JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (9): 55-61.doi: 10.6040/j.issn.1671-9352.0.2017.606

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Design and approximation of SISO three layers feedforward neural network based on Bernstein polynomials

XIAO Wei-ming, WANG Gui-jun*   

  1. School of Mathematical Science, Tianjin Normal University, Tianjin 300387, China
  • Received:2017-11-24 Online:2018-09-20 Published:2018-09-10

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Abstract: A single input single output(SISO)three layers feedforward neural network was designed by using the difference value between adjacent equidistant subdivision points of unary Bernstein polynomial with a Sigmodial transfer function, and a method of selecting the connection weights and thresholds was given. In addition, according to the approximation theorem for unary Bernstein polynomial, we proved that SISO three layers feedforward neural network could also approximate a continuous function. The analytical expression of the neural network was obtained by an example.

Key words: equidistant subdivision, Bernstein polynomials, Sigmodial transfer function, feedforward neural network, approximation

CLC Number: 

  • TP183
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