Estimating the Number of Hidden Neurons in Recurrent Neural Networks for Nonlinear System Identification

The problem of complexity is here addressed by defining an upper bound for the number of the hidden layer's neurons. This majorant is evaluated by applying a singular value decomposition to the contaminated oblique subspace projection of the row space of future outputs into the past inputs-outputs row space, along the future inputs row space. Full rank projections are dealt with by i) computing the number of dominant singular values, on the basis of a threshold related to the Euclidean norm of an artificial error matrix and ii) finding the argument of minimizing the singular value criterion. Results on a benchmark three-tank system demonstrate the effectiveness of the proposed methodology.