Performance Analysis of Fractional Learning Algorithms

TL;DR

This paper rigorously analyzes fractional learning algorithms in signal processing, revealing their strengths and weaknesses, and proposes remedies to improve their convergence and efficiency in stochastic environments.

Contribution

It provides the first comprehensive analysis of fractional LMS and steepest descent algorithms, identifying key issues and proposing solutions.

Findings

Identified critical issues in fractional learning algorithms.

Analyzed convergence behavior in stochastic environments.

Proposed remedies to enhance algorithm performance.

Abstract

Fractional learning algorithms are trending in signal processing and adaptive filtering recently. However, it is unclear whether the proclaimed superiority over conventional algorithms is well-grounded or is a myth as their performance has never been extensively analyzed. In this article, a rigorous analysis of fractional variants of the least mean squares and steepest descent algorithms is performed. Some critical schematic kinks in fractional learning algorithms are identified. Their origins and consequences on the performance of the learning algorithms are discussed and swift ready-witted remedies are proposed. Apposite numerical experiments are conducted to discuss the convergence and efficiency of the fractional learning algorithms in stochastic environments.