



@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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Santos, J., Alexandre, L., Marques De S{\'a}, J., The error entropy minimization algorithm for neural network classification (2004) Int. Conf. on Recent Advances in Soft Computing, , Nottingham, U.K.: Nottingham Trent University; 
Santos, J., Marques De Sa, J., Alexandre, L., 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. Dagli, A. Buczak, D. Enke, M. Embrechts, \& O. Ersoy (Eds.), New York: American Society of Mechanical Engineers; 
Shannon, C.E., A mathematical theory of communication (1948) Bell System Technical Journal, 27, pp. 379-423; 
Silva, L., Marques De Sa, J., Alexandre, L., Neural network classification using Shannon{\textquoteright}s entropy (2005) European Symposium on Artificial Neural Networks, , Bruges, Belgium: d-side publications; 
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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.}
}
@article {2590,
	title = {Classification of foetal heart rate sequences based on fractal features},
	journal = {Medical and Biological Engineering and ComputingMed. Biol. Eng. Comput.},
	volume = {36},
	year = {1998},
	note = {Cited By (since 1996): 13Export Date: 21 November 2012Source: ScopusCODEN: MBECDdoi: 10.1007/BF02510743PubMed ID: 9684460Language of Original Document: EnglishCorrespondence Address: Felguiras, C.S.; Instituto de Engenharia Biomedica, Praca Coronel Pacheco 1, 4050 Porto, PortugalReferences: Bernardes, J., (1993) Leitura Automatizada Do Cardiotocograma. Desenvolvimento e Availia{\c c}{\`a}o, , Ph.D. thesis, Faculdade de Medicina da Universidade do Porto, Portugal;Bernardes, J., Moura, C., Marques De S{\'a}, J.P., Pereira Leite, L., Van Geijn, H.P., The Porto system (1994) A Critical Appraisal of Foetal Surveillance, pp. 315-324. , VAN GEIJN H. P. and COPRAY, F. J. A. (Eds.) Elsevier Science, Amsterdam; 
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Marques De Sa, J.P., Moura, A.C., Bernardes, J., Pereira Leite, L., An{\'a}lise autom{\'a}tica de sinais cardiotocogr{\'a}ficos (1992) Acta M{\'e}dica Portuguesa 11 S{\'e}rie, 5 (1), pp. 28-30; 
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Schulman, H., Schulman, S., Lai, P., Schneider, E., Farmakides, G., Dawes, G., Antepartum computerized foetal heart rate, chaos analysis, blood gases and perinatal outcome (1994) J. Maternal-Fetal Invest., 4, pp. 59-63
},
	month = {1998///},
	pages = {197 - 201},
	publisher = {Peter Peregrinus Ltd},
	abstract = {Visual inspection of foetal heart rate (FHR) sequences is an important means of foetal well-being evaluation. The application of fractal features for classifying physiologically relevant FHR sequence patterns is reported. The use of fractal features is motivated by the difficulties exhibited by traditional classification schemes to discriminate some classes of FHR sequence and by the recognition that this type of signal exhibits features on different scales of observation, just as fractal signals do. To characterise the signals by fractal features, two approaches are taken. The first models the FHR sequences as temporal fractals. The second uses techniques from the chaos-theory field and aims to model the attractor based on FHR sequences. The fractal features determined by both approaches are used to design a Bayesian classification scheme. Classification results for three classes are presented; they are quite satisfactory and illustrate the importance of this type of methodology.Visual inspection of foetal heart rate (FHR) sequences is an important means of foetal well-being evaluation. The application of fractal features for classifying physiologically relevant FHR sequence patterns is reported. The use of fractal features is motivated by the difficulties exhibited by traditional classification schemes to discriminate some classes of FHR sequence and by the recognition that this type of signal exhibits features on different scales of observation, just as fractal signals do. To characterise the signals by fractal features, two approaches are taken. The first models the FHR sequences as temporal fractals. The second uses techniques from the chaos-theory field and aims to model the attractor based on FHR sequences. The fractal features determined by both approaches are used to design a Bayesian classification scheme. Classification results for three classes are presented; they are quite satisfactory and illustrate the importance of this type of methodology.
},
	keywords = {article, Bayes Theorem, Cardiology, Chaos techniques, Chaos theory, Classification, Computer aided analysis, Computer simulation, Electrocardiography, Female, Fetal monitoring, fetus, fetus heart rate, FHR classification, FHR sequence, Foetal heart rate sequences, fractal analysis, Fractal features, Fractals, Heart Rate, Fetal, human, Humans, Pattern recognition, Pregnancy, Signal Processing, Computer-Assisted, technique},
	isbn = {01400118 (ISSN)},
	url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-0032033010\&partnerID=40\&md5=563144fcdb064dd777002155aaa62f73},
	author = {Felgueiras, C.S. and De Marques S{\'a}, J.P. and Bernardes, J. and Gama, S.}
}
