



@article {3282,
	title = {Can artificial neural networks be used to predict the origin of ozone episodes?},
	journal = {Science of the Total Environment},
	volume = {488-489},
	year = {2014},
	note = {Export Date: 21 November 2014},
	month = {2014},
	pages = {197 - 207},
	abstract = {Tropospheric ozone is a secondary pollutant having a negative impact on health and environment. To control and minimize such impact the European Community established regulations to promote a clean air all over Europe. However, when an episode is related with natural mechanisms as Stratosphere-Troposphere Exchanges (STE), the benefits of an action plan to minimize precursor emissions are inefficient. Therefore, this work aims to develop a tool to identify the sources of ozone episodes in order to minimize misclassification and thus avoid the implementation of inappropriate air quality plans. For this purpose, an artificial neural network model - the Multilayer Perceptron - is used as a binary classifier of the source of an ozone episode. Long data series, between 2001 and 2010, considering the ozone precursors, 7Be activity and meteorological conditions were used. With this model, 2-7\% of a mean error was achieved, which is considered as a good generalization. Accuracy measures for imbalanced data are also discussed. The MCC values show a good performance of the model (0.65-0.92). Precision and F1-measure indicate that the model specifies a little better the rare class. Thus, the results demonstrate that such a tool can be used to help authorities in the management of ozone, namely when its thresholds are exceeded due natural causes, as the above mentioned STE. Therefore, the resources used to implement an action plan to minimize ozone precursors could be better managed avoiding the implementation of inappropriate measures. {\textcopyright} 2014 Elsevier B.V.},
	keywords = {artificial neural network, Classification, Human health, Ozone, Stratosphere, Troposphere},
	url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-84900308360\&partnerID=40\&md5=5bb79ec9cf75f45b1556274bf83ce812},
	author = {Fontes, T. and Silva, L.M. and Silva, M. P. and Barros, N. and Carvalho, A. C.}
}
@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.}
}
@article {2335,
	title = {Data classification with multilayer perceptrons using a generalized error function},
	journal = {Neural NetworksNeural Netw.},
	volume = {21},
	year = {2008},
	note = {Cited By (since 1996): 6Export Date: 21 November 2012Source: ScopusCODEN: NNETEdoi: 10.1016/j.neunet.2008.04.004PubMed ID: 18572384Language of Original Document: EnglishCorrespondence Address: Silva, L.M.; INEB-Instituto de Engenharia Biom{\'e}dica, Porto, Portugal; email: lmsilva@fe.up.ptReferences: Baum, E.B., Wilczek, F., Supervised learning of probability distributions by neural networks (1987) NIPS, pp. 52-61. , Anderson D.Z. (Ed), American Institute of Physics;Bishop, C., (1995) Neural networks for pattern recognition, , Oxford University Press; 
Blake, C., \& Merz, C. (1998). UCI repository of machine learning databases. University of California, Irvine, Dept. of Information and Computer SciencesForina, M., Armanino, C., Eigenvector projection and simplified non-linear mapping of fatty acid content of italian olive oils (1981) Annali di Chimica (Rome), 50, pp. 127-155; 
Gish, H. (1990). A probabilistic approach to the understanding and training of neural network classifiers. In Proceedings of the 1990 IEEE international conference on acoustics, speech, and signal processingHampshire, J., Waibel, A., A novel objective function for improved phoneme recognition using time-delay neural networks (1990) IEEE Transactions on Neural Networks, 1 (2), pp. 216-228; 
Hinton, G.E., Connectionist learning procedures (1989) Artificial Intelligence, 40 (1-3), pp. 185-234; 
Jacobs, R., Jordan, M., Nowlan, S., Hinton, G., Adaptive mixtures of local experts (1991) Neural Computation, 3, pp. 79-87; 
