Performance evaluation of the maximum complex correntropy criterion with adaptive kernel width update

Manoel B L Aquino,Allan M Martins,João P F Guimarães,Aluísio I R Fontes,Leandro L S Linhares

doi:10.1186/s13634-019-0652-2

Abstract

The complex correntropy is a recently defined similarity measure that extends the advantages of conventional correntropy to complex-valued data. As in the real-valued case, the maximum complex correntropy criterion (MCCC) employs a free parameter called kernel width, which affects the convergence rate, robustness, and steady-state performance of the method. However, determining the optimal value for such parameter is not always a trivial task. Within this context, several works have introduced adaptive kernel width algorithms to deal with this free parameter, but such solutions must be updated to manipulate complex-valued data. This work reviews and updates the most recent adaptive kernel width algorithms so that they become capable of dealing with complex-valued data using the complex correntropy. Besides that, a novel gradient-based solution is introduced to the Gaussian kernel and its respective convergence analysis. Simulations compare the performance of adaptive kernel width algorithms with different fixed kernel sizes in an impulsive noise environment. The results show that the iterative kernel adjustment improves the performance of the gradient solution for complex-valued data.

Highlights

The correntropy consists in a similarity measure based on Rényi entropy capable of extracting high-order statistical information from real-valued data [1]
The performance of the adaptive filters is evaluated by the weight signal-to-noise ratio (WSNR), which is defined as WSNRdb = 10 log10 w H w (w − wi)H (w − wi) where wis the correct weights, which are randomly select at each Monte Carlo trial from a Gaussian distribution with mean 0 and variance 1. wi is the complex weights computed by the aforementioned methods in the ith iteration
5 Conclusion This paper has proposed a novel gradient method employing the complex correntropy as a cost function based on the Wirtinger calculus

Summary

Introduction

The correntropy consists in a similarity measure based on Rényi entropy capable of extracting high-order statistical information from real-valued data [1]. This is why it has been widely used as a cost function in optimization problems such as adaptive filtering in an approach called maximum correntropy criterion (MCC), providing better performance than second-order methods in nonGaussian noise environments [2,3,4,5,6]. The correntropy concept has been extended to complex-valued random variables using the maximum complex correntropy criterion (MCCC)[7, 8] Both MCC and MCCC employ a free parameter called kernel width or kernel size. Since the task of obtaining an optimum value for this parameter is time consuming and not trivial, a series of adaptive kernel width algorithms has been proposed in order to choose a proper value for this parameter at each iteration in optimization problems

Methods

Results

Conclusion