Learning Algorithm of Neural Networks on Spherical Cap

This paper investigates the learning algorithm of neural network on the spherical cap. Firstly, we construct the inner weights and biases from sample data, such that the network has the interpolation property on the sampling points. Secondly, we construct the BP network and BP learning algorithm. Finally, we analyze the generalization ability for the constructed networks and give the numerical experiments

[1]  Renato Spigler,et al.  Multivariate neural network operators with sigmoidal activation functions , 2013, Neural Networks.

[2]  M. Urner.  Scattered Data Approximation , 2016 .

[3]  Zongben Xu,et al.  The estimate for approximation error of neural networks: A constructive approach , 2008, Neurocomputing.

[4]  Feilong Cao,et al.  The estimate for approximation error of spherical neural networks , 2011 .

[5]  Feilong Cao,et al.  The approximation operators with sigmoidal functions , 2009, Comput. Math. Appl..

[6]  Xuli Han,et al.  Constructive Approximation to Multivariate Function by Decay RBF Neural Network , 2010, IEEE Transactions on Neural Networks.

[7]  Feilong Cao,et al.  The essential rate of approximation for radial function manifold , 2011 .

[8]  Feilong Cao,et al.  The capability of approximation for neural networks interpolant on the sphere , 2010 .

[9]  Chen Debao.  Degree of approximation by superpositions of a sigmoidal function , 1993, Approximation Theory and its Applications.

[10]  Ken-ichi Funahashi,et al.  On the approximate realization of continuous mappings by neural networks , 1989, Neural Networks.

[11]  George A. Anastassiou,et al.  Multivariate sigmoidal neural network approximation , 2011, Neural Networks.

[12]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1989, Math. Control. Signals Syst..

[13]  Andrew R. Barron,et al.  Universal approximation bounds for superpositions of a sigmoidal function , 1993, IEEE Trans. Inf. Theory.

[14]  Philip Crotwell.  Constructive Approximation on the Sphere , 2000 .

[15]  Hrushikesh Narhar Mhaskar,et al.  Approximation properties of zonal function networks using scattered data on the sphere , 1999, Adv. Comput. Math..

[16]  Renato Spigler,et al.  Convergence of a family of neural network operators of the Kantorovich type , 2014, J. Approx. Theory.

[17]  Hong Chen,et al.  Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems , 1995, IEEE Trans. Neural Networks.

[18]  Zongben Xu,et al.  Essential rate for approximation by spherical neural networks , 2011, Neural Networks.