Fractional Extreme Value Adaptive Training Method: Fractional Steepest Descent Approach

被引：106

作者：

Pu, Yi-Fei ^{[1
]}

Zhou, Ji-Liu ^{[1
]}

Zhang, Yi ^{[1
]}

Zhang, Ni ^{[2
]}

Huang, Guo ^{[3
]}

Siarry, Patrick ^{[4
]}

机构：

[1] Sichuan Univ, Sch Comp Sci & Technol, Chengdu 610065, Peoples R China

[2] Sichuan Univ, Lib, Chengdu 610065, Peoples R China

[3] Leshan Normal Univ, Coll Comp Sci & Technol, Leshan 614000, Peoples R China

[4] Univ Paris 12, F-94010 Creteil, France

来源：

IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS | 2015年 / 26卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Fractional calculus; fractional differential; fractional energy norm; fractional extreme point; fractional gradient; BROWNIAN-MOTION; CALCULUS; IMAGE;

D O I：

10.1109/TNNLS.2013.2286175

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

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.

引用

页码：653 / 662

页数：10

共 51 条

[1] SEQUENTIAL REGRESSION CONSIDERATIONS OF ADAPTIVE FILTERING [J].

AHMED, N ;

SOLDAN, DL ;

HUMMELS, DR ;

PARIKH, DD .

ELECTRONICS LETTERS, 1977, 13 (15) :446-447

[2]

ALEXANDER TS, 1986, ADAPTIVE SIGNAL PROC

[3]

[Anonymous], 2000, Applications of fractional calculus in physics

[4]

[Anonymous], 2002, Adaptive Filter Theory

[5]

[Anonymous], 2002, The Fractional Calculus: Theory and Applications of Differentiation and Integration to Aribitrary Order

[6]

[Anonymous], IDENTIFICATION SYSTE

[7] Fractional-order anisotropic diffusion for image denoising [J].

Bai, Jian ;

Feng, Xiang-Chu .

IEEE TRANSACTIONS ON IMAGE PROCESSING, 2007, 16 (10) :2492-2502

[8]

Belfiore M. G., 1988, ADAPTIVE FILTERS SIG

[9] CONVERGENCE PROPERTIES OF LMS ADAPTIVE ESTIMATORS WITH UNBOUNDED DEPENDENT INPUTS [J].

BITMEAD, RR .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1984, 29 (05) :477-479

[10] PERFORMANCE OF ADAPTIVE ESTIMATION ALGORITHMS IN DEPENDENT RANDOM-ENVIRONMENTS [J].

BITMEAD, RR ;

ANDERSON, BDO .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1980, 25 (04) :788-794

← 1 2 3 4 5 6 →