An Incremental Clustered Gradient Method for Wireless Sensor Networks

Abstract

In wireless sensor networks, clustering is a very crucial problem. Basically clustering means grouping some specific objects based on their behavior and functionality. Clustering can be formulated for different optimization problems, such as nonsmooth, nonconvex problems. This paper is based on the review of the optimization algorithm that was proposed in the paper A Convergent Incremental Gradient Method With Constant Step Size by Blatt et al called Incremental Aggregate Gradient method. A novel algorithm called Incremental Clustered Aggregate Gradient Method was proposed in this paper to counter the shortcomings of the previous one. It has many similarities with the earlier method but it is more efficient for wireless sensor networks. The main aim of Incremental Gradient Method was to minimize the sum of continuously differentiable functions and also it required a single gradient evaluation per iteration and used a constant step size. For quadratic functions, a global linear rate of convergence was proved. It was claimed that it is more suitable for sensor networks. Although the experiments performed in this work confirm the convergence properties of it, it was found that it is not suitable for sensor networks. The proposed method addresses the flaws of the previous method as regards to sensor networks. When both algorithms operate with their respective optimal step sizes, they require approximately the same number of gradient evaluations for convergence.