M{\o}ller, M. (1993). Efficient training of feed-forward neural networks. Ph.D. thesis. Computer Science Department - Aarhus UniversityMarques de S{\'a}, J., (2001) Pattern recognition: Concepts, methods and applications, , Springer Verlag; 
Matsuoka, K., \& Yi, J. (1991). Backpropagation based on the logarithmic error function and elimination of local minima. In Proceedings of the 1990 IEEE international joint conference on neural networksRichard, M., Lippmann, R., Neural network classifiers estimate bayesian a posteriori probabilities (1991) Neural Computation, 3, pp. 461-483; 
Santos, J., Alexandre, L., \& Marques~de S{\'a}, J. (2004). The error entropy minimization algorithm for neural network classification. In int. conf. on recent advances in soft computingSilva, L., Alexandre, L., Marques de S{\'a}, J., Neural network classification: Maximizing zero-error density (2005) LNCS, 3686, pp. 127-135. , ICAPR 2005; 
Silva, L., Alexandre, L.A., \& Marques~de S{\'a}, J. (2006). New developments of the Z-EDM algorithm. In Proceedings of the sixth international conference intelligent systems design and applications: Vol.~1 (pp. 1067-1072)Silva, L., Marques~de S{\'a}, J., \& Alexandre, L. (2005). Neural network classification using Shannon{\textquoteright}s entropy. In European symposium on artificial neural networksSilverman, B., (1986) Density estimation for statistics and data analysis, , Chapman \& Hall; 
Solla, S.A., Levin, E., Fleisher, M., Accelerated learning in layered neural networks (1988) Complex Systems, 2 (6), pp. 625-639
},
	month = {2008///},
	pages = {1302 - 1310},
	abstract = {The learning process of a multilayer perceptron requires the optimization of an error function E (y, t) comparing the predicted output, y, and the observed target, t. We review some usual error functions, analyze their mathematical properties for data classification purposes, and introduce a new one, E                        Exp, inspired by the Z-EDM algorithm that we have recently proposed. An important property of E
                        Exp is its ability to emulate the behavior of other error functions by the sole adjustment of a real-valued parameter. In other words, E
                        Exp is a sort of generalized error function embodying complementary features of other functions. The experimental results show that the flexibility of the new, generalized, error function allows one to obtain the best results achievable with the other functions with a performance improvement in some cases. {\textcopyright} 2008 Elsevier Ltd. All rights reserved.
},
	keywords = {algorithm, Algorithms, analytical error, article, calculation, Classification, Complementary features, Cybernetics, data analysis, Data classification, Data classifications, Data Interpretation, Statistical, Electric loads, entropy, Error functions, learning, Learning processes, mathematical analysis, Mathematical properties, Models, Statistical, Multilayer neural networks, Multilayer perceptron, Multilayer perceptrons, Multilayers, Neural networks, Neural Networks (Computer), Pattern recognition systems, perceptron, Performance improvements, priority journal, Probability density function},
	isbn = {08936080 (ISSN)},
	url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-54449100428\&partnerID=40\&md5=30f8de18c0272f4a440395045bd3c164},
	author = {Silva, L.M. and Marques de S{\'a}, J. and Alexandre, L.A.}
}
@book {2331,
	title = {The influence of the risk functional in data classification with MLPs},
	series = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)Lect. Notes Comput. Sci.},
	volume = {5163 LNCS},
	year = {2008},
