



@article {2405,
	title = {Error entropy in classification problems: A univariate data analysis},
	journal = {Neural ComputationNeural Comp.},
	volume = {18},
	year = {2006},
	note = {Cited By (since 1996): 7Export Date: 21 November 2012Source: Scopusdoi: 10.1162/neco.2006.18.9.2036PubMed ID: 16846386Language of Original Document: EnglishCorrespondence Address: Silva, L.M.; Institute de Engenharia Biom{\'e}dica, Laborat{\'o}rio Sinal e Imagem Biom{\'e}dica, 4200-465, Porto, Portugal; email: lmsilva@fe.up.ptReferences: Devroye, L., Gyorfi, L., Lugosi, G., (1996) A Probabilistic Theory of Pattern Recognition, , Berlin: Springer-Verlag;Erdogmus, D., Principe, J., 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. , Helsinki, Finland; 
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},
	month = {2006///},
	pages = {2036 - 2061},
	abstract = {Entropy-based cost functions are enjoying a growing attractiveness in unsupervised and supervised classification tasks. Better performances in terms both of error rate and speed of convergence have been reported. In this letter, we study the principle of error entropy minimization (EEM) from a theoretical point of view. We use Shannon{\textquoteright}s entropy and study univariate data splitting in two-class problems. In this setting, the error variable is a discrete random variable, leading to a not too complicated mathematical analysis of the error entropy. We start by showing that for uniformly distributed data, there is equivalence between the EEM split and the optimal classifier. In a more general setting, we prove the necessary conditions for this equivalence and show the existence of class configurations where the optimal classifier corresponds to maximum error entropy. The presented theoretical results provide practical guidelines that are illustrated with a set of experiments with both real and simulated data sets, where the effectiveness of EEM is compared with the usual mean square error minimization. {\textcopyright} 2006 Massachusetts Institute of Technology.},
	keywords = {article, Classification, entropy, methodology, Models, Theoretical, normal distribution, theoretical model},
	isbn = {08997667 (ISSN)},
	url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-33748288090\&partnerID=40\&md5=47b51b3d90bc273df156889a92fef01d},
	author = {Silva, L.M. and Felgueiras, C.S. and Alexandre, L.A. and Marques de S{\'a}, J.}
}
