A rapid supervised learning neural network for function interpolation and approximation

This paper presents a neural-network architecture and an instant learning algorithm that rapidly decides the weights of the designed single-hidden layer neural network. For an n-dimensional N-pattern training set, with a constant bias, a maximum of N-r-1 hidden nodes is required to learn the mapping within a given precision (where r is the rank, usually the dimension, of the input patterns). For off-line training, the proposed network and algorithm is able to achieve "one-shot" training as opposed to most iterative training algorithms in the literature. An online training algorithm is also presented. Similar to most of the backpropagation type of learning algorithms, the given algorithm also interpolates the training data. To eliminate outlier data which may appear in some erroneous training data, a robust weighted least squares method is proposed. The robust weighted least squares learning algorithm can eliminate outlier samples and the algorithm approximates the training data rather than interpolates them. The advantage of the designed network architecture is also mathematically proved. Several experiments show very promising results.