This letter focuses on the issue of whether risk functionals derived from information-theoretic principles, such as Shannon or Rényi'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.

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'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.