A Fractional Gradient Descent-Based RBF Neural Network

Shujaat Khan, Imran Naseem, Muhammad Ammar Malik, Roberto Togneri, Mohammed Bennamoun

Research output: Contribution to journal › Article

4 Citations (Scopus)

Abstract

In this research, we propose a novel fractional gradient descent-based learning algorithm (FGD) for the radial basis function neural networks (RBF-NN). The proposed FGD is the convex combination of the conventional, and the modified Riemann–Liouville derivative-based fractional gradient descent methods. The proposed FGD method is analyzed for an optimal solution in a system identification problem, and a closed form Wiener solution of a least square problem is obtained. Using the FGD, the weight update rule for the proposed fractional RBF-NN (FRBF-NN) is derived. The proposed FRBF-NN method is shown to outperform the conventional RBF-NN on four major problems of estimation namely nonlinear system identification, pattern classification, time series prediction and function approximation.
Original languageEnglish
Pages (from-to)5311-5332
Number of pages22
JournalCircuits, Systems and Signal Processing
Volume37
Issue number12
Early online date19 May 2018
DOIs
Publication statusPublished - Dec 2018

Fingerprint

RBF Neural Network
Gradient Descent
Radial Basis Function Neural Network
Fractional
Neural networks
Identification (control systems)
Nonlinear System Identification
Gradient Descent Method
Time Series Prediction
Pattern Classification
Convex Combination
Least Squares Problem
Identification Problem
Function Approximation
System Identification
Learning algorithms
Pattern recognition
Nonlinear systems
Time series
Learning Algorithm

Cite this

Khan, Shujaat ; Naseem, Imran ; Malik, Muhammad Ammar ; Togneri, Roberto ; Bennamoun, Mohammed. / A Fractional Gradient Descent-Based RBF Neural Network. In: Circuits, Systems and Signal Processing. 2018 ; Vol. 37, No. 12. pp. 5311-5332.
@article{9f83085905f14626aaa76311665f4af4,
title = "A Fractional Gradient Descent-Based RBF Neural Network",
abstract = "In this research, we propose a novel fractional gradient descent-based learning algorithm (FGD) for the radial basis function neural networks (RBF-NN). The proposed FGD is the convex combination of the conventional, and the modified Riemann–Liouville derivative-based fractional gradient descent methods. The proposed FGD method is analyzed for an optimal solution in a system identification problem, and a closed form Wiener solution of a least square problem is obtained. Using the FGD, the weight update rule for the proposed fractional RBF-NN (FRBF-NN) is derived. The proposed FRBF-NN method is shown to outperform the conventional RBF-NN on four major problems of estimation namely nonlinear system identification, pattern classification, time series prediction and function approximation.",
author = "Shujaat Khan and Imran Naseem and Malik, {Muhammad Ammar} and Roberto Togneri and Mohammed Bennamoun",
year = "2018",
month = "12",
doi = "10.1007/s00034-018-0835-3",
language = "English",
volume = "37",
pages = "5311--5332",
journal = "Circuits, Systems and Signal Processing",
issn = "0278-081X",
publisher = "Springer",
number = "12",

}

Khan, S, Naseem, I, Malik, MA, Togneri, R & Bennamoun, M 2018, 'A Fractional Gradient Descent-Based RBF Neural Network' Circuits, Systems and Signal Processing, vol. 37, no. 12, pp. 5311-5332. https://doi.org/10.1007/s00034-018-0835-3

A Fractional Gradient Descent-Based RBF Neural Network. / Khan, Shujaat; Naseem, Imran; Malik, Muhammad Ammar; Togneri, Roberto; Bennamoun, Mohammed.

In: Circuits, Systems and Signal Processing, Vol. 37, No. 12, 12.2018, p. 5311-5332.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A Fractional Gradient Descent-Based RBF Neural Network

AU - Khan, Shujaat

AU - Naseem, Imran

AU - Malik, Muhammad Ammar

AU - Togneri, Roberto

AU - Bennamoun, Mohammed

PY - 2018/12

Y1 - 2018/12

N2 - In this research, we propose a novel fractional gradient descent-based learning algorithm (FGD) for the radial basis function neural networks (RBF-NN). The proposed FGD is the convex combination of the conventional, and the modified Riemann–Liouville derivative-based fractional gradient descent methods. The proposed FGD method is analyzed for an optimal solution in a system identification problem, and a closed form Wiener solution of a least square problem is obtained. Using the FGD, the weight update rule for the proposed fractional RBF-NN (FRBF-NN) is derived. The proposed FRBF-NN method is shown to outperform the conventional RBF-NN on four major problems of estimation namely nonlinear system identification, pattern classification, time series prediction and function approximation.

AB - In this research, we propose a novel fractional gradient descent-based learning algorithm (FGD) for the radial basis function neural networks (RBF-NN). The proposed FGD is the convex combination of the conventional, and the modified Riemann–Liouville derivative-based fractional gradient descent methods. The proposed FGD method is analyzed for an optimal solution in a system identification problem, and a closed form Wiener solution of a least square problem is obtained. Using the FGD, the weight update rule for the proposed fractional RBF-NN (FRBF-NN) is derived. The proposed FRBF-NN method is shown to outperform the conventional RBF-NN on four major problems of estimation namely nonlinear system identification, pattern classification, time series prediction and function approximation.

U2 - 10.1007/s00034-018-0835-3

DO - 10.1007/s00034-018-0835-3

M3 - Article

VL - 37

SP - 5311

EP - 5332

JO - Circuits, Systems and Signal Processing

JF - Circuits, Systems and Signal Processing

SN - 0278-081X

IS - 12

ER -

Khan S, Naseem I, Malik MA, Togneri R, Bennamoun M. A Fractional Gradient Descent-Based RBF Neural Network. Circuits, Systems and Signal Processing. 2018 Dec;37(12):5311-5332. https://doi.org/10.1007/s00034-018-0835-3

Access to Document