	note = {Conference code: 73798Cited By (since 1996): 2Export Date: 21 November 2012Source: Scopusdoi: 10.1007/978-3-540-87536-9_20Language of Original Document: EnglishCorrespondence Address: Silva, L. M.; INEB -Instituto de Engenharia Biom{\'e}dica, Divis{\~a}o de Sinal e Imagem, Campus FEUP, Rua Dr. Roberto Frias, 4200 - 465 Porto, Portugal; email: lmsilva@fe.up.ptReferences: Silva, L.M., Alexandre, L.A., Marques de S{\'a}, J.: Data classification with multilayer perceptrons using a generalized error function. Neural Networks (2008) doi:10.1016/j.neunet.2008.04,004Erdogmus, D., Principe, J.C., Generalized information potential criterion for adaptive system training (2002) IEEE Transactions on Neural Networks, 13 (5), pp. 1035-1044;Erdogmus, D., Principe, 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; 
Santos, J.M., Alexandre, L.A., Marques de S{\'a}, J., The Error Entropy Minimization Algorithm for Neural Network Classification (2004) Int. Conf. on Recent Advances in Soft Computing, , Nottingham, United Kingdom; 
Duda, R., Hart, P., Stork, D., (2001) Pattern Classification, , Wiley-Interscience, Chichester; 
Newman, D., Hettich, S., Blake, C., Merz, C., (1998) UCI repository of machine learning databases; 
Baum, E.B., Haussler, D., What size net gives valid generalization? (1990) Neural Computation, 1 (1), pp. 151-160; 
Santos, J.M., Marques de S{\'a}, J., Alexandre, L.A., Neural Networks Trained with the EEM Algorithm: Tuning the Smoothing Parameter (2005) WSEAS Transactions on Systems, 4 (4), pp. 295-300; 
Marques de S{\'a}, J., (2007) Using SPSS, STATISTICA, MATLAB and R, , 2nd edn. Springer, Heidelberg; 
Embrechts, M.J., Szymanski, B., Sternickel, M., Introduction to Scientific Data Mining: Direct Kernel Methods and Applications (2004) Computationally Intelligent Hybrid Systems, pp. 317-363. , ch. 10, pp, Wiley Interscience, Chichester; 
Bennett, K.P., Embrechts, M.J., An Optimization Perspective on Kernel Partial Least Squares Regression (2003) Models and Applications. NATO Science Series, 3, pp. 227-249. , Advances in Learning Theory: Methods, 190, pp, IOS Press, Amsterdam; 
Suykens, J.A.K., Vandewalle, J., Least squares support vector machine classifiers (1999) Neural Processing Letters, 9 (3), pp. 293-300; 
Suykens, J.A.K., Gestel, T.V., Brabanter, J.D., Moor, B.D., Vandewalle, J., (2003) Least Squares Support Vector Machines, , World Scientific Pub. Co, Singapore; 
Keerthi, S.S., Shevade, S.K., SMO algorithm for least squares SVM formulations (2003) Neural Computation, 15, pp. 487-507; 
Cristianini, N., Shawe-Taylor, J., (2000) Support Vector Machines and Other KernelBased Learning Methods, , Cambridge University Press, Cambridge; 
Vapnik, V., (1998) Statistical Learning Theory, , Wiley-Interscience, Chichester; 
Sch{\"o}lkopf, B., Smola, A.J., (2002) Learning with Kernels, , MIT Press, Cambridge
},
	month = {2008///},
	pages = {185 - 194},
	address = {Prague},
	abstract = {We investigate the capability of multilayer perceptrons using specific risk functionals attaining the minimum probability of error (optimal performance) achievable by the class of mappings implemented by the multilayer perceptron (MLP). For that purpose we have carried out a large set of experiments using different risk functionals and datasets. The experiments were rigorously controlled so that any performance difference could only be attributed to the different risk functional being used. Statistical analysis was also conducted in a careful way. From the several conclusions that can be drawn from our experimental results it is worth to emphasize that a risk functional based on a specially tuned exponentially weighted distance attained the best performance in a large variety of datasets. As to the issue of attaining the minimum probability of error we also carried out classification experiments using non-MLP classifiers that implement complex mappings and are known to provide the best results until this date. These experiments have provided evidence that at least in many cases, by using an adequate risk functional, it will be possible to reach the optimal performance. {\textcopyright} Springer-Verlag Berlin Heidelberg 2008.},
