Donald M. Hummels

Original Contribution: On the training of radial basis function classifiers

An approach for the implementation of the Radial Basis Function (RBF) technique is presented and applied to a network of the appropriate architecture. The paper explores a methodology for selecting kernel function parameters and the extent to which the number of RBF nodes can be reduced without significantly affecting the overall training error. These objectives are accomplished through algorithms that shall be described in detail. Emphasis is also placed on the problems faced by a technique that has been proved superior to the more traditional training algorithms, particularly in terms of processing speed and solvability of nonlinear patterns. Solutions are consequently proposed in view of making RBF a more efficient method for interpolation and classification purposes.

Bayes Error Estimation Using Parzen and k-NN Procedures

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.

Leave-one-out procedures for nonparametric error estimates

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. >

Bias of Nearest Neighbor Error Estimates

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.

Using sine wave histograms to estimate analog-to-digital converter dynamic error functions

This paper describes a new method for developing analog-to-digital converter (ADC) error function models using modified sinewave histogram methods. The error models may be used to digitally compensate for nonlinearities introduced by the converter. The histogram modification involves sorting of converter output samples based upon an estimated associated input derivative signal. This error model is based upon a previously unpublished result which shows that sinewave histograms yield distinctly different expected errors for each state based upon input signal slope associated with each output sample. This result thus provides a dynamic dependence for expected errors measured by means of histogram methods. Sorted sinewave histograms are used to estimate slope dependent expected errors at each ADC output state (code). The method provides improved error representation by providing error basis functions for every output code. Simulated results prove that this method removes all slope dependent errors for complex ADC architectures while experimental results for an 8-bit 200 MSPS ADC yielded more than 10 dB improvement in spurious-free-dynamic-range (SFDR) over the full Nyquist band. The new method is thus shown to possess wideband dynamic error character.

The modulo time plot-a useful data aquisition diagnostic tool

This paper illustrates the use of the Modulo Time Plot to facilitate diagnosis of data acquisition systems and components. While conventional techniques, involving spectral analysis and histograms, provide certain useful and necessary measures of performance, the use of reordered sample sets has gained considerable popularity in recent work aimed at characterizing analog-to-digital converter error mechanisms. Examples show that the Modulo Time Plot is useful for quick visual inspection of system performance including dynamic range, distortion and error plots, the detection of random bit errors, and timing errors between the test signal and the sample clock.

A probabilistic model for evaluation of neural network classifiers

Abstract A technique for evaluation of the generalization ability in artificial neural network (ANN) classifiers is presented. A probabilistic input model is proposed to account for all possible input ranges. The expected value of a square error function over the defined input range is taken as a measure of generalization ability. The minimization of the error function outlines the boundary of the decision region for a minimum error neural network (MENN) classifier. Two essential elements for carrying out the proposed technique are the estimation of the input density and numerical integration. A non-parametric method is used to locally estimate the distribution around each training pattern. The Monte Carlo method has been used for numerical integration. The evaluation technique was tested for measuring the generalization ability of back propagation (BP), radial basis function (RBF), probabilistic neural network (PNN) and MENN classifiers for different problems.

The noise power ratio-theory and ADC testing

This paper develops theory behind the noise power ratio (NPR) testing of ADCs. A mid-riser formulation is used for mathematical simplicity. Simulated results, using DAC generated signals, suggests that the uniformly distributed signal is easier to implement and is more sensitive to amplitude dependent distortions.

Distortion compensation for time-interleaved analog to digital converters

A common technique to achieve high sample rates for analog-to-digital converters (ADCs) is to time interleave two or more devices. A drawback of this approach is that mismatches between the devices cause distortion in the sample sequence. This distortion limits the dynamic range which may be achieved using a particular ADC. Although phase-plane compensation techniques exist to improve the dynamic range of ADCs, these techniques are ineffective for time-interleaved structures. This paper extends the existing phase-plane modeling techniques to time-interleaved architectures. The modified algorithms are tested using a 500 MSPS ADC and are shown to reduce harmonic and intermodulation distortion terms by well over 10 dB.

Wireless acoustic wave sensors and systems for harsh environment applications

This paper reviews current progress in the area of wireless microwave acoustic sensor technology, and discusses advances in wireless interrogation systems that can operate in harsh environments. The use of wireless, battery-free, low maintenance surface acoustic wave (SAW) sensors has been successfully demonstrated in applications including high temperature turbine engines and inflatable aerospace structures. Wireless interrogation of multiple sensors up to 910°C has been established and sensor tests in gas turbine engine are reported. This paper elaborates on several aspects of the technology, including: high-temperature thin-film electrode and sensor development, temperature cycling, thermal-shock behavior, testing in turbine engine environments, sensor packaging and attachment, wireless operation, and adaptation to energy and industrial applications.