Complex Correntropy: Definition, Properties and Applications
Correntropy, complex data, similarity measure
Recent studies have demonstrated that correntropy is an efficient tool for analyzing higher-order statistical moments in non-Gaussian noise environments. Although corren- tropy has been used with complex data, no theoretical study was pursued to elucidate its properties, nor how to best use it for optimization. By using a probabilistic inter- pretation, this work presents a novel similarity measure between two complex random variables, which is defined as complex correntropy. It’s properties are studied as well as a new recursive solution for the Maximum Complex Correntropy Criteria (MCCC) and two algorithms are derived, one based in the ascendent gradient and a second one on a fixed-point solution. Simulations were made in order to evaluate how the robust this new measure is to impulsive noise in different problems: liner system identification, chan- nel 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 clas- sical algorithms from the literature.