Generalized Minimum Error with Fiducial Points Criterion for Robust Learning

TL;DR

This paper introduces a generalized minimum error criterion using the GGD kernel with fiducial points, improving robustness and computational efficiency in various adaptive learning tasks.

Contribution

It proposes GMEEF with GGD kernel and quantization to enhance robustness and reduce complexity in error-based learning algorithms.

Findings

Enhanced performance in system identification and echo cancellation

Reduced computational load with quantized GMEEF

Superior accuracy in classification and prediction tasks

Abstract

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.