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This paper focuses on recent work which analyzes the expectation maximization (EM) evolution of mixtures based estimators. The goal of this research is the development of effective visualization techniques to portray the mixture model parameters as they change in time. This is an inherently high dimensional process. Techniques are presented which portray the time evolution of univariate, bivariate, and trivariate finite and adaptive mixtures estimators. Adaptive mixtures is a recently developed variable bandwidth kernel estimator where each of the kernels is not constrained to reside at a sample location. The future role of these techniques in developing new versions of the adaptive mixtures procedure are also discussed.

The existence of outliers in a data set and how to deal with them is an important problem in statistics. The Minimum Volume Ellipsoid (MVE) estimator is a robust estimator of location and shape; however its use has been limited because few computationally attractive methods exist to calculate it. Determining the MVE consists of two parts: finding the subset of points to be used in the estimate and finding the ellipse that covers this set. This paper will address the first problem. The proposed method of subset selection is called the Effective Independence Distribution (ElD) method which chooses the subset by mnimizing determinants of matrices containing the data. This method is deterministic yielding reproducible estimates of location and scatter for a given data set. The ElD method of finding the MVE is applied to several regression data sets where the true estimate is known. Results show that the EID method produces the subset of data in less than a second and that there is less than 6% relative error in the estimates. (AN)

Given i.i.d. observations x1,x2,x3,,,,xn drawn from a mixture of normal terms one is often interested in determining the number of terms in the mixture and their defining parameters. Although the problem of determining the number of terms is intractable under the most general assumptions there is hope of elucidating the mixture structure given appropriate caveats on the underlying mixture. This paper examines a new approach to this problem based on the use of Akaike Information Criterion (AIC) based pruning of data driven mixture models which are obtained from resampled data sets. Results of the application of this procedure to artificially generated and real world data sets are provided., Sponsored in part by Grants N00014-92-J-1303, N00014-93-1-0527.

A modification of the kernel estimator for density estimation is proposed which allows the incorporation of local information about the smoothness of the density. The estimator used a small set of local bandwidths rather than a single global one as in the standard kernel estimator. It uses a set of filtering functions which determines the extent of influence of the local bandwidths. Various versions of the idea are discussed. The estimator is shown to be consistent and is illustrated by comparison to the single bandwidth kernel estimator for the case in which the filter functions are derived from finite mixture models.

This report describes an analog method to extract gray-scale texture features. This method uses a nonlinear resistive grid to perform a two- dimensional pseudowavelet transform of the initial input image. Texture features are computed using first- and second- order variance estimates of the transform coefficients. Some preliminary results are presented indicating the natural segmentation that the nonlinearity provides at the boundary of two dissimilar textures.

A multi-layer neural network is provided for the detection and correction of local boundary misalignments in a two-dimensional pixel space between a reference and transformed image.

Given an object and a copy of itself produced by an unknown two dimensional affine transformation, a new neural network architecture has been developed that recovers this transformation by minimizing the symmetric difference between the object and the copy. This architecture performs a gradient descent in symmetric difference error space and is designated as visual gradient descent (VGD). The VGD network has applications to both two- and three- dimensional model based automatic target recognition (ATR) and image compression using iterated function systems.

Radar signal processing with multilayered perceptrons was investigated. Networks with no hidden layer and a single hidden layer were tested on field collected millimeter wave target returns that have been corrupted with artificial Gaussian noise at a signal to noise level of 3 dB. Performance as a function of network architecture was characterized. Keywords: Radar signal processing, Multilayered perceptrons, Single hidden layer, Field collected millimeter wave target.

The Attack and Defense of Maritime Resources in Adverse Locales Simulator (ADMRALS) system is a distributed multiwarfare simulation system that allows variable fidelity/complexity modeling of engagements between user designed naval battle force architectures (existing or proposed) and largescale threat scenarios. ADMRALS utilizes TCP/IP, a heterogeneous processor suite, and a locally developed distributed network environment to give concurrent processor capability to a systems level multiwarfare naval simulation. It is believed that ADMRALS will fill the apparent 'systems level' void existent in multiwarfare analysis capabilities within the Navy and provide a sound foundation for potential evolutionary growth into a key system test and analysis facility for the Navy. The first warfare area investigated was that of naval air defense. Central to the naval air defense role is the F-14, and central to a simulation of this type is a battle management algorithm for the F-14s.

A simple selective learning algorithm for use with Multilayer Perceptrons (MLPs) is presented. This algorithm has proved useful in certain types of problems where learning failure occurs using standard back propagation. Examples of these problems are included. The algorithm is based on the rms output error, computed across all output nodes and all training patterns. The learning rate is decreased for all individual output nodes each time the error is less than a user chosen multiple of the rms error corresponding to the previous pass. This algorithm has produced convergence where the standard fixed gain back propagation failed.