An optimum weight initialization which strongly improves the performance of the back propagation (BP) algorithm is suggested. By statistical analysis, the scale factor, R (which is proportional to the maximum magnitude of the weights), is obtained as a function of the paralyzed neuron percentage (PNP). Also, by computer simulation, the performances on the convergence speed have been related to PNP. An optimum range for R is shown to exist in order to minimize the time needed to reach the minimum of the cost function. Normalization factors are properly defined, which leads to a distribution of the activations independent of the neurons, and to a single nondimensional quantity, R, the value of which can be quickly found by computer simulation.

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Incremental neural networks have received increasing interest in the neural

In the work presented in this paper, an Interval Arithmetic Perceptron (IAP) is used to detect the region in the input space to which an uncertainty decision should be appropriately associated. This region may be originated both by sub-regions which are not represented in the training set, and by subregions where the probabilities of the two classes are very similar. To train the IAP, an algorithm will be presented which in particular is able detect the two certainty regions and the uncertainty one. From the interval weights thus obtained, a confidence interval of the probability will also be evaluated. The algorithm has been used for studying a simple artificial problem and two real-world applications, the Iris and Breast Cancer databases. Regarding the latter application in particular, a statistical analysis of the results is presented, together with a discussion of the possible alternative classifications of the patterns attributed to the uncertainty region.