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192
Canonical correlation analysis; An overview with application to learning methods
, 2007
"... We present a general method using kernel Canonical Correlation Analysis to learn a semantic representation to web images and their associated text. The semantic space provides a common representation and enables a comparison between the text and images. In the experiments we look at two approaches o ..."
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Cited by 162 (14 self)
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We present a general method using kernel Canonical Correlation Analysis to learn a semantic representation to web images and their associated text. The semantic space provides a common representation and enables a comparison between the text and images. In the experiments we look at two approaches of retrieving images based only on their content from a text query. We compare the approaches against a standard crossrepresentation retrieval technique known as the Generalised Vector Space Model.
Development of Parallel Methods for a 1024Processor Hypercube
 SIAM Journal on Scientific and Statistical Computing
, 1988
"... paper. JLG 1995) ..."
Estimating differential quantities using polynomial fitting of osculating jets
"... This paper addresses the pointwise estimation of differential properties of a smooth manifold S —a curve in the plane or a surface in 3D — assuming a point cloud sampled over S is provided. The method consists of fitting the local representation of the manifold using a jet, and either interpolation ..."
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Cited by 87 (2 self)
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This paper addresses the pointwise estimation of differential properties of a smooth manifold S —a curve in the plane or a surface in 3D — assuming a point cloud sampled over S is provided. The method consists of fitting the local representation of the manifold using a jet, and either interpolation or approximation. A jet is a truncated Taylor expansion, and the incentive for using jets is that they encode all local geometric quantities —such as normal, curvatures, extrema of curvature. On the way to using jets, the question of estimating differential properties is recasted into the more general framework of multivariate interpolation / approximation, a wellstudied problem in numerical analysis. On a theoretical perspective, we prove several convergence results when the samples get denser. For curves and surfaces, these results involve asymptotic estimates with convergence rates depending upon the degree of the jet used. For the particular case of curves, an error bound is also derived. To the best of our knowledge, these results are among the first ones providing accurate estimates for differential quantities of order three and more. On the algorithmic side, we solve the interpolation/approximation problem using Vandermonde systems. Experimental results for surfaces of R 3 are reported. These experiments illustrate the asymptotic convergence results, but also the robustness of the methods on general Computer Graphics models.
Electrical Impedance Tomography
 SIAM REVIEW
, 1999
"... This paper surveys some of the work our group has done in electrical impedance tomography. ..."
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Cited by 82 (1 self)
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This paper surveys some of the work our group has done in electrical impedance tomography.
A Practical Approach to Dynamic Load Balancing
, 1995
"... algorithm for load balancing. The following sections elaborate on each step in the above algorithm, presenting various design decisions that one encounters. 2.1 Load Evaluation The efficacy of any load balancing scheme is directly dependent on the quality of load evaluation. Good load measurement i ..."
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Cited by 69 (7 self)
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algorithm for load balancing. The following sections elaborate on each step in the above algorithm, presenting various design decisions that one encounters. 2.1 Load Evaluation The efficacy of any load balancing scheme is directly dependent on the quality of load evaluation. Good load measurement is necessary both to determine that a load imbalance exists and to calculate how much work should be transferred to alleviate that imbalance. One can determine the load associated with a given task analytically, empirically or by a combination of those two methods. 6 CHAPTER 2. METHODOLOGY 2.1.1 Analytic Load Evaluation The load for a task is estimated based on knowledge of the time complexity of the algorithm(s) that task is executing along with the data structures on which it is operating. For example, if one knew that a task involved merge sorting a list of 64 elements, one might estimate the load to be 384, since merge sort is an O(N log 2 N) sorting algorithm, and since 64 log 2 (64) ...
Pattern clustering by multivariate mixture analysis
 Multivariate Behavioral Research
, 1970
"... Cluster analysis is reformulated as a problem of estimating the parameters of a mixture of multivariate distributions. The maximumlikelihood theory and numerical solution techniques are developed for a fairly general class of distributions. The theory is applied to mixtures of multivariate normal ..."
