A Fractional Gradient Descent-Based RBF Neural Network

作者：Khan, Shujaat; Naseem, Imran^*; Malik, Muhammad Ammar; Togneri, Roberto; Bennamoun, Mohammed

来源：Circuits, Systems, and Signal Processing, 2018, 37(12): 5311-5332.

DOI：10.1007/s00034-018-0835-3

• Artificial neural networks
• Radial basis function
• Nonlinear system identification
• Time series prediction
• Kernel function
• Function approximation
• Fractional-order calculus
• modified Riemann-Liouville derivative
• Wiener solution

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.

• 出版日期2018-12