A correntropy function based on coincidence detection

- Correntropy can be easily adapted to discrete or even categorical observations.
- Standard correntropy computation is done through soft collision detection.
- Hard collision detection allows for correntropy generalization.

This work presents a new generalized correlation function (correntropy) estimator based on collision entropy. Both the proposed approach and the standard correntropy estimator, published in 2006, can be regarded as coincidence counting methods, one using soft coincidence detection, whereas ours detects hard coincidences. Estimation experiments are performed over discrete, categorical and continuous signals. Despite its conceptual simplicity, the proposed method is qualitatively equivalent to the standard one, as highlighted by the last experiment. Furthermore, it has two potential advantages: providing estimates that are easier to interpret (coincidence rate instead of information potential); and meaningful dependence analysis for discrete/categorical data, cases where the standard method cannot be directly applied. Additionally, the importance of a proper coincidence definition for a meaningful signal analysis is illustrated through experiments.