Volterra Models and Three-Layer Perceptrons  

Oleh:

Marmarelis, V.Z. ; Zhao, X.

Jenis: Article from Journal - ilmiah internasional
Dalam koleksi: IEEE Transactions on Neural Networks vol. 8 no. 6 (1997), page 1421-1433.
Topik: perceptron; volterra models; three - layer perceptrons

Ketersediaan

Perpustakaan Pusat (Semanggi) Nomor Panggil: II36.2 Non-tandon: 1 (dapat dipinjam: 0) Tandon: tidak ada

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Isi artikel

This paper proposes the use of a class of feedforward artificial neural networks with polynomial activation functions (distinct for each hidden unit) for practical modeling of high - order Volterra systems. Discrete - time Volterra models (DVM s) are often used in the study of nonlinear physical and physiological systems using stimulus - response data. However, their practical use has been hindered by computational limitations that confine them to low-order nonlinearities (i. e., only estimation of low-order kernels is practically feasible). Since three - layer perceptrons (TLP s) can be used to represent input-output nonlinear mappings of arbitrary order, this paper explores the basic relations between DVM s and TLP s with tapped - delay inputs in the context of nonlinear system modeling. A variant of TLP with polynomial activation functions-termed “separable Volterra networks” (SVN s) - is found particularly useful in deriving explicit relations with DVM and in obtaining practicable models of highly nonlinear systems from stimulus - response data. The conditions under which the two approaches yield equivalent representations of the input-output relation are explored, and the feasibility of DVM estimation via equivalent SVN training using backpropagation is demonstrated by computer - simulated examples and compared with results from the Laguerre expansion technique (LET). The use of SVN models allows practicable modeling of high - order non linear systems, thus removing the main practical limitation of the DVM approach.

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