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Multidimensional vector product
, 2002
"... It is shown that multidimensional generalization of the vector product is only possible in seven dimensional space. The threedimensional vector product proved to be useful in various physical problems. A natural question is whether multidimensional generalization of the vector product is possible ..."
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Cited by 1 (0 self)
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It is shown that multidimensional generalization of the vector product is only possible in seven dimensional space. The threedimensional vector product proved to be useful in various physical problems. A natural question is whether multidimensional generalization of the vector product
Snakes, Shapes, and Gradient Vector Flow
 IEEE TRANSACTIONS ON IMAGE PROCESSING
, 1998
"... Snakes, or active contours, are used extensively in computer vision and image processing applications, particularly to locate object boundaries. Problems associated with initialization and poor convergence to boundary concavities, however, have limited their utility. This paper presents a new extern ..."
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Cited by 755 (16 self)
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external force for active contours, largely solving both problems. This external force, which we call gradient vector flow (GVF), is computed as a diffusion of the gradient vectors of a graylevel or binary edge map derived from the image. It differs fundamentally from traditional snake external forces
Estimating the Support of a HighDimensional Distribution
, 1999
"... Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S is bounded by some a priori specified between 0 and 1. We propo ..."
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Cited by 783 (29 self)
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of the weight vector in an associated feature space. The expansion coefficients are found by solving a quadratic programming problem, which we do by carrying out sequential optimization over pairs of input patterns. We also provide a preliminary theoretical analysis of the statistical performance of our
Sonification of ThreeDimensional Vector Fields
 in Proceedings of the SCS High Perfor mance Computing Symposium
, 2004
"... We describe and analyze a new technique for sonification of threedimensional vector fields. This technique allows the user to use commodity hardware and widely available 3D sound interfaces to map vectors in a listener’s local neighborhood into smooth windlike sound (aerodynamic sound). The four ..."
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Cited by 7 (0 self)
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We describe and analyze a new technique for sonification of threedimensional vector fields. This technique allows the user to use commodity hardware and widely available 3D sound interfaces to map vectors in a listener’s local neighborhood into smooth windlike sound (aerodynamic sound). The four
Inverse Operation of Fourdimensional Vector Matrix
"... Abstract—This is a new series of study to define and prove multidimensional vector matrix mathematics, which includes fourdimensional vector matrix determinant, fourdimensional vector matrix inverse and related properties. There are innovative concepts of multidimensional vector matrix mathematic ..."
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Abstract—This is a new series of study to define and prove multidimensional vector matrix mathematics, which includes fourdimensional vector matrix determinant, fourdimensional vector matrix inverse and related properties. There are innovative concepts of multidimensional vector matrix
The Vector Field Histogram  Fast Obstacle Avoidance For Mobile Robots
 IEEE JOURNAL OF ROBOTICS AND AUTOMATION
, 1991
"... A new realtime obstacle avoidance method for mobile robots has been developed and implemented. This method, named the vector field histogram(VFH), permits the detection of unknown obstacles and avoids collisions while simultaneously steering the mobile robot toward the target. The VFH method uses a ..."
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Cited by 484 (24 self)
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A new realtime obstacle avoidance method for mobile robots has been developed and implemented. This method, named the vector field histogram(VFH), permits the detection of unknown obstacles and avoids collisions while simultaneously steering the mobile robot toward the target. The VFH method uses
Computing semantic relatedness using Wikipediabased explicit semantic analysis
 In Proceedings of the 20th International Joint Conference on Artificial Intelligence
, 2007
"... Computing semantic relatedness of natural language texts requires access to vast amounts of commonsense and domainspecific world knowledge. We propose Explicit Semantic Analysis (ESA), a novel method that represents the meaning of texts in a highdimensional space of concepts derived from Wikipedi ..."
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Cited by 562 (9 self)
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Computing semantic relatedness of natural language texts requires access to vast amounts of commonsense and domainspecific world knowledge. We propose Explicit Semantic Analysis (ESA), a novel method that represents the meaning of texts in a highdimensional space of concepts derived from
Reversible jump Markov chain Monte Carlo computation and Bayesian model determination
 Biometrika
, 1995
"... Markov chain Monte Carlo methods for Bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some xed standard underlying measure. They have therefore not been available for application to Bayesian model determi ..."
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Cited by 1345 (23 self)
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determination, where the dimensionality of the parameter vector is typically not xed. This article proposes a new framework for the construction of reversible Markov chain samplers that jump between parameter subspaces of di ering dimensionality, which is exible and entirely constructive. It should therefore
Training Linear SVMs in Linear Time
, 2006
"... Linear Support Vector Machines (SVMs) have become one of the most prominent machine learning techniques for highdimensional sparse data commonly encountered in applications like text classification, wordsense disambiguation, and drug design. These applications involve a large number of examples n ..."
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Cited by 549 (6 self)
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Linear Support Vector Machines (SVMs) have become one of the most prominent machine learning techniques for highdimensional sparse data commonly encountered in applications like text classification, wordsense disambiguation, and drug design. These applications involve a large number of examples n
Maxmargin Markov networks
, 2003
"... In typical classification tasks, we seek a function which assigns a label to a single object. Kernelbased approaches, such as support vector machines (SVMs), which maximize the margin of confidence of the classifier, are the method of choice for many such tasks. Their popularity stems both from the ..."
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Cited by 604 (15 self)
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In typical classification tasks, we seek a function which assigns a label to a single object. Kernelbased approaches, such as support vector machines (SVMs), which maximize the margin of confidence of the classifier, are the method of choice for many such tasks. Their popularity stems both from
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