This paper addresses the use of a fast orthogonalization process to find the nodes of an RBF network which produce the best match to a target function. Several applications of RBF networks using this fast orthogonal search technique have been investigated and a classification problem is presented. The problem involves classification of human chromosomes, which is a highly complicated 30 dimensional and 24 class problem. Experimental results show that the fast orthogonal search technique not only outperforms the traditional technique, but it also uses much less time and effort.

This paper addresses the measurement of random sample-time jitter in the characterization of ADC's. A straightforward test is developed which allows for measurement of both additive noise power and RMS sample-time jitter. Simulations are used to assess the accuracy of the technique. Experimental results are also given for a commercially available ADC.

This paper addresses the application of locally optimum (LO) signal detection techniques to environments in which the noise density is not known a priori. For small signal levels, the LO detection rule is shown to involve a nonlinearity which depends on the noise density. The estimation of the noise density is a major part of the computational burden of LO detection rules. In this paper, adaptive estimation of the noise density is implemented using a radial basis function neural network. Unlike existing algorithms, the present technique places few assumptions on the properties of the noise, and performs well under a wide variety of circumstances. Experimental results are shown which illustrate the system performance as a variety of noise densities are encountered.

This paper addresses the application of locally optimum (LO) signal detection techniques to environments in which the noise density is not known a-priori. For small signal levels, the LO detection rule is shown to involve a nonlinearity which depends on the noise density. The estimation of the noise density is a major part of the computational burden of LO detection rules. In this paper, adaptive estimation of the noise density is implemented using a radial basis function neural network. The technique places few assumptions on the properties of the noise, and performs well under a wide variety of circumstances. Experimental results illustrate the system performance as a variety of noise densities are encountered.>

This paper describes procedures to obtain optimum error models for ADCs using a non-iterative technique. The goal of "phase-plane" compensation for ADCs is to determine the error which is introduced by a converter as a function of the ADC state and the (estimated) slope of the input signal. Past calibration schemes have been frustrated by uncertainties about the input calibration signal. In this paper, the error characteristic is expressed as a linear combination of a set of basis functions, which is then optimised to minimize the harmonic distortion in the output sample sequence. Degradation in performance due to inaccurate estimates of the input signal is avoided. The theories developed in this paper are applied to an 8-bit ADC sampling at 204.8 MSPS. Experimental results show that dynamic range performance can be improved by as much as 12 dB over the Nyquist band. A further interesting result is that an error function measured for one ADC is found to work equally well for another ADC taken from the same production run. The errors determined are thus found to be unique to the ADC design and production, and not to the test and representation methods. It is believed that this is the first time that results of this nature have been reported in the literature.>

This correspondence presents a method for evaluation of artificial neural network (ANN) classifiers. In order to find the performance of the network over all possible input ranges, a probabilistic input model is defined. The expected error of the output over this input range is taken as a measure of generalization ability. Two essential elements for carrying out the proposed evaluation technique are estimation of the input probability density and numerical integration. A nonparametric method, which depends on the nearest M neighbors, is used to locally estimate the distribution around each training pattern. An orthogonalization procedure is utilized to determine the covariance matrices of local densities. A Monte Carlo method is used to perform the numerical integration. The proposed evaluation technique has been used to investigate the generalization ability of back propagation (BP), radial basis function (RBF) and probabilistic neural network (PNN) classifiers for three test problems.>

The use of nonparametric error estimates may lead to biased results if the kernel covariances are estimated from the same data as are used to form the error estimate. If additional design samples are available, one may eliminate this bias by estimating the class covariances using an independent set of data. If, however, additional samples are not available, one may resort to leave-one-out type estimates of the kernel (for Parzen estimates) or metric (for nearest-neighbor estimates) for every sample being tested. The authors present an efficient algorithm for computation of these leave-one-out type estimates that requires little additional computational burden over procedures currently in use. The presentation is applicable to both Parzen and k-nearest neighbor (k-NN) type estimates. Experimental results demonstrating the efficiency of the algorithm are provided.>

The bias of the finite-sample nearest neighbor (NN) error from its asymptotic value is examined. Expressions are obtained which relate the bias of the NN and 2-NN errors to sample size, dimensionality, metric, and distributions. These expressions isolate the effect of sample size from that of the distributions, giving an explicit relation showing how the bias changes as the sample size is increased. Experimental results are given which suggest that the expressions accurately predict the bias. It is shown that when the dimensionality of the data is high, it may not be possible to estimate the asymptotic error simply by increasing the sample size. A new procedure is suggested to alleviate this problem. This procedure involves measuring the mean NN errors at several sample sizes and using our derived relationship between the bias and the sample size to extrapolate an estimate of the asymptotic NN error. The results are extended to the multiclass problem. The choice of an optimal metric to minimize the bias is also discussed.

The use of k nearest neighbor (k-NN) and Parzen density estimates to obtain estimates of the Bayes error is investigated under limited design set conditions. By drawing analogies between the k-NN and Parzen procedures, new procedures are suggested, and experimental results are given which indicate that these procedures yield a significant improvement over the conventional k-NN and Parzen procedures. We show that, by varying the decision threshold, many of the biases associated with the k-NN or Parzen density estimates may be compensated, and successful error estimation may be performed in spite of these biases. Experimental results are given which demonstrate the effect of kernel size and shape (Parzen), the size of k (k-NN), and the number of samples in the design set.