Generalized minimum error entropy for robust learning

The applications of error entropy (EE) are sometimes limited because its shape cannot be flexibly adjusted by the default Gaussian kernel function to adapt to noise variation and thus lowers the performance of algorithms based on minimum error entropy (MEE) criterion. In this paper, a generalized EE (GEE) is proposed by introducing the generalized Gaussian density (GGD) as its kernel function to improve the robustness of EE. In addition, GEE can be further improved to reduce its computational load by the quantized GEE (QGEE). Furthermore, two learning criteria, called generalized minimum error entropy (GMEE) and quantized generalized minimum error entropy (QGMEE), are developed based on GEE and QGEE, and new adaptive filtering (AF), kernel recursive least squares (KRLS), and multilayer perceptron (MLP) based on the proposed criteria are presented. Several numerical simulations indicate that the performance of proposed algorithms performs better than that of algorithms based on MEE.