# Correntropy

From ITL Wiki

## Contents |

## Introduction

Correntropy is a nonlinear similarity measure between two random variables.

## History

The name *Correntropy* comes from *correlation* and *entropy*.

## Definition

There are several possible definitions depending on the interpretation which are not necessarily equivalent.
Let *X*,*Y* be two random variables.

### Ideal view

where δ is the Dirac delta distribution function.

### Similarity view

where κ is a non-negative definite function. It is not necessary that κ is shift invariant as in the ideal view case.

### Estimator view

where is the set of observations.

## Generalizations

### Centered correntropy

### Parametric correntropy

### Multidimensional correntropy

## References

- Santamaria, I.; Pokharel, P. & PrÃncipe, J. C. Generalized Correlation Function: Definition, Properties, and Application to Blind Equalization IEEE Transactions on Signal Processing, 2006, 54, 2187-2197
- Liu, W.; Pokharel, P. P. & PrÃncipe, J. C. Correntropy: Properties and Applications in Non-Gaussian Signal Processing IEEE Trans. on Signal Processing,