Complex Correntropy: Probabilistic Interpretation and Application to Complex-Valued Data

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 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. A new recursive solution for the maximum complex correntropy criterion is introduced based on a fixed-point solution. This technique is applied to a system identification, and the results demonstrate prominent advantages when compared against three other algorithms: the complex least mean square, complex recursive least squares, and least absolute deviation. By the aforementioned probabilistic interpretation, correntropy can now be applied to solve several problems involving complex data in a more straightforward way.