Probabilistic Interpretation for Correntropy with Complex Data

TL;DR

This paper introduces a probabilistic interpretation of correntropy for complex data, leading to a new recursive solution that enhances system identification and outperforms traditional methods like RLS.

Contribution

It presents the first generic form of complex correntropy and an analytical recursive solution for the maximum complex correntropy criterion, improving complex data analysis.

Findings

The proposed method outperforms complex RLS in system identification.

Complex correntropy provides a more straightforward approach for complex data analysis.

The recursive solution offers computational advantages in practical applications.

Abstract

Recent studies have demonstrated that correntropy is an efficient tool for analyzing higher-order statistical moments in nonGaussian noise environments. Although it has been used with complex data, some adaptations were then necessary without deriving a generic form so that similarities between complex random variables can be aggregated. This paper presents a novel probabilistic interpretation for correntropy using complex-valued data called complex correntropy. An analytical recursive solution for the maximum complex correntropy criterion (MCCC) is introduced as based on the fixedpoint solution. This technique is applied to a simple system identification case study, as the results demonstrate prominent advantages regarding the proposed cost function if compared to the complex recursive least squares (RLS) algorithm. By using such probabilistic interpretation, correntropy can be applied to solve several problems involving complex data in a more straightforward way.