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Cited by 67 (0 self)
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Cluster analysis is reformulated as a problem of estimating the parameters of a mixture of multivariate distributions. The maximumlikelihood theory and numerical solution techniques are developed for a fairly general class of distributions. The theory is applied to mixtures of multivariate normals (“NORMIX”) and mixtures of multivariate Bernoulli distributions (“Latent Classes”). The feasibility of the procedures is demonstrated by two examples of computer solutions for normal mixture models of the Fisher Iris data and of artificially generated clusters with unequal covariance matrices. This paper is addressed to the problem which has been variously called cluster analysis, Qanalysis, typology, grouping, clumping, classif ication, numerical taxonomy, and unsupervised pattern recognition. The variety of nomenclature may be due to the importance of the subject in such diverse fields as psychology, biology, signal detection, artificial intelligence, and information retrieval.
Convergence analysis of pseudotransient continuation
 SIAM J. Num. Anal
, 1998
"... Abstract. Pseudotransient continuation (Ψtc) is a wellknown and physically motivated technique for computation of steady state solutions of timedependent partial differential equations. Standard globalization strategies such as line search or trust region methods often stagnate at local minima. Ψ ..."
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Cited by 61 (25 self)
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Abstract. Pseudotransient continuation (Ψtc) is a wellknown and physically motivated technique for computation of steady state solutions of timedependent partial differential equations. Standard globalization strategies such as line search or trust region methods often stagnate at local minima. Ψtc succeeds in many of these cases by taking advantage of the underlying PDE structure of the problem. Though widely employed, the convergence of Ψtc is rarely discussed. In this paper we prove convergence for a generic form of Ψtc and illustrate it with two practical strategies.
Elimination algorithms for data flow analysis
 ACM Computing Surveys
, 1986
"... A unified model of a family of data flow algorithms, called elimination methods, is presented. The algorithms, which gather information about the definition and use of data in a program or a set of programs, are characterized by the manner in which they solve the systems of equations that describe d ..."
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Cited by 53 (8 self)
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A unified model of a family of data flow algorithms, called elimination methods, is presented. The algorithms, which gather information about the definition and use of data in a program or a set of programs, are characterized by the manner in which they solve the systems of equations that describe data flow problems of interest. The unified model
Efficient Solution Of Parabolic Equations By Krylov Approximation Methods
 SIAM J. Sci. Statist. Comput
, 1992
"... . In this paper we take a new look at numerical techniques for solving parabolic equations by the method of lines. The main motivation for the proposed approach is the possibility of exploiting a high degree of parallelism in a simple manner. The basic idea of the method is to approximate the action ..."
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Cited by 49 (3 self)
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. In this paper we take a new look at numerical techniques for solving parabolic equations by the method of lines. The main motivation for the proposed approach is the possibility of exploiting a high degree of parallelism in a simple manner. The basic idea of the method is to approximate the action of the evolution operator on a given state vector by means of a projection process onto a Krylov subspace. Thus, the resulting approximation consists of applying an evolution operator of very small dimension to a known vector which is, in turn, computed accurately by exploiting highorder rational Chebyshev and Pad'e approximations to the exponential. Because the rational approximation is only applied to a small matrix, the only operations required with the original large matrix are matrixbyvector multiplications, and as a result the algorithm can easily be parallelized and vectorized. Further parallelism is introduced by expanding the rational approximations into partial fractions. Some ...
RungeKutta Methods in Optimal Control and the Transformed Adjoint System
 Numerische Mathematik
, 1999
"... The convergence rate is determined for RungeKutta discretizations of nonlinear control problems. The analysis utilizes a connection between the KuhnTucker multipliers for the discrete problem and the adjoint variables associated with the continuous minimum principle. This connection can also be exp ..."
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Cited by 47 (5 self)
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The convergence rate is determined for RungeKutta discretizations of nonlinear control problems. The analysis utilizes a connection between the KuhnTucker multipliers for the discrete problem and the adjoint variables associated with the continuous minimum principle. This connection can also be exploited in numerical solution techniques that require the gradient of the discrete cost function.