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Error Estimate for Spherical Neural Networks Interpolation

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Abstract

We present a type of spherical neural network (SNN) with bounded sigmoidal activation function and study its interpolation capability. We find that the provided SNN can exactly interpolate the training samples. Furthermore, based on the special structure of the presented SNN, we can bound the interpolation error by the modulus of smoothness of the target function, which is different from the previous results on the spherical scattered data interpolation problem.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Wenzhou University, Wenzhou, 325035, Zhejiang, People’s Republic of China

    Shaobo Lin

  2. School of Mathematics and Statistics, Institute for Information and System Sciences, Xi’an Jiaotong University, Xi’an, 710049, Shaanxi, People’s Republic of China

    Shaobo Lin, Jinshan Zeng & Zongben Xu

Authors
  1. Shaobo Lin
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  2. Jinshan Zeng
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  3. Zongben Xu
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Corresponding author

Correspondence to Shaobo Lin.

Additional information

The research was supported by the National 973 Programming (2013CB329404), and the Key Program of National Natural Science Foundation of China (Grant No. 11131006).

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Lin, S., Zeng, J. & Xu, Z. Error Estimate for Spherical Neural Networks Interpolation. Neural Process Lett 42, 369–379 (2015). https://doi.org/10.1007/s11063-014-9361-x

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  • DOI: https://doi.org/10.1007/s11063-014-9361-x

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