  The conventional Minimum Error Entropy criterion (MEE) has its limitations,
showing reduced sensitivity to error mean values and uncertainty regarding
error probability density function locations. To overcome this, a MEE with
fiducial points criterion (MEEF), was presented. However, the efficacy of the
MEEF is not consistent due to its reliance on a fixed Gaussian kernel. In this
paper, a generalized minimum error with fiducial points criterion (GMEEF) is
presented by adopting the Generalized Gaussian Density (GGD) function as
kernel. The GGD extends the Gaussian distribution by introducing a shape
parameter that provides more control over the tail behavior and peakedness. In
addition, due to the high computational complexity of GMEEF criterion, the
quantized idea is introduced to notably lower the computational load of the
GMEEF-type algorithm. Finally, the proposed criterions are introduced to the
domains of adaptive filter, kernel recursive algorithm, and multilayer
perceptron. Several numerical simulations, which contain system identification,
acoustic echo cancellation, times series prediction, and supervised
classification, indicate that the novel algorithms' performance performs
excellently.
