Performance Analysis of Fractional Learning Algorithms

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.

arXiv comment29 pages, 6 figures

References in corpus (5)

• Geometric and Physical Interpretation of Fractional Integration and Fractional Differentiation
• Design of generalized fractional order gradient descent method
• Lyapunov functions for nabla discrete fractional order systems
• Convolutional neural networks with fractional order gradient method
• Towards a geometric interpretation of generalized fractional integrals - Erdelyi-Kober type integrals on $R^N$ as an example