An Effective Adaptive Combination Strategy for Distributed Learning Network

Chundong Xu,Qinglin Li,Dongwen Ying

doi:10.3390/app11125723

Abstract

In this paper, we develop a modified adaptive combination strategy for the distributed estimation problem over diffusion networks. We still consider the online adaptive combiners estimation problem from the perspective of minimum variance unbiased estimation. In contrast with the classic adaptive combination strategy which exploits orthogonal projection technology, we formulate a non-constrained mean-square deviation (MSD) cost function by introducing Lagrange multipliers. Based on the Karush–Kuhn–Tucker (KKT) conditions, we derive the fixed-point iteration scheme of adaptive combiners. Illustrative simulations validate the improved transient and steady-state performance of the diffusion least-mean-square LMS algorithm incorporated with the proposed adaptive combination strategy.

Highlights

It is generally beneficial to exploit diffusion strategies for distributed parameter estimation issues over adaptive networks [1,2,3,4,5,6]
Many studies resort to the adaptive combination (AC) strategies [12,13,14,15,16,17,18], most of which are developed for the adapt--combine (ATC) diffusion LMS algorithm [1]
According to the fixed-point iteration methodology and KKT necessary conditions, we develop an effective adaptive combination strategy, which solely relies on the previous instantaneous intermediate weight estimates without resorting to the knowledge of measurement data and noises

Summary

Introduction

It is generally beneficial to exploit diffusion strategies for distributed parameter estimation issues over adaptive networks [1,2,3,4,5,6]. Each node of the network is allowed to receive the intermediate estimates from its neighboring nodes to improve the accuracy of its local estimate Such cooperation enables each node to leverage the spatial diversity of noise profile over the entire network. There have been several static combination rules [1,12], e.g., Metropolis rule, Laplacian rule, Uniform rule and Relative-degree rule These static combiners are designed based solely on the topology of network, so they would generally be unadjustable to adapt to the spatial variation of signal and noise statistics. A decoupled adapt--combine (D-ATC) algorithm is proposed, for, the least-squares (LS)-based AC scheme is developed [17,18], which could achieve rather approximate performance as the ATC algorithm with the classic AC in homogeneous networks

Motivation and Contribution

ATC Algorithm

Fixed-Point Iteration Solution

Mean Convergence

Simulation Results

Conclusions