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113,191
The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted LowRank Matrices
, 2009
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Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming
 Journal of the ACM
, 1995
"... We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution ..."
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Cited by 1231 (13 self)
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We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds
Learning the Kernel Matrix with SemiDefinite Programming
, 2002
"... Kernelbased learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information ..."
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Cited by 780 (22 self)
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is contained in the socalled kernel matrix, a symmetric and positive definite matrix that encodes the relative positions of all points. Specifying this matrix amounts to specifying the geometry of the embedding space and inducing a notion of similarity in the input spaceclassical model selection
LOWRANK OPTIMIZATION ON THE CONE OF POSITIVE SEMIDEFINITE MATRICES ∗
"... Abstract. We propose an algorithm for solving optimization problems defined on a subset of the cone of symmetric positive semidefinite matrices. This algorithm relies on the factorization X = YYT, where the number of columns of Y fixes an upper bound on the rank of the positive semidefinite matrix X ..."
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Cited by 28 (6 self)
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is evaluated on two applications: the maximal cut of a graph and the problem of sparse principal component analysis. Key words. lowrank constraints, cone of symmetric positive definite matrices, Riemannian quotient manifold, sparse principal component analysis, maximumcut algorithms, largescale algorithms
Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
 SIAM Journal on Optimization
, 1993
"... We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to S ..."
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Cited by 557 (12 self)
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We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized
Finding community structure in networks using the eigenvectors of matrices
, 2006
"... We consider the problem of detecting communities or modules in networks, groups of vertices with a higherthanaverage density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as “modularity ” over possible div ..."
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Cited by 500 (0 self)
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number of possible algorithms for detecting community structure, as well as several other results, including a spectral measure of bipartite structure in networks and a new centrality measure that identifies those vertices that occupy central positions within the communities to which they belong
Learning lowrank kernel matrices
 In ICML
, 2006
"... Kernel learning plays an important role in many machine learning tasks. However, algorithms for learning a kernel matrix often scale poorly, with running times that are cubic in the number of data points. In this paper, we propose efficient algorithms for learning lowrank kernel matrices; our algori ..."
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Cited by 48 (8 self)
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algorithms scale linearly in the number of data points and quadratically in the rank of the kernel. We introduce and employ Bregman matrix divergences for rankdeficient matrices—these divergences are natural for our problem since they preserve the rank as well as positive semidefiniteness of the kernel
Approximating Semidefinite Programs in Sublinear Time
"... In recent years semidefinite optimization has become a tool of major importance in various optimization and machine learning problems. In many of these problems the amount of data in practice is so large that there is a constant need for faster algorithms. In this work we present the first sublinear ..."
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Cited by 9 (3 self)
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sublinear time approximation algorithm for semidefinite programs which we believe may be useful for such problems in which the size of data may cause even linear time algorithms to have prohibitive running times in practice. We present the algorithm and its analysis alongside with some theoretical lower
Time Varying World Market Integration
 Journal of Finance
, 1995
"... We propose a measure of capital market integration arising from a conditional regimeswitching model. Our measure allows us to describe expected returns in countries that are segmented from world capital markets in one part of the sample and become integrated later in the sample. We find that a numb ..."
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Cited by 527 (39 self)
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number of emerging markets exhibit timevarying integration. Some markets appear more integrated than one might expect based on prior knowledge of investment restrictions. Other markets appear segmented even though foreigners have relatively free access to their capital markets. While there is a
Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones
, 1998
"... SeDuMi is an addon for MATLAB, that lets you solve optimization problems with linear, quadratic and semidefiniteness constraints. It is possible to have complex valued data and variables in SeDuMi. Moreover, large scale optimization problems are solved efficiently, by exploiting sparsity. This pape ..."
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Cited by 1334 (4 self)
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SeDuMi is an addon for MATLAB, that lets you solve optimization problems with linear, quadratic and semidefiniteness constraints. It is possible to have complex valued data and variables in SeDuMi. Moreover, large scale optimization problems are solved efficiently, by exploiting sparsity
Results 1  10
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113,191