Adaptive Filters With Robust Augmented Space Linear Model: A Weighted $k$-NN Method

Abstract

As a new member of convex universal learning machines (CULMs), an augmented space linear model (ASLM) demonstrates strong learning and tracking capabilities in the fields of signal process and machine learning. Unfortunately, the ASLM is only suitable for offline learning, and its estimated accuracy and noise immunity highly depend on the estimated error learned from a generated error table. To address these two issues and apply ASLM into adaptive filtering, online ASLM algorithms with a weighted k nearest neighbor (k-NN) method, based on an updated orthogonal error table, are therefore proposed in this paper. To further improve the robustness of ASLM to heavy-tail noises, a robust ASLM (RASLM) algorithm is proposed with the help of kernel function, and thus a novel robust adaptive filtering algorithm named maximum correntropy criterion RASLM (MCC-RASLM) is developed based the maximum correntropy criterion. However, the linear growth error table existing in MCC-RASLM incurs an ever-growing computational burden. Therefore, to reduce the computational complexity of MCC-RASLM, another novel online variable-centroid clustering is proposed to generate a maximum correntropy criterion cluster RASLM (MCC-C-RASLM) algorithm. Finally, the theoretical analyses regarding robustness and the error bound of RASLM with weighted k-NN regression are performed to verify the effectiveness of MCC-RASLM. Simulation results based on synthetic and real-world data validate the superiorities of the proposed algorithms from aspects of filtering accuracy and robustness.