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Adaptive radial basis function networks with kernel shape parameters

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Abstract

Radial basis function network (RBFN), commonly used in the classification applications, has two parameters, kernel center and radius that can be determined by unsupervised or supervised learning. But it has a disadvantage that it considers that all the independent variables have the equal weights. In that case, the contour lines of the kernel function are circular, but in fact, the influence of each independent variable on the model is so different that it is more reasonable if the contour lines are oval. To overcome this disadvantage, this paper presents an adaptive radial basis function network (ARBFN) with kernel shape parameters and derives the learning rules from supervised learning. To verify that this architecture is superior to that of the traditional RBFN, we make a comparison between three artificial and fifteen real examples in this study. The results show that ARBFN is much more accurate than the traditional RBFN, illustrating that the shape parameters can actually improve the accuracy of RBFN.

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Abbreviations

C :

Center of kernel of Gaussian unit

E :

Error function (Energy function)

f :

Transfer function

f′:

Differential of transfer function

h :

Output of the hidden unit

net:

Net of the processing unit

N :

Number of the processing unit

Q :

Reciprocal of the kernel radius of Gaussian unit

t :

Target output of output unit

V :

Weight of input variables in Gaussian unit

W :

Connection weight from Gaussian unit to the output unit

x :

Input

y :

Inference output of the output unit

δ :

Gap between the target output and the inference output

Δ(•):

Modification of parameter

η :

Learning rate

i :

Processing unit of input layer

j :

Processing unit of output layer

k :

Processing unit of hidden layer

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Authors and Affiliations

  1. Department of Information Management, Chung Hua University, Hsinchu City, Taiwan

    I-Cheng Yeh & Chung-Chih Chen

  2. Department of Management Science and Engineering in School of Economy and Management, Harbin Institute of Technology, Harbin, China

    Xinying Zhang & Chong Wu

  3. Department of Computer Science and Information Engineering, National Cheng-Kung University, Tainan City, Taiwan

    Kuan-Chieh Huang

Authors
  1. I-Cheng Yeh
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  2. Chung-Chih Chen
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  3. Xinying Zhang
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  4. Chong Wu
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  5. Kuan-Chieh Huang
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Correspondence to I-Cheng Yeh.

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Yeh, IC., Chen, CC., Zhang, X. et al. Adaptive radial basis function networks with kernel shape parameters. Neural Comput & Applic 21, 469–480 (2012). https://doi.org/10.1007/s00521-010-0485-2

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