Probabilistic neural networks
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Cites methods from "Probabilistic neural networks"
...This is known as the Nadaraya-Watson estimator (Nadaraya, 1964; Watson, 1964), and has been re-discovered relatively recently in the context of neural networks (Specht, 1990; Schi0ler and Hartmann, 1992)....
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Cites methods from "Probabilistic neural networks"
...The real value of Parzen classifier lies in the fact that it is the statistical counterpart of several important classification methods such as radial basis function networks [41,42], the probabilistic neural network (PNN) [43], and a number of fuzzy classifiers [44–46]....
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References
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"Probabilistic neural networks" refers methods in this paper
...The nearest neighbor decision rule has been investigated in detail by Cover and Hart (1967). In general, neither limiting case provides optimal separation of the two distributions. A degree of averaging of nearest neighbors, dictated by the density of training samples, provides better generalization than basing the decision on a single nearest neighbor. The network proposed is similar in effect to the knearest neighbor classifier. Specht (1966) contains an involved discussion of how one should choose a value of the smoothing parameter, a, as a function of the dimension of the problem, p, and the number of training patterns, n....
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...The nearest neighbor decision rule has been investigated in detail by Cover and Hart (1967). In general, neither limiting case provides optimal separation of the two distributions. A degree of averaging of nearest neighbors, dictated by the density of training samples, provides better generalization than basing the decision on a single nearest neighbor. The network proposed is similar in effect to the knearest neighbor classifier. Specht (1966) contains an involved discussion of how one should choose a value of the smoothing parameter, a, as a function of the dimension of the problem, p, and the number of training patterns, n. However, it has been found that in practical problems it is not difficult to find a good value of a, and that the misclassification rate does not change dramatically with small changes in a. Specht (1967b) describes an experiment in which electrocardiograms were classified as normal or abnormal using the two-category classification of eqns (1) and (12)....
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...The nearest neighbor decision rule has been investigated in detail by Cover and Hart (1967). In general, neither limiting case provides optimal separation of the two distributions....
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...The nearest neighbor decision rule has been investigated in detail by Cover and Hart (1967)....
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10,114 citations
"Probabilistic neural networks" refers background in this paper
...Alternate estimators suggested by Cacoullos (1966) and Parzen (1962) are given in Table 1, where f.,(X) n,;?...
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...Parzen (1962) showed how one may construct a family of estimates of f(X), .f°(x) n~,,,~°, , (4) which is consistent at all points X at which the PDF...
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...Parzen (1962) showed how one may construct a family of estimates of f (X) ,...
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...Further application of Cacoullos (1966), Theorem 4,1, to other univariate kernels suggested by Parzen (1962) yields the following multivariate estimators (which are products of univariate kernels): 1 ~1, when alllX~-XA,jI --2 (18) fa(X) --n(22)p ,=, fA(X) n~ p = = ~ , when all IX~ -Xa0....
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...In his classic paper, Parzen (1962) showed that a class of PDF estimators asymptotically approaches the underlying parent density provided only that it is continuous....
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"Probabilistic neural networks" refers background in this paper
...Cacoullos (1966) has also extended Parzen's resuits to cover the multivariate case. Theorem 4.1 in Cacoullos (1966)indicates how the Parzen results can be extended to estimates in the special ease that the multivariate kernel is a product of univariate kernels....
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...Further application of Cacoullos (1966), Theorem 4,1, to other univariate kernels suggested by Parzen (1962) yields the following multivariate estimators (which are products of univariate kernels):...
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...Cacoullos (1966) has also extended Parzen's resuits to cover the multivariate case....
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...Alternate estimators suggested by Cacoullos (1966) and Parzen (1962) are given in Table 1, where f.,(X) n,;?...
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...Further application of Cacoullos (1966), Theorem 4,1, to other univariate kernels suggested by Parzen (1962) yields the following multivariate estimators (which are products of univariate kernels): 1 ~1, when alllX~-XA,jI --2 (18) fa(X) --n(22)p ,=, fA(X) n~ p = = ~ , when all IX~ -Xa0....
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