Dictionary adaptation for online prediction of time series data with kernels

During the last few years, kernel methods have been very useful to solve nonlinear identification problems. The main drawback of these methods resides in the fact that the number of elements of the kernel development, i.e., the size of the dictionary, increases with the number of input data, making the solution not suitable for online problems especially time series applications. Recently, Richard, Bermudez and Honeine investigated a method where the size of the dictionary is controlled by a coherence criterion. In this paper, we extend this method by adjusting the dictionary elements in order to reduce the residual error and/or the average size of the dictionary. The proposed method is implemented for time series prediction using the kernel-based affine projection algorithm.