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Interpolation neural network constructed by the step path and its approximation performance

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Abstract

Traditional neural network is a nonlinear dynamic system formed by a large number of neurons connected to each other, it can be widely used in many research fields, such as data mining, system identification and intelligent control. The neural networks can not only deal with data problems through the unique thinking of the human brain, but can also solve the multi input and multi output problem which is difficult to be completed by the traditional computer. In this paper, in the sense of an equidistance dissection of two-dimensional input space, some new connection weights and thresholds are determined by the interpolations and arithmetic mean values of some data pairs at the adjacent intersecting points, respectively, and a new forward interpolation neural network is constructed by a step path of two-dimensional dissection. Secondly, it is proved that the interpolation neural network can approximate to a continuous function by using characteristic properties of a Sigmoidal activation function. Finally, the approximation performance of the constructed network is tested in the light of the t- hypothesis test method in statistical inference, and the approximation errors of the interpolation network are compared with that of another polynomial neural network.

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Funding

This work has been supported by National Natural Science Foundation of China (Grant No. 61374009).

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Authors and Affiliations

  1. School of Mathematical Science, Tianjin Normal University, Tianjin, 300387, China

    Guijun Wang & Weiming Xiao

  2. School of Mathematics, Tonghua Normal University, Tonghua, Jilin, 134002, China

    Yujie Tao

Authors
  1. Guijun Wang
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  2. Weiming Xiao
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  3. Yujie Tao
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Correspondence to Yujie Tao.

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Wang, G., Xiao, W. & Tao, Y. Interpolation neural network constructed by the step path and its approximation performance. Cluster Comput 24, 1397–1411 (2021). https://doi.org/10.1007/s10586-020-03197-w

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  • DOI: https://doi.org/10.1007/s10586-020-03197-w

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