Browsing by Author "de Figueiredo, Rui J.P."
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Item An Adaptive Orthogonal-Series Estimator for Probability Density Functions(1978-02-20) Anderson, G. Leigh; de Figueiredo, Rui J.P.Given a sample set X1,...,XN of independent identically distributed real-valued random variables, each with the unknown probability density function f(â ¢), the problem considered is to estimate f from the sample set. The function f is assumed to be in L2(a,b); f is not assumed to be in any parametric family. This paper constructs an adaptive "two-pass" solution to the problem: In a pre-processing step (the first pass), a preliminary rough estimate of f is obtained by means of a standard orthogonal-series estimator. In the second pass, the preliminary estimate is used to transform the orthogonal series. The new, transformed orthogonal series is then used to obtain the final estimate. The paper establishes consistency of the estimator and derives asymptotic (large sample set) estimates of the bias and variance. It is shown that the adaptive estimator offers reduced bias (better resolution) in comparison to the conventional orthogonal series estimator. computer simulations are presented which demonstrate the small sample set behavior. A case study of a bimodal density confirms the theoretical conclusions.Item An Algorithm for Extraction of More than One Optimal Linear Feature from Several Gaussian Pattern Classes(1976-04-20) de Figueiredo, Rui J.P.; Pau, K.C.; Sagar, A. D.; Starks, S.A.; Van Rooy, D.L.Two algorithms have been developed at Rice University for optimal linear feature extraction based on the minimization risk (probability) of misclassification under the assumption that the class conditional probability density functions are Gaussian. One of these algorithms, which applieds to the case in which the dimensionality of the feature space (reduced space) is unity, has been described elsewhere [Rice University ICSA Technical Reports Nos. 275-025-022 and 275-025-025 (EE Technical Reports Nos. 7520 and 7603)]. In the present report, we describe the second algorithm which is used when the dimension of the feature space is greater than one. Numerical results obtained from the application of the present algorithm to remotely sensed data from the Purdue C1 flight line are mentioned. Brief comparisons are made of these results with those obtained using a feature selection technique based on maximizing the Bhattacharyya distance. For the example considered, a significant improvement in classification is obtained by the present technique.Item An Algorithm for Optimal Single Linear Feature Extraction from Several Gaussian Pattern Classes(1975-11-20) Starks, S.A.; de Figueiredo, Rui J.P.; Van Rooy, D.L.A computational algorithm is presented for the extraction of an optimal single linear feature from several Gaussian pattern classes. The algorithm minimizes the increase in the probability of misclassification in the transformed (feature) space. The general approach used in this procedure was developed in a recent paper by R.J.P. de Figueiredo. Numerical results on the application of this procedure to the remotely sensed data from the Purdue C1 flight line as well as LANDSAT data are presented. It was found that classification using the optimal single linear feature yielded a value for the probability of misclassification on the order of 30% less than that obtained by using the best single untransformed feature. Also, the optimal single linear feature gave performance results comparable to those obtained by using the two features which maximized the average divergence.Item Algorithms for Optimal Numerical Quadrature Based on Signal Class Models(1979-11-01) de Figueiredo, Rui J.P.A framework is presented for constructing various types of numerical quadrature algorithms which take into account the a-priori known or estimated properties of the signal being processed. This is done by appropriately modeling the signal class to which such a signal belongs. Both linear and nonlinear signal class models are considered and wide use of generalized spine theory is made. For the nonlinear case, a new type of nonlinear generalized spline is defined.Item Application of a Frequency Domain Prony Method to Wide Bandwidth Radar Signature Classification(1979-09-20) de Figueiredo, Rui J.P.; Hu, C.L.A frequency domain Prony approach is presented for extracting features of return signals from targets illuminated by wide bandwidth (short pulse) radar. Theoretical details pertaining to this approach are described in a separate paper. The features mentioned above consist of the relative delays and reflection coefficients pertaining to scattering centers on the target representing differently shaped regions on the target surface. The dimensionality of the feature vectors thus constructed is very low (less than ten). Moreover, when used in the classification of targets by a nearest neighbor classification