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Criteria for minimal RBF artificial neural network’s center vectors set definition


M.A. Abrosimov - Post-graduate Student, Department of Applied Information Technologies,  Yuri Gagarin State Technical University of Saratov (SSTU)
A.V. Brovko - Dr.Sc. (Phys.-Math.), Professor, Department of Applied Information Technologies, Yuri Gagarin State Technical University of Saratov (SSTU)

The problem of determining the center vector set of RBF ANN is considered in the paper. This problem is solved by deriving criteria by considering no information loss condition for hidden layer, that allow to calculate the input vector by hidden layer outputs.
The training set data for determining the center vector set consists of the elements of the scattering matrix of turnstile waveguide junction within which the sample is placed. The ANN topology to be compared with the new built by criteria was used in the same source.
Center vector set sufficiency criteria is derived with use of Kronecker-Capelli theorem. An algorithm of calculating a mi-nimal sufficient center vector set by presented criteria from training set is based on binary search and k-means algorithm.
To illustrate the performance of the proposed method, the paper presents numerical results of the reconstruction of three test profiles defined with non-polynomial functions. For all three profiles a RBF ANN built by criteria and a non-modified RBF ANN. In all profile cases ANNs built by criteria show a significant training time reduction and lower error values growth by training set reduction.

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