Fixed-Point Minimum Error Entropy With Fiducial Points

Compared with traditional learning criteria, such as minimum mean square error (MMSE), the minimum error entropy (MEE) criterion has received increasing attention in the domains of nonlinear and non-Gaussian signal processing and machine learning. Since the MEE criterion is shift-invariant, one has to add a bias to achieve zero-mean error over training datasets. Thus, a modification of the MEE called minimization of error entropy with fiducial points (MEEF) was proposed, which controls the bias for MEE in a more elegant and efficient way. In the present paper, we propose a fixed-point minimization of error entropy with fiducial points (MEEF-FP) as an alternative to the gradient based MEEF for training a linear-in-parameters (LIP) model because of its fast convergence speed, robustness and step-size free. Also, we provide a sufficient condition that guarantees the convergence of the MEEF-FP algorithm. Moreover, we develop a recursive MEEF-FP (RMEEF-FP) for online adaptive learning with low-complexity. Finally, illustrative examples are presented to show the excellent performance of the new methods.