, 30 (1), pp. 62-75; 
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, pp. 81-86. , C. Dagli, A. Buczak, D. Enke, M. Embrechts, \& O. Ersoy (Eds.), Washington, DC: ASME; 
Silva, L.M., (2008) Neural networks with error-density risk functionals for data classification, , Unpublished doctoral dissertation, University of Porto; 
Silva, L.M., Embrechts, M., Santos, J.M., Marques de S{\'a}, J., The influence of the risk functional in data classification with MLPs (2008) Proceedings of the International Conference on Artificial Neural Networks, pp. 185-194. , Berlin: Springer-Verlag; 
Silva, L.M., Felgueiras, C., Alexandre, L.A., Marques de S{\'a}, J., Error entropy in classification problems: A univariate data analysis (2006) Neural Computation, 18 (9), pp. 2036-2061; 
Silva, L.M., Marques de S{\'a}, J., Alexandre, L.A., Neural network classification using Shannon{\textquoteright}s entropy (2005) Proceedings of the European Symposium on Artificial Neural Networks, pp. 217-222. , Bruges: d-side; 
Stoller, D., Univariate two-population distribution free discrimination (1954) Journal of the American Statistical Association, 49, pp. 770-777; 
Thompson, J., Tapia, R., (1978) Nonparametric probability density estimation, , Baltimore, MD: Johns Hopkins University Press; 
Watanabe, S., Pattern recognition as a quest for minimum entropy (1981) Pattern Recognition, 13 (5), pp. 381-387
},
	month = {2010///},
	pages = {2698 - 2728},
	abstract = {This letter focuses on the issue of whether risk functionals derived from information-theoretic principles, such as Shannon or R{\'e}nyi{\textquoteright}s entropies, are able to cope with the data classification problem in both the sense of attaining the risk functional minimum and implying the minimum probability of error allowed by the family of functions implemented by the classifier, here denoted by min Pe. The analysis of this so-called minimization of error entropy (MEE) principle is carried out in a single perceptron with continuous activation functions, yielding continuous error distributions. In spite of the fact that the analysis is restricted to single perceptrons, it reveals a large spectrum of behaviors that MEE can be expected to exhibit in both theory and practice. In what concerns the theoretical MEE, our study clarifies the role of the parameters controlling the perceptron activation function (of the squashing type) in often reaching the minimum probability of error. Our study also clarifies the role of the kernel density estimator of the error density in achieving the minimum probability of error in practice. {\textcopyright} 2010 Massachusetts Institute of Technology.},
	keywords = {algorithm, Algorithms, artificial intelligence, artificial neural network, automated pattern recognition, Computer simulation, entropy, letter, Mathematical Concepts, mathematical phenomena, Models, Statistical, Neural Networks (Computer), Pattern Recognition, Automated, standard, statistical model},
	isbn = {08997667 (ISSN)},
	url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-78149334887\&partnerID=40\&md5=97c7445cfa4693d406d979afc4b42319},
	author = {Silva, L.M. and Marques de S{\'a}, J. and Alexandre, L.A.}
}
