Fractional Extreme Value Adaptive Training Method: Fractional Steepest Descent Approach

Author

Yi-Fei Pu ; Ji-Liu Zhou ; Yi Zhang ; Ni Zhang ; Guo Huang ; Siarry, Patrick

Author_Institution

Sch. of Comput. Sci. & Technol., Sichuan Univ., Chengdu, China

Volume

26

Issue

4

fYear

2015

fDate

Apr-15

Firstpage

653

Lastpage

662

Abstract

The application of fractional calculus to signal processing and adaptive learning is an emerging area of research. A novel fractional adaptive learning approach that utilizes fractional calculus is presented in this paper. In particular, a fractional steepest descent approach is proposed. A fractional quadratic energy norm is studied, and the stability and convergence of our proposed method are analyzed in detail. The fractional steepest descent approach is implemented numerically and its stability is analyzed experimentally.

Keywords

gradient methods; signal processing; adaptive learning; fractional calculus; fractional extreme value adaptive training method; fractional quadratic energy norm; fractional steepest descent approach; signal processing; Adaptive control; Convergence; Equations; Fractional calculus; Signal processing algorithms; Training; Fractional calculus; fractional differential; fractional energy norm; fractional extreme point; fractional gradient; fractional gradient.;

fLanguage

English

Journal_Title

Neural Networks and Learning Systems, IEEE Transactions on

Publisher

ieee

ISSN

2162-237X

Type

jour

DOI

10.1109/TNNLS.2013.2286175

Filename

6650068