Complex Correntropy: A similarity measure between complex random variables
Correntropy, complex data, similarity measure
Recent studies have demonstrated that correntropy is an efficient tool for analyzing higher-order statistical moments in nonGaussian noise environments. Although correntropy 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 interpretation, 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 criterion (MCCC) is introduced based on a fixed-point (FP) solution. This technique is applied to a system identification
and also in a channel equalization problem. The results demonstrate prominent advantages when compared against three other algorithms: the complex least mean square (CLMS), complex recursive least squares (RLS) and least absolute deviation (LAD) in both scenarios. By the aforementioned probabilistic interpretation, correntropy can now be applied to solve several problems involving complex data in a more straightforward way.
Keywords: Correntropy, complex-valued data, Similarity measure