strategy, such feature vectors permit accurate discrimination between targets that do not differ much in shape; and also they are in a large measure insensitive to noise. The above results wer corroborated by computer simulations performed on the data base created by the coherent X-band short pulse (0.5 nanosecond) radar at the Fort Worth operation Radar Range of General Dynamics Convair Aerospace Division. The three objects on which extensive simulations were carried out were: an AGENA space vehicle with rectangular cross-sectional first stage, an AGENA space vehicle with cylindrical cross-sectional first stage and an AGENA space vehicle payload. the results of these simulations, which were rather successful, are discussed in detail.Item Computation of a Unimodular Matrix(1979-12-01) Kontos, Athanassios; de Figueiredo, Rui J.P.An algorithm for computing a unimodular matrix U(λ) satisfying the equation [A(λ) B(λ)] U(λ) = [1 0] is presented where A(λ) and B(λ) are relatively left prime polynomial matrices. The approach used avoids Euclidean-type operations used in standard Gaussian elimination and thus appears to be superior to any direct approach based on the computation of Smith forms.Item Computationally Efficient Estimators for the Bayes Risk(1978-05-20) Wilcox, Lynn D.; de Figueiredo, Rui J.P.A computationally efficient estimator for the Bayes risk is one which achieves a desired accuracy with a minimum of computation. In many problems, for example speech recognition, point evaluations of the class conditional densities are computationally costly. Density evaluations are the single most important factor contributing to the computational effort in Bayes risk estimation, thus the amount of computation required by a bayes risk estimator is defined as the average number of conditional density evaluations it performs. The accuracy of a risk estimator is defined by its variance.Item Design of Optimal Feature Extractors by Mathematical Programming Techniques(1976-06-20) de Figueiredo, Rui J.P.In an automatic pattern recognition system, the processor that selects and measures features fo the data, on the basis of which classification is made, is called a "feature selector" or "feature extractor". This paper presents a mathematical programming approach for the design of a feature extractor.Item Feature Extraction Techniques for Classification and Identification of Spectral Signatures(1976-04-20) de Figueiredo, Rui J.P.Some of the results obtained at Rice University on the extraction of features from spectral signatures for the purpose of classifying and identifying these signatures are described.Item A Fourier-Prony Tauberian Approach to the Analysis of a Mixture of Delayed Signals(1979-09-20) de Figueiredo, Rui J.P.; Hu, C.L.Let x and y be signals (i.e. real-valued functions of time) of finite duration and energy. In the present paper, we develop a frequency domain Prony approach for interpolating, or in general, approximating y(t) by ....Item LM-g SPLINES(1975-07-20) de Figueiredo, Rui J.P.As an extension of the notion of an L-g spline, three mathematical structures called LM-g splines of types, I, II and II are introduced. (partial abstract)Item Nonlinear System Identification Based on a Fock Space Framework(1979-05-20) Zyla, Lou; de Figueiredo, Rui J.P.A method is presented for the identification of a nonlinear system represented by an operator V:E->Y, where the input space E is a separable Hilbert space over the field of complex numbers and the output space Y is the Sobolev space H2n(1) of complex-valued functions y on an interval I of the real line such that d,y/dtk, k=0,...,n-1, are absolutely continuous and dny/dtn∈L2(I)....Item On a Class of Minimum Energy Controls Related to Spline Functions(1975-07-20) Netravali, Arun N.; de Figueiredo, Rui J.P.The problem of determining a minimum energy control for a dynamically interconnected set of p single-input single-output finite-dimensional linear time-varying dynamical systems, for which the outputs are constrained to assume prescribed values at different points in time is considered. It is shown that the solution (optimal controller) is obtained by performing a linear operation on an appropriate vector-valued generalized interpolating spline.Item Optimization Techniques for Feature Extraction in Automatic Pattern Recognition(1979-10-20) de Figueiredo, Rui J.P.This report summarizes the work performed under the AFOSR grant 75-2777 over the almost five year period during which the grant was in effect.Item A recursive algorithm for digital Image Processing using Local Statistics(1979-06-20) de Figueiredo, Rui J.P.An algorithm is presented for digital image processing based on local statistics. The algorithm constitutes a recursive implementaiton of an approach proposed and implemented nonrecursively by J.S. Lee (Naval Research Laboratory Report 8192, March 1978). Calculations show that the proposed recursion introduces considerable improvement in efficiency.