	keywords = {Backpropagation, Complex mapping, Data classification, Data sets, Electric loads, Experiments, Functionals, Minimum probability of error, MLP classifiers, Multi layer perceptron, Multi-layer perceptrons, Multilayer neural networks, Multilayers, Optimal performance, Pattern recognition systems, Probability density function, risks, Statistical analysis, Weighted distance},
	isbn = {03029743 (ISSN); 3540875352 (ISBN); 9783540875352 (ISBN)},
	url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-58849129862\&partnerID=40\&md5=d9d0d90a540a21b191eebbf1956ed6e9},
	author = {Silva, L.M. and Embrechts, M. and Santos, J.M. and De S{\'a}, J.M.}
}
@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; 
Erdogmus, D., Principe, 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; 
Kapur, J., (1993) Maximum-entropy Models in Science and Engineering (Rev. Ed), , New York: Wiley; 
Kullback, S., (1959) Statistics and Information Theory, , New York: Wiley; 
Linsker, R., Self-organization in a perceptual network (1988) IEEE Computer, 21, pp. 105-117; 
Marques De Sa, J., (2001) Pattern Recognition: Concepts, Methods and Applications, , Berlin: Springer-Verlag; 
Newman, D., Hettich, S., Blake, C., Merz, C., (1998) UCI Repository of Machine Learning Databases, , http://www.ics.uci.edu/~mlearn/MLRepository.html, Irvine: University of California, Irvine, Department of Information and Computer Sciences; 
Parzen, E., On the estimation of a probability density function and the mode (1962) Annals of Mathematical Statistics, 33, pp. 1065-1076; 
Press, W., Teukolsky, S., Vetterling, W., Flannery, B., (1992) Numerical Recipes in C: The Art of Scientific Computing, , Cambridge: Cambridge University Press; 
Principe, J.C., Xu, D., Fisher, J., Information theoretic learning (2000) Unsupervised Adaptive Filtering, Vol. 1: Blind Source Separation, 1, pp. 265-319. , S. Haykin (Ed.), New York: Wiley; 
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; 
Silverman, B., (1986) Density Estimation for Statistics and Data Analysis, , London: Chapman \& Hall; 
Stoller, D., Univariate two-population distribution free discrimination (1954) Journal of the American Statistical Association, 49, pp. 770-777
},
	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.}
}
@conference {2389,
	title = {New developments of the Z-EDM algorithm},
	booktitle = {Proceedings - ISDA 2006: Sixth International Conference on Intelligent Systems Design and ApplicationsProc. ISDA Sixth Int. Conf. Intelligent Syst. Design Applic.},
	series = {ISDA 2006: Sixth International Conference on Intelligent Systems Design and Applications},
	volume = {1},
	year = {2006},
	note = {Conference code: 69992Cited By (since 1996): 2Export Date: 21 November 2012Source: ScopusArt. No.: 4021587doi: 10.1109/ISDA.2006.204Language of Original Document: EnglishCorrespondence Address: Silva, L.M.; INEB - Instituto de Engenharia Biom{\'e}dica, Porto, Portugal; email: lmsilva@fe.up.ptReferences: Bishop, C., (1995) Neural Networks for Pattern Recognition, , Oxford University Press;Blake, C., Merz, C., (1998) UCI Repository of machine learning databases University of California, , http://www.ics.uci.edu/~mlearn/MLRepository.html, Irvine, Dept. of Information and Computer Sciences; 
Erdogmus, D., Principe, 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; 
Forina, M., Armanino, C., Eigenvector projection and simplified non-linear mapping of fatty acid content of Italian olive oils (1981) Ann. Chim. (Rome), 50, pp. 127-155; 
Marques de S{\'a}, J., (2001) Pattern Recognition: Concepts, Methods and Applications, , Springer Verlag; 
J. Santos, L. Alexandre, and J. Marques de S{\'a}. The Error Entropy Minimization Algorithm for Neural Network Classification. In Int. Conf. on Recent Advances in Soft Computing, Nottingham, United Kingdom, 2004Silva, L., Alexandre, L., Marques de S{\'a}, J., Neural network classification: Maximizing zero-error density (2005) LNCS, 3686, pp. 127-135. , ICAPR 2005; 
Silva, L., Marques de S{\'a}, J., Alexandre, L., Neural Network Classification using Shannon{\textquoteright}s Entropy (2005) European Symposium on Artificial Neural Networks; 
