LAUSR

Kernel adaptive filtering (KAF) has gained widespread popularity among the machine learning community for online applications due to its convexity, simplicity, and universal approximation ability. However, the network generated by KAF keeps growing with the accumulation of the training samples, which leads to the increasing memory requirement and computational burden. To address this issue, a pruning approach that attempts to restrict the network size to a fixed value is incorporated into a kernel recursive least squares (KRLS) algorithm, yielding a novel KAF algorithm called parsimonious KRLS (PKRLS). The basic idea of the pruning technique is to remove the center with the least importance from the existing dictionary. The importance of a center is quantified by its contribution to minimizing the cost function. The calculation of the importance measure is formulated in an efficient manner, which facilitates its implementation in online settings. Experimental results on the benchmark tasks show that PKRLS obtains a parsimonious network structure with the satisfactory prediction accuracy. Finally, a multi-sensor health diagnosis approach based on PKRLS is developed for identifying the health state of a degraded aero-engine in real time. A case study in a turbofan engine degradation data set demonstrates that PKRLS provides an effective and efficient candidate for modeling the performance deterioration of real complex systems.