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146
Collaborative Filtering with Privacy
, 2002
"... Serverbased collaborative filtering systems have been very successful in ecommerce and in direct recommendation applications. In future, they have many potential applications in ubiquitous computing settings. But today's schemes have problems such as loss of privacy, favoring retail monopolie ..."
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Cited by 171 (9 self)
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Serverbased collaborative filtering systems have been very successful in ecommerce and in direct recommendation applications. In future, they have many potential applications in ubiquitous computing settings. But today's schemes have problems such as loss of privacy, favoring retail monopolies, and with hampering diffusion of innovations. We propose an alternative model in which users control all of their log data. We describe an algorithm whereby a community of users can compute a public "aggregate" of their data that does not expose individual users' data. The aggregate allows personalized recommendations to be computed by members of the community, or by outsiders. The numerical algorithm is fast, robust and accurate. Our method reduces the collaborative filtering task to an iterative calculation of the aggregate requiring only addition of vectors of user data. Then we use homomorphic encryption to allow sums of encrypted vectors to be computed and decrypted without exposing individual data. We give verification schemes for all parties in the computation. Our system can be implemented with untrusted servers, or with additional infrastructure, as a fully peertopeer (P2P) system. 1
APPROXIMATIONS OF A GINZBURGLANDAU MODEL FOR SUPERCONDUCTING HOLLOW SPHERES BASED ON Spherical Centroidal Voronoi Tessellations
, 2004
"... In this paper the numerical approximations of the GinzburgLandau model for a superconducting hollow spheres are constructed using a gauge invariant discretization on spherical centroidal Voronoi tessellations. A reduced model equation is used on the surface of the sphere which is valid in the thin ..."
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Cited by 125 (24 self)
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In this paper the numerical approximations of the GinzburgLandau model for a superconducting hollow spheres are constructed using a gauge invariant discretization on spherical centroidal Voronoi tessellations. A reduced model equation is used on the surface of the sphere which is valid in the thin spherical shell limit. We present the numerical algorithms and their theoretical convergence as well as interesting numerical results on the vortex configurations. Properties of the spherical centroidal Voronoi tessellations are also utilized to provide a high resolution scheme for computing the supercurrent and the induced magnetic field.
OptimizationBased Reconstruction of a 3D Object From a Single Freehand Line Drawing
 ComputerAided Design
, 1996
"... This paper describes an optimizationbased algorithm for reconstructing a 3D model from a single, inaccurate, 2D edgevertex graph. The graph, which serves as input for the reconstruction process, is obtained from an inaccurate freehand sketch of a 3D wireframe object. Compared with traditional reco ..."
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Cited by 114 (10 self)
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This paper describes an optimizationbased algorithm for reconstructing a 3D model from a single, inaccurate, 2D edgevertex graph. The graph, which serves as input for the reconstruction process, is obtained from an inaccurate freehand sketch of a 3D wireframe object. Compared with traditional reconstruction methods based on line labeling, the proposed approach is more tolerant of faults in handling both inaccurate vertex positioning and sketches with missing entities. Furthermore, the proposed reconstruction method supports a wide scope of general (manifold and nonmanifold) objects containing flat and cylindrical faces. Sketches of wireframe models usually include enough information to reconstruct the complete body. The optimization algorithm is discussed, and examples from a working implementation are given.
Bspline snakes: a flexible tool for parametric contour detection
 IEEE Transactions on Image Processing
"... Abstract—We present a novel formulation for Bspline snakes that can be used as a tool for fast and intuitive contour outlining. We start with a theoretical argument in favor of splines in the traditional formulation by showing that the optimal, curvatureconstrained snake is a cubic spline, irrespe ..."
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Cited by 88 (16 self)
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Abstract—We present a novel formulation for Bspline snakes that can be used as a tool for fast and intuitive contour outlining. We start with a theoretical argument in favor of splines in the traditional formulation by showing that the optimal, curvatureconstrained snake is a cubic spline, irrespective of the form of the external energy field. Unfortunately, such regularized snakes suffer from slow convergence speed because of a large number of control points, as well as from difficulties in determining the weight factors associated to the internal energies of the curve. We therefore propose an alternative formulation in which the intrinsic scale of the spline model is adjusted a priori; this leads to a reduction of the number of parameters to be optimized and eliminates the need for internal energies (i.e., the regularization term). In other words, we are now controlling the elasticity of the spline implicitly and rather intuitively by varying the spacing between the spline knots. The theory is embedded into a multiresolution formulation demonstrating improved stability in noisy image environments. Validation results are presented, comparing the traditional snake using internal energies and the proposed approach without internal energies, showing the similar performance of the latter. Several biomedical examples of applications are included to illustrate the versatility of the method. I.
Optimization techniques on Riemannian manifolds
 FIELDS INSTITUTE COMMUNICATIONS
, 1994
"... The techniques and analysis presented in this paper provide new methods to solve optimization problems posed on Riemannian manifolds. A new point of view is offered for the solution of constrained optimization problems. Some classical optimization techniques on Euclidean space are generalized to Ri ..."