Silverman, B., (1986) Density Estimation for Statistics and Data Analysis, , Chapman \& Hall
},
	month = {2006///},
	pages = {1067 - 1072},
	address = {Jinan},
	abstract = {In this paper we address some open questions on the recently proposed Zero-Error Density Maximization algorithm for MLP training. We propose a new version of the cost function that solves a training problem encountered in previous work and prove that the use of a nonparametric density estimator preserves the optimal solution. Some experiments are reported comparing this cost function to the usual mean-square error and cross entropy cost junctions. {\textcopyright} 2006 IEEE.},
	keywords = {Algorithms, Cost functions, Mean square error, MLP training, Nonparametric density estimators, Optimization, Personnel training, Problem solving, Zero-Error Density Maximization algorithm},
	isbn = {0769525288 (ISBN); 9780769525280 (ISBN)},
	url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-34547496988\&partnerID=40\&md5=65cadef393b0843f5b21f6534bc122ff},
	author = {Silva, L.M. and Marques de S{\'a}, J. and Alexandre, L.A.}
}
@conference {2442,
	title = {Neural network classification: Maximizing zero-error density},
	booktitle = {Lecture Notes in Computer ScienceLect. Notes Comput. Sci.},
	series = {Third International Conference on Advances in Patten Recognition, ICAPR 2005},
	volume = {3686},
	year = {2005},
	note = {Conference code: 65875Cited By (since 1996): 2Export Date: 21 November 2012Source: ScopusLanguage of Original Document: EnglishCorrespondence Address: Silva, L.M.; Instituto de Engenharia Biom{\'e}dica, Lab. de Sinai e Imagem Biom{\'e}dica, Campus da FEUP, Rua Dr. Roberto Frias, 4200 - 465 Porto, PortugalReferences: Erdogmus, D., Principe, 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., Principe, J., Generalized information potential criterion for adaptive system training (2002) IEEE Transactions on Neural Networks, 13 (5), pp. 1035~1044; 
Santos, J.M., Alexandre, L.A., Marques De S{\'a}, J., The error entropy minimization algorithm for neural network classification (2004) Int. Conf. on Recent Advances in Soft Computing, , Nottingham, United Kingdom; 
Santos, J.M., Alexandre, L.A., De Sa, J.M., 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, and O. Ersoy, editors, ASME Press Series; 
Silva, L.M., De Sa, J.M., Alexandre, L.A., Neural network classification using shannon{\textquoteright}s entropy (2005) European Symposium on Artificial Neural Networks; 
Jacobs, R., Jordan, M., Nowlan, S., Hinton, G., Adaptive mixtures of local experts (1991) Neural Computation, 3, pp. 79-87; 
Blake, C.L., Merz, C.J., (1998) UCI Repository of Machine Learning Databases, , http://www.ics.uci.edu/~mlearn/MLRepository.html, University of California, Irvine, Dept. of Information and Computer Sciences
},
	month = {2005///},
	pages = {127 - 135},
	address = {Bath},
	abstract = {We propose a new cost function for neural network classification: the error density at the origin. This method provides a simple objective function that can be easily plugged in the usual backpropagation algorithm, giving a simple and efficient learning scheme. Experimental work shows the effectiveness and superiority of the proposed method when compared to the usual mean square error criteria in four well known datasets. {\textcopyright} Springer-Verlag Berlin Heidelberg 2005.},
	keywords = {Algorithms, Backpropagation, Backpropagation algorithm, Classification (of information), Costs, Error analysis, Function evaluation, Learning systems, Mean square error, Neural network classification, Neural networks, Zero-error density},
	isbn = {03029743 (ISSN)},
	url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-27244450344\&partnerID=40\&md5=73ee3c0c073fb3bc7bc85013bf7dcce6},
	author = {Silva, L.M. and Alexandre, L.A. and De S{\'a}, J.M.},
	editor = {Singh S. and Singh M. and Apte C. and Perner P.}
}
