Learning from data streams using kernel least-mean-square with multiple kernel-sizes and adaptive step-size

Abstract

A learning task is sequential if its data samples become available over time; kernel adaptive filters (KAFs) are sequential learning algorithms. There are three main challenges in KAFs: (1) selection of an appropriate Mercer kernel; (2) the lack of an effective method to determine kernel-sizes in an online learning context; (3) how to tune the step-size parameter. This work introduces a framework for online prediction that addresses the latter two of these open challenges. The kernel-sizes, unlike traditional KAF formulations, are both created and updated in an online sequential way. Further, to improve convergence time, we propose an adaptive step-size strategy that minimizes the mean-square-error (MSE) using a stochastic gradient algorithm. The proposed framework has been tested on three real-world data sets; results show both faster convergence to relatively low values of MSE and better accuracy when compared with KAF-based methods, long short-term memory, and recurrent neural networks.