  Some novel strategies have recently been proposed for single hidden layer
neural network training that set randomly the weights from input to hidden
layer, while weights from hidden to output layer are analytically determined by
pseudoinversion. These techniques are gaining popularity in spite of their
known numerical issues when singular and/or almost singular matrices are
involved. In this paper we discuss a critical use of Singular Value Analysis
for identification of these drawbacks and we propose an original use of
regularisation to determine the output weights, based on the concept of
critical hidden layer size. This approach also allows to limit the training
computational effort. Besides, we introduce a novel technique which relies an
effective determination of input weights to the hidden layer dimension. This
approach is tested for both regression and classification tasks, resulting in a
significant performance improvement with respect to alternative methods.