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Cited by 84 (1 self)
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The techniques and analysis presented in this paper provide new methods to solve optimization problems posed on Riemannian manifolds. A new point of view is offered for the solution of constrained optimization problems. Some classical optimization techniques on Euclidean space are generalized to Riemannian manifolds. Several algorithms are presented and their convergence properties are analyzed employing the Riemannian structure of the manifold. Specifically, two apparently new algorithms, which can be thought of as Newton’s method and the conjugate gradient method on Riemannian manifolds, are presented and shown to possess, respectively, quadratic and superlinear convergence. Examples of each method on certain Riemannian manifolds are given with the results of numerical experiments. Rayleigh’s quotient defined on the sphere is one example. It is shown that Newton’s method applied to this function converges cubically, and that the Rayleigh quotient iteration is an efficient approximation of Newton’s method. The Riemannian version of the conjugate gradient method applied to this function gives a new algorithm for finding the eigenvectors corresponding to the extreme eigenvalues of a symmetric matrix. Another example arises from extremizing the function tr ΘTQΘN on the special orthogonal group. In a similar example, it is shown that Newton’s method applied to the sum of the squares of the offdiagonal entries of a symmetric matrix converges cubically.
A Computationally Efficient Feasible Sequential Quadratic Programming Algorithm
 SIAM Journal on Optimization
, 2001
"... . A sequential quadratic programming (SQP) algorithm generating feasible iterates is described and analyzed. What distinguishes this algorithm from previous feasible SQP algorithms proposed by various authors is a reduction in the amount of computation required to generate a new iterate while the pr ..."
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Cited by 56 (0 self)
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. A sequential quadratic programming (SQP) algorithm generating feasible iterates is described and analyzed. What distinguishes this algorithm from previous feasible SQP algorithms proposed by various authors is a reduction in the amount of computation required to generate a new iterate while the proposed scheme still enjoys the same global and fast local convergence properties. A preliminary implementation has been tested and some promising numerical results are reported. Key words. sequential quadratic programming, SQP, feasible iterates, feasible SQP, FSQP AMS subject classifications. 49M37, 65K05, 65K10, 90C30, 90C53 PII. S1052623498344562 1.
Interior Point Methods For Optimal Control Of DiscreteTime Systems
 Journal of Optimization Theory and Applications
, 1993
"... . We show that recently developed interior point methods for quadratic programming and linear complementarity problems can be put to use in solving discretetime optimal control problems, with general pointwise constraints on states and controls. We describe interior point algorithms for a discrete ..."
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Cited by 54 (5 self)
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. We show that recently developed interior point methods for quadratic programming and linear complementarity problems can be put to use in solving discretetime optimal control problems, with general pointwise constraints on states and controls. We describe interior point algorithms for a discrete time linearquadratic regulator problem with mixed state/control constraints, and show how it can be efficiently incorporated into an inexact sequential quadratic programming algorithm for nonlinear problems. The key to the efficiency of the interiorpoint method is the narrowbanded structure of the coefficient matrix which is factorized at each iteration. Key words. interior point algorithms, optimal control, banded linear systems. 1. Introduction. The problem of optimal control of an initial value ordinary differential equation, with Bolza objectives and mixed constraints, is min x;u Z T 0 L(x(t); u(t); t) dt + OE f (x(T )); x(t) = f(x(t); u(t); t); x(0) = x init ; (1.1) g(x(t); u(...
Theory and implementation of numerical methods based on RungeKutta integration for solving optimal control problems
, 1996
"... ..."
APPLYING NEW OPTIMIZATION ALGORITHMS TO MODEL PREDICTIVE CONTROL
"... The connections between optimization and control theory have been explored by many researchers, and optimization algorithms have been applied with success to optimal control. The rapid pace of developments in model predictive control has given rise to a host of new problems to which optimization has ..."
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Cited by 39 (2 self)
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The connections between optimization and control theory have been explored by many researchers, and optimization algorithms have been applied with success to optimal control. The rapid pace of developments in model predictive control has given rise to a host of new problems to which optimization has yet to be applied. Concurrently, developments in optimization, and especially in interiorpoint methods, have produced a new set of algorithms that may be especially helpful in this context. In this paper, we reexamine the relatively simple problem of control of linear processes subject to quadratic objectives and general linear constraints. We show how new algorithms for quadratic programming can be applied efficiently to this problem. The approach extends to several more general problems in straightforward ways.
A New Efficient and Direct Solution for Pose Estimation Using Quadrangular Targets: Algorithm and Evaluation
 IEEE Trans. on Pattern Analysis and Machine Intelligence
, 1995
"... Pose estimation is an important operation for many vision tasks. In this paper, we propose a new algorithm for pose estimation based on the volume measurement of tetrahedra composed of feature point triplets extracted from an arbitrary quadrangular target and the lens center of the vision system. T ..."
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Cited by 34 (0 self)
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Pose estimation is an important operation for many vision tasks. In this paper, we propose a new algorithm for pose estimation based on the volume measurement of tetrahedra composed of feature point triplets extracted from an arbitrary quadrangular target and the lens center of the vision system. The input to this algorithm are the six distances joining all feature pairs and the image coordinates of the quadrangular target. The output of this aigorithm are the effective focal length of the vision system, the interior orientation parameters of the target, the exterior orientation parameters of the camera with respect to an arbitrary coordinate system if the target coordinates are known in this frame, and the final pose of the camera. We have aiso developed a shape restoration technique which is applied prior to pose recovery in order to reduce the effects of inaccuracies caused by image projection.