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450,980
Very simple classification rules perform well on most commonly used datasets
 Machine Learning
, 1993
"... The classification rules induced by machine learning systems are judged by two criteria: their classification accuracy on an independent test set (henceforth "accuracy"), and their complexity. The relationship between these two criteria is, of course, of keen interest to the machin ..."
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Cited by 542 (5 self)
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The classification rules induced by machine learning systems are judged by two criteria: their classification accuracy on an independent test set (henceforth "accuracy"), and their complexity. The relationship between these two criteria is, of course, of keen interest
Global Optimization with Polynomials and the Problem of Moments
 SIAM Journal on Optimization
, 2001
"... We consider the problem of finding the unconstrained global minimum of a realvalued polynomial p(x) : R R, as well as the global minimum of p(x), in a compact set K defined by polynomial inequalities. It is shown that this problem reduces to solving an (often finite) sequence of convex linear mat ..."
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Cited by 569 (47 self)
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matrix inequality (LMI) problems. A notion of KarushKuhnTucker polynomials is introduced in a global optimality condition. Some illustrative examples are provided. Key words. global optimization, theory of moments and positive polynomials, semidefinite programming AMS subject classifications. 90C22
Rendering of Surfaces from Volume Data
 IEEE COMPUTER GRAPHICS AND APPLICATIONS
, 1988
"... The application of volume rendering techniques to the display of surfaces from sampled scalar functions of three spatial dimensions is explored. Fitting of geometric primitives to the sampled data is not required. Images are formed by directly shading each sample and projecting it onto the picture ..."
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Cited by 867 (11 self)
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boundary surfaces are presented. Independence of shading and classification calculations insures an undistorted visualization of 3D shape. Nonbinary classification operators insure that small or poorly defined features are not IosL The resulting colors and opacities am composited from back to front along
Simulating Physics with Computers
 SIAM Journal on Computing
, 1982
"... A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. ..."
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Cited by 601 (1 self)
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computer. These algorithms take a number of steps polynomial in the input size, e.g., the number of digits of the integer to be factored. AMS subject classifications: 82P10, 11Y05, 68Q10. 1 Introduction One of the first results in the mathematics of computation, which underlies the subsequent development
The Lifting Scheme: A Construction Of Second Generation Wavelets
, 1997
"... . We present the lifting scheme, a simple construction of second generation wavelets, wavelets that are not necessarily translates and dilates of one fixed function. Such wavelets can be adapted to intervals, domains, surfaces, weights, and irregular samples. We show how the lifting scheme leads to ..."
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Cited by 541 (16 self)
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to a faster, inplace calculation of the wavelet transform. Several examples are included. Key words. wavelet, multiresolution, second generation wavelet, lifting scheme AMS subject classifications. 42C15 1. Introduction. Wavelets form a versatile tool for representing general functions or data sets
Stochastic Perturbation Theory
, 1988
"... . In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a firstorder perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating the variatio ..."
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Cited by 886 (35 self)
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and the eigenvalue problem. Key words. perturbation theory, random matrix, linear system, least squares, eigenvalue, eigenvector, invariant subspace, singular value AMS(MOS) subject classifications. 15A06, 15A12, 15A18, 15A52, 15A60 1. Introduction. Let A be a matrix and let F be a matrix valued function of A
The knowledge complexity of interactive proof systems
 in Proc. 27th Annual Symposium on Foundations of Computer Science
, 1985
"... Abstract. Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/nonHamiltoni ..."
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Cited by 1267 (42 self)
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for the languages of quadratic residuosity and quadratic nonresiduosity. These are the first examples of zeroknowledge proofs for languages not known to be efficiently recognizable. Key words, cryptography, zero knowledge, interactive proofs, quadratic residues AMS(MOS) subject classifications. 68Q15, 94A60 1
Convergence Properties of the NelderMead Simplex Method in Low Dimensions
 SIAM Journal of Optimization
, 1998
"... Abstract. The Nelder–Mead simplex algorithm, first published in 1965, is an enormously popular direct search method for multidimensional unconstrained minimization. Despite its widespread use, essentially no theoretical results have been proved explicitly for the Nelder–Mead algorithm. This paper pr ..."
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Cited by 566 (3 self)
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methods, Nelder–Mead simplex methods, nonderivative optimization AMS subject classifications. 49D30, 65K05
Attention, similarity, and the identificationCategorization Relationship
, 1986
"... A unified quantitative approach to modeling subjects ' identification and categorization of multidimensional perceptual stimuli is proposed and tested. Two subjects identified and categorized the same set of perceptually confusable stimuli varying on separable dimensions. The identification dat ..."
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Cited by 663 (28 self)
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data were modeled using Sbepard's (1957) multidimensional scalingchoice framework. This framework was then extended to model the subjects ' categorization performance. The categorization model, which generalizes the context theory of classification developed by Medin and Schaffer (1978
A Lattice Model of Secure Information Flow
, 1976
"... This paper investigates mechanisms that guarantee secure information flow in a computer system. These mechanisms are examined within a mathematical framework suitable for formulating the requirements of secure information flow among security classes. The central component of the model is a lattice s ..."
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Cited by 697 (2 self)
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view of all systems that restrict information flow, enables a classification of them according to security objectives, and suggests some new approaches. It also leads to the construction of automatic program certification mechanisms for verifying the secure flow of information through a program.
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