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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 64
Edited by: B.H.V. Topping
Paper I.9

The Scattered Data Interpolation Procedure based on a Counterpropagation Neural Network

S. Lukaszyk

Institute of Computer Methods in Civil Engineering, Crakow University of Technology, Crakow, Poland

Full Bibliographic Reference for this paper
S. Lukaszyk, "The Scattered Data Interpolation Procedure based on a Counterpropagation Neural Network", in B.H.V. Topping, (Editor), "Computational Engineering using Metaphors from Nature", Civil-Comp Press, Edinburgh, UK, pp 59-63, 2000. doi:10.4203/ccp.64.1.9
The Scattered Data Interpolation Procedure (SDP) based on a modified Counterpropagation Neural Network (CPN) is presented. Matrix representation of SDIP facilitate the description of learning and working algorithms in comparison to a two-layered representation of CPN with competition and interpolation layers. The data matrix in SDP corresponds to the competition layer in CPN and the value matrix in SDIP corresponds to the interpolation layer in CPN. It is shown that during the working phase SDP, having an input vector X and output vector Y of size G, maps G scalar functions of vector argument Y_g = F_g(X), where g = 0,1, ..., G-1, rather than one vector function of vector argument Y = F(X). Two presented SDP learning algorithms allow compression of information stored in SDIP matrices during the learning phase, in dependence of a resolution parameter and thus allowing faster interpolation during the working phase. The results of a numerical example show that SDIP algorithms are superior to the weighted summation function used as an interpolation formula in CPN. The New Output Compression Algorithm (OCA), which evaluates the current efficiency of interpolation at each step of the learning process, is proposed.

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