Distributed Adaptive Learning with Multiple Kernels in Diffusion Networks

TL;DR

This paper introduces a distributed adaptive learning algorithm using multiple kernels and hyperslab projections, enabling efficient nonlinear function estimation across networks with proven convergence and improved performance.

Contribution

It presents a novel distributed learning scheme combining multiple kernels, hyperslab projections, and a modified consensus matrix for enhanced nonlinear function approximation.

Findings

Effective convergence demonstrated through theoretical analysis.

Reduced computational complexity with minimal performance loss.

Superior results compared to existing methods in synthetic and real data experiments.

Abstract

We propose an adaptive scheme for distributed learning of nonlinear functions by a network of nodes. The proposed algorithm consists of a local adaptation stage utilizing multiple kernels with projections onto hyperslabs and a diffusion stage to achieve consensus on the estimates over the whole network. Multiple kernels are incorporated to enhance the approximation of functions with several high and low frequency components common in practical scenarios. We provide a thorough convergence analysis of the proposed scheme based on the metric of the Cartesian product of multiple reproducing kernel Hilbert spaces. To this end, we introduce a modified consensus matrix considering this specific metric and prove its equivalence to the ordinary consensus matrix. Besides, the use of hyperslabs enables a significant reduction of the computational demand with only a minor loss in the performance. Numerical evaluations with synthetic and real data are conducted showing the efficacy of the proposed algorithm compared to the state of the art schemes.