A Diffusion Kernel LMS algorithm for nonlinear adaptive networks

TL;DR

This paper introduces a diffusion kernel LMS algorithm for nonlinear adaptive networks, enabling distributed learning with theoretical guarantees and superior performance over existing LMS variants.

Contribution

It proposes a novel diffusion-based KLMS algorithm with theoretical analysis and demonstrates its effectiveness through comparative experiments.

Findings

Algorithm achieves no regret bound under certain conditions.

Outperforms other LMS variants in experiments.

Provides theoretical analysis of convergence properties.

Abstract

This work presents a distributed algorithm for nonlinear adaptive learning. In particular, a set of nodes obtain measurements, sequentially one per time step, which are related via a nonlinear function; their goal is to collectively minimize a cost function by employing a diffusion based Kernel Least Mean Squares (KLMS). The algorithm follows the Adapt Then Combine mode of cooperation. Moreover, the theoretical properties of the algorithm are studied and it is proved that under certain assumptions the algorithm suffers a no regret bound. Finally, comparative experiments verify that the proposed scheme outperforms other variants of the LMS.