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 modes 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.

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.