Complexity reduction in probabilistic neural networks
Probability density estimation using the probabilistic neural network or the kernel method is considered. In its basic form this method can be computationally prohibitive, as all training data need to be stored and each individual training vector gives rise to a new term of the estimate. Given an original training sample of size N in a d-dimensional space, a simple binned kernel estimate with O(Nd/d+4) terms can be shown to attain an estimation accuracy only marginally inferior to the standard kernel method. This can be taken to indicate the order of complexity reduction generally achievable when a radial basis function style expansion is used in place of the probabilistic neural network.
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- 1.P. Hall. The influence of rounding errors on some nonparametric estimators of a density and its derivatives. SIAM J. Appl. Math., 42(2):390–399, April 1982.Google Scholar
- 2.A. Hämäläinen. Self-organizing map and reduced kernel density estimation. PhD Thesis, Research Reports A11, Rolf Nevanlinna Institute, University of Helsinki, 1995.Google Scholar
- 3.L. Holmström and A. Hämäläinen. The self-organizing reduced kernel density estimator. In Proceedings of the 1993 IEEE International Conference on Neural Networks, San Francisco, California, March 28–April 1, volume 1, pages 417–421, 1993.Google Scholar
- 4.T. Kohonen. Self-Organizing Maps. Springer-Verlag, 1995.Google Scholar
- 5.D. W. Scott and S. J. Sheather. Kernel density estimation with binned data. Comm. Statist. A-Theory Methods, 14(6):1353–1359, 1985.Google Scholar
- 6.B. W. Silverman. Density Estimation for Statistics and Data Analysis. Chapman and Hall, 1986.Google Scholar
- 7.D. F. Specht. Probabilistic neural networks. Neural Networks, 3(1):109–118, 1990.Google Scholar