Correntropia complexa: definição, propriedades e aplicações

Abstract

Recent studies have demonstrated that correntropy is an efficient tool for analyzing higher-order statistical moments in non-Gaussian noise environments. Although correntropy has been used with complex-valued data, no theoretical study was pursued to elucidate its properties, nor how to best use it for optimization. By using a probabilistic interpretation, this work presents a novel similarity measure between two complex-valued random variables, which is defined as complex correntropy. Its properties are studied as well as a new recursive solution for the Maximum Complex Correntropy Criterion (MCCC) and two algorithms are derived, one based on the ascendent gradient and a second one on a fixed-point solution. Simulations were made in order to evaluate how robust this new measure is to impulsive noise in different problems: liner system identification, channel equalization and in a compressive sensing problem. It is also shown the application of complex correntropy as a tool to analyse the similarity between angles. The results demonstrate prominent advantages of the proposed method when compared with the classical algorithms in the literature.