Lee J. White

A Domain Strategy for Computer Program Testing

This paper presents a testing strategy desiged to detect errors in the control flow of a computer program, and the conditions under which this strategy is reliable are given and characterized. The control flow statements in a computer progam partition the input space into a set of mutually exclusive domains, each of which corresponds to a particular program path and consists of input data points which cause that path to be executed. The testing strategy generates test points to examine the boundaries of a domain to detect whether a domain error has occurred, as either one or more of these boundaries will have shifted or else the corresponding predicate relational operator has changed. If test points can be chosen within e of each boundary, under the appropriate assumptions, the strategy is shown to be reliable in detecting domain errons of magnitude greater than ∈. Moreover, the number of test points required to test each domain grows only linearly with both the dimensionality of the input space and the number of predicates along the path being tested.

A Maxmin Location Problem

The problem considered is to locate a point in a given convex polyhedron which maximizes the minimum Euclidean distance from a given set of points. The paper describes several possible application areas and shows the existence of a finite set of candidates for the optimal solution. A combinatorial algorithm is presented for the problem in three dimensions, and it is compared with existing nonconvex programming algorithms.

A distance measure for automatic document classification by sequential analysis

Abstract This research has investigated the feasibility of using a distance measure, called the Bayesian distance , for automatic sequential document classification. It has been shown that by observing the variation of this distance measure as keywords are extracted sequentially from a document, the occurrence of noisy keywords may be detected. This property of the distance measure has been utilized to design a sequential classification algorithm which works in two phases. In the first phase keywords extracted from a document are partitioned into two groups—the good keyword group and the noisy keyword group. In the second phase these two groups of keywords are analyzed separately to assign primary and secondary classes to a document. The algorithm has been applied to several data bases of documents and very encouraging results have been obtained.

A characterization of nearest-neighbor rule decision surfaces and a new approach to generate them

Abstract The paper considers generating nearest-neighbor rule decision surfaces as an application of a maxmin problem. The maxmin problem is to locate a point in a given convex polyhedron which maximizes the minimum distance from a given set of points in the polyhedron. A characterization of the decision surfaces in n-dimensions is given, and the difficulty involved in generating the decision surfaces in higher dimensional spaces is brought out through this characterization. However, a novel method is presented to generate the surfaces in three dimensions using the algorithm for the maxmin problem.

Aircraft identification using a bilinear surface representation of radar data

Abstract Low frequency radar scattering data is used for the identification of aircraft. It is shown that such radar data lies on two-dimensional surfaces in n -space. A bilinear approximation for these surfaces is described. Surface intersections using this approximation can be found simply and directly without solving a system of n simultaneous nonlinear equations. This intersection information can be used to show separability and effect feature reduction. The approximation is utilized to construct a modified nearest neighbor algorithm, which is evaluated by computer simulation experiments. These experiments showed a phenomenon of “bias”, where one aircraft data surface is more susceptible to misclassification in the presence of noise than the surface corresponding to another aircraft. This “bias” observed is shown to be related to the surface characteristics of the data surfaces involved, specifically proximity and relative curvature of corresponding points on the two surfaces.

The Weakening of Taxonomic Inferences by Homological Errors

In the past decade there has been a growing concern in devising classification algorithms which are applicable to large bodies of data. Such algorithms are characterized necessarily by a sacrifice of statistical sophistication for a gain in computational simplicity. Accordingly, inferences drawn from taxonomic studies in which these algorithms have been employed may be affected by accidental and poorly understood features of such algorithms. An error analytic technique is presented which reduces this possibility. It is applicable to many of the classification algorithms currently in use. The combinatorial problems encountered in the error analysis are discussed and a computationally viable method for their solution is formulated. The technique is illustrated by an experiment with a small set of data.

Identity conditions for Nearest-Neighbor and Potential-Function Classifiers*

The nearest-neighbor rule and the potential-function classifier are nonparametric discrimination methods that require the storage of a set of sample patterns. Here, a relationship between the two methods in terms of subclasses and superclasses is developed. Considering an exponential potential function, necessary and sufficient conditions for identity of their decision surfaces are obtained. Based on these conditions, an algorithm for establishing identity is introduced.

Optimum concentrator location in telecommunications design

This paper discusses the problem of the allocation of concentrators in the initial phases of telecommunications design. A model for this problem is presented in which the trade-off between line cost and the number of concentrators can be examined. An approach to obtaining a solution for this formulation involves minimum k-cover configurations, for which an efficient algorithm is presented.

An algorithm for determining identity of nearest-neighbor and potential function decision rules

Abstract The nearest-neighbor and potential function decision rules are nonparametric techniques that partition the feature space based on a set of labelled sample points. Determining whether the partitions of the two rules are identical for a given set of points is an interesting problem in computational geometry. Here, a relationship between the two methods in terms of subclasses and composite classes is developed. Considering an exponential potential function, necessary and sufficient conditions for identity of their decision surfaces are obtained. Based on conditions of symmetry, weighting, and the Voronoi region of a point, an algorithm for establishing identity in IRd is introduced.

Effect of random errors on generalized distance computations

Abstract There is growing interest in devising non-statistical classification algorithms for multivariate populations. Statistical algorithms are not appropriate if an adequate statistical model for the population does not exist. Such algorithms may be sensitive (unstable) to errors in their data. The particular case of populations of objects characterized by binary attributes susceptible to independent and equiprobable errors is examined. The determination of stability requires the prior computation of the expectation of a statistical function of the object-pair similarities. The order and convergence of a numerical approxiamation for determining these expectation with prescribed accuracy is examined in the sub-asymptotic case in which normality does not occur.