Error-adaptive modeling of streaming time-series data using radial basis functions

Abstract

Abstract We propose an error-adaptive method for constructing time-series models for novelty detection using radial basis functions. The optimization problem is implemented in an incremental, or online manner, and permits the balancing of the quality of the data fit and the sparsity of the model in the objective function of a linear program. The resulting algorithm is applied to several examples of streaming time-series data. Novel data points are identified using an infeasibility criterion while feasible data points are not used for training and may be discarded. In practice, only a small fraction of observed streaming data points are actually required to update the model. The sparsity promoting term in the objective function serves to determine the location and number of RBFs required to fit the data. Balancing sparsity with the accuracy of the model allows the user to adjust model complexity. It appears that the ability to adapt the error bound in the optimization problem may help to prevent over-fitting. We illustrate the approach with several examples and show that the fitting procedure is robust to additive Gaussian noise with non-stationary variance. We compare the proposed algorithm with several other methods in the literature, including both online and batch algorithms.