Abstract
A systolic array for multi-dimensional fitting and interpolation using (nonlinear) radial basis functions is proposed. The fit may be constrained very simply to ensure that the resulting surface takes a pre-determined value at one or more specific points. The processor, which constitutes a form of nonlinear adaptive filter, behaves like a neural network based on the multi-layer, feed-forward perceptron model. One obvious application of such a network is as a pattern classifier, the constraints being used to ensure the correct classification of selected patterns.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D.E. Rumelhart, G.E. Hinton and R.I. Williams, “Learning internal representations by error propagation,” inParallel Distributed Processing, vol. 1, (eds D.E. Rumelhart and I.L. McClelland), Cambridge, MA: MIT Press, 1987, pp. 318–362.
D.S. Broomhead and D. Lowe, “Multi-variable function interpolation and adaptive networks,”Complex Systems, vol. 2, 1988, pp. 321–355.
M.I.D. Powell, “Radial basis functions for multivariable interpolation: a review,”Proc. IMA Conference on Algorithms for the Approximation of Functions and Data, RMCS Shrivenham, 1985.
D.S. Broomhead, R. Jones, J.G. McWhirter and T.J. Shepherd, “A systolic array for nonlinear adaptive filtering and pattern recognition,”Proc. IEEE Int. Symposium on Circuits and Systems, New Orleans, 1990.
W.M. Gentleman, “Least squares computations by Givens rotations without square roots,”J. Inst Maths. Applics., vol. 12, 1973, pp. 329–336.
J.G. McWhirter and T.J. Shepherd, “A pipelined array for linearly constrained least squares optimization,” inMathematics in Signal Processing, (ed T.S. Durrani et al., Oxford: Clarendon Press, 1987, pp. 457–483.
W.M. Gentleman and H.T. Kung, “Matrix triangulation by systolic arrays,Proc. SPIE, vol. 298, “Real Time Signal Processing IV,” 1981, pp. 298–303.
S. Haykin,Adaptive Filter Theory, Englewood Cliffs, NJ: Prentice Hall, 1986.
D. Lowe, “Adaptive radial basis function non-linearities and the problem of generalization,”Proc. IEE Int. Conf. on Artificial Neural Networks, London, Oct. 1989.
S. Renals and R. Rohwer, “Learning phoneme recognition using neural networks,”Proc. IEEE Int. Conf. on Acoustics, Speech and Signal Processing, Glasgow, 1989.
D. G. Bounds, P. Lloyd and B.G. Matthew, “A comparison of neural networks and other pattern recognition approaches to the diagnosis of low back disorders,” forthcoming.
G. Vrckovnik, C.R. Carter and S. Haykin, “Radial basis function classification of impulse radar waveforms,” private communication.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Whirter, J.G.M., Broomhead, D.S. & Shepherd, T.J. A systolic array for nonlinear adaptive filtering and pattern recognition. J VLSI Sign Process Syst Sign Image Video Technol 3, 69–75 (1991). https://doi.org/10.1007/BF00927835
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF00927835