Complex Correntropy: Probabilistic Interpretation and Optimization

TL;DR

This paper introduces a probabilistic interpretation of complex correntropy, develops a recursive optimization method, and demonstrates its advantages over traditional algorithms in complex data analysis.

Contribution

It provides the first theoretical analysis of complex correntropy and proposes a fixed point solution for the maximum complex correntropy criterion.

Findings

The proposed method outperforms complex RLS in system identification.

Probabilistic interpretation simplifies the application of correntropy to complex data.

The recursive solution is efficient and effective for non-Gaussian noise environments.

Abstract

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. This paper presents a probabilistic interpretation for correntropy using complex-valued data called complex correntropy. A recursive solution for the maximum complex correntropy criterion (MCCC) is introduced based on a fixed point solution. This technique is applied to a simple system identification case study, and the results demonstrate prominent advantages when 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. Keywords: complex-valued data correntropy, maximum complex correntropy criterion, fixed-point algorithm.