# Generalized Correntropy for Robust Adaptive Filtering

arXiv: https://arxiv.org/abs/1504.02931 · HTML: https://mlsanity.com/paper/1504.02931/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Apr 2015.

## Built on by (most cited first, 10 of 10)

- [Adaptive sparseness for correntropy-based robust regression via automatic relevance determination](https://mlsanity.com/paper/2302.00082/) (2023)
- [Error Loss Networks](https://mlsanity.com/paper/2106.03722/) (2021)
- [Study of Proximal Normalized Subband Adaptive Algorithm for Acoustic Echo Cancellation](https://mlsanity.com/paper/2108.10219/) (2021)
- [Study of Robust Sparsity-Aware RLS algorithms with Jointly-Optimized Parameters for Impulsive Noise Environments](https://mlsanity.com/paper/2204.08990/) (2022)
- [Study of General Robust Subband Adaptive Filtering](https://mlsanity.com/paper/2208.08856/) (2022)
- [Quantized criterion-based kernel recursive least squares adaptive filtering for time series prediction](https://mlsanity.com/paper/2307.01442/) (2023)
- [Deep Learning Evidence for Global Optimality of Gerver's Sofa](https://mlsanity.com/paper/2407.11106/) (2024)
- [Low-Communication Resilient Distributed Estimation Algorithm Based on Memory Mechanism](https://mlsanity.com/paper/2508.02705/) (2025)
- [Deep Neural Network-Driven Adaptive Filtering](https://mlsanity.com/paper/2508.04258/) (2025)
- [Structured Adaptive Tensor Prediction for Streaming Data](https://mlsanity.com/paper/2606.10085/) (2026)

## Abstract (arXiv)

As a robust nonlinear similarity measure in kernel space, correntropy has received increasing attention in domains of machine learning and signal processing. In particular, the maximum correntropy criterion (MCC) has recently been successfully applied in robust regression and filtering. The default kernel function in correntropy is the Gaussian kernel, which is, of course, not always the best choice. In this work, we propose a generalized correntropy that adopts the generalized Gaussian density (GGD) function as the kernel (not necessarily a Mercer kernel), and present some important properties. We further propose the generalized maximum correntropy criterion (GMCC), and apply it to adaptive filtering. An adaptive algorithm, called the GMCC algorithm, is derived, and the mean square convergence performance is studied. We show that the proposed algorithm is very stable and can achieve zero probability of divergence (POD). Simulation results confirm the theoretical expectations and demonstrate the desirable performance of the new algorithm.