Fast adaptive gradient RBF networks for online learning of nonstationary time series

For a learning model to be effective in online modeling of nonstationary data, it must not only be equipped with high adaptability to track the changing data dynamics but also maintain low complexity to meet online computational restrictions. Based on these two important principles, in this paper, we propose a fast adaptive gradient radial basis function (GRBF) network for nonlinear and nonstationary time series prediction. Specifically, an initial compact GRBF model is constructed on the training data using the orthogonal least squares algorithm, which is capable of modeling variations of local mean and trend in the signal well. During the online operation, when the current model does not perform well, the worst performing GRBF node is replaced by a new node, whose structure is optimized to fit the current data. Owing to the local one-step predictor property of GRBF node, this adaptive node replacement can be done very efficiently. Experiments involving two chaotic time series and two real-world signals are used to demonstrate the superior online prediction performance of the proposed fast adaptive GRBF algorithm over a range of benchmark schemes, in terms of prediction accuracy and real-time computational complexity