In this paper, we introduce a sparse variant of the Correntropy Kernel Learning (CKL) model for online system identification in the presence of outliers. The proposed Online Sparse CKL (OS-CKL) improves the original CKL in three important aspects. Firstly, it is modified to operate as a kernel adaptive filter, i.e. model-building is a continuous process and executed on-the-fly for each new incoming sample. Secondly, a sparsification procedure is used in order to build a parsimonious model with time. Finally, we reduce the computational complexity of the proposed algorithm with respect to CKL by computing inverse matrices recursively instead of in batch mode. We evaluate the proposed model using four benchmarking datasets, two synthetic and two related to process industry (CSTR and pH neutralization), for different levels of outlier contamination. The consistent results achieved by the proposed model reveal its ability to keep high predictive power under an online learning regime with a reduced dictionary size in comparison to several state-of-the-art alternatives.
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