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Solving Euclidean Distance Matrix Completion Problems Via Semidefinite Programming
, 1997
"... Given a partial symmetric matrix A with only certain elements specified, the Euclidean distance matrix completion problem (IgDMCP) is to find the unspecified elements of A that make A a Euclidean distance matrix (IgDM). In this paper, we follow the successful approach in [20] and solve the IgDMCP by ..."
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Cited by 82 (15 self)
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Given a partial symmetric matrix A with only certain elements specified, the Euclidean distance matrix completion problem (IgDMCP) is to find the unspecified elements of A that make A a Euclidean distance matrix (IgDM). In this paper, we follow the successful approach in [20] and solve the Ig
Polynomial Instances Of The Positive Semidefinite And Euclidean Distance Matrix Completion Problems
 SIAM J. Matrix Anal. Appl
, 1998
"... Given an undirected graph G = (V; E) with node set V = [1; n], a subset S ` V and a rational vector a 2 Q S[E , the positive semidefinite matrix completion problem consists of determining whether there exists a real symmetric n \Theta n positive semidefinite matrix X = (x ij ) satisfying: x ii = a ..."
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Cited by 17 (6 self)
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= a i (i 2 S) and x ij = a ij (ij 2 E). Similarly, the Euclidean distance matrix completion problem asks for the existence of a Euclidean distance matrix completing a partially defined given matrix. It is not known whether these problems belong to NP. We show here that they can be solved
EUCLIDEAN DISTANCE MATRIX COMPLETION PROBLEMS HAWREN FANG ∗ AND DIANNE P. O’LEARY †
, 2010
"... Abstract. A Euclidean distance matrix is one in which the (i, j) entry specifies the squared distance between particle i and particle j. Given a partiallyspecified symmetric matrix A with zero diagonal, the Euclidean distance matrix completion problem (EDMCP) is to determine the unspecified entries ..."
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Abstract. A Euclidean distance matrix is one in which the (i, j) entry specifies the squared distance between particle i and particle j. Given a partiallyspecified symmetric matrix A with zero diagonal, the Euclidean distance matrix completion problem (EDMCP) is to determine the unspecified
Approximate and exact completion problems for Euclidean distance matrices using semidefinite programming
 Linear Algebra Appl
, 2005
"... Abstract A partial predistance matrix A is a matrix with zero diagonal and with certain elements fixed to given nonnegative values; the other elements are considered free. The Euclidean distance matrix completion problem chooses nonnegative values for the free elements in order to obtain a Euclidea ..."
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Cited by 18 (8 self)
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Abstract A partial predistance matrix A is a matrix with zero diagonal and with certain elements fixed to given nonnegative values; the other elements are considered free. The Euclidean distance matrix completion problem chooses nonnegative values for the free elements in order to obtain a
EUCLIDEAN MATRIX COMPLETION PROBLEMS IN TRACKING AND GEOLOCALIZATON
"... We consider the problem of emitter tracking using received signal strength (RSS) measured at a number of inrange access points (AP) when some of the AP locations are unknown. This can be formulated as a Euclidean distance matrix completion problem (EDMCP) to which an iterative distributed weighted ..."
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Cited by 6 (0 self)
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We consider the problem of emitter tracking using received signal strength (RSS) measured at a number of inrange access points (AP) when some of the AP locations are unknown. This can be formulated as a Euclidean distance matrix completion problem (EDMCP) to which an iterative distributed weighted
A Singular Value Thresholding Algorithm for Matrix Completion
, 2008
"... This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem, and arises in many important applications as in the task of reco ..."
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Cited by 555 (22 self)
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remarkable features making this attractive for lowrank matrix completion problems. The first is that the softthresholding operation is applied to a sparse matrix; the second is that the rank of the iterates {X k} is empirically nondecreasing. Both these facts allow the algorithm to make use of very minimal
Exact Matrix Completion via Convex Optimization
, 2008
"... We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover the entries that we have not seen? We show that one can perfe ..."
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Cited by 873 (26 self)
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We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover the entries that we have not seen? We show that one can
Gromovhausdorff distances in Euclidean spaces
 In Proc. Computer Vision and Pattern Recognition (CVPR
"... The purpose of this paper is to study the relationship between measures of dissimilarity between shapes in Euclidean space. We first concentrate on the pair GromovHausdorff distance (GH) versus Hausdorff distance under the action of Euclidean isometries (EH). Then, we (1) show they are comparable i ..."
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Cited by 18 (6 self)
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the problem of computing GH and EH and the family of Euclidean Distance Matrix completion problems. The second pair of dissimilarity notions we study is the so called LpGromovHausdorff distance versus the Earth Mover’s distance under the action of Euclidean isometries. We obtain results about comparability
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 775 (21 self)
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problems in machine learning. In this paper we show how the kernel matrix can be learned from data via semidefinite programming (SDP) techniques. When applied
Nonnegative matrix factorization with sparseness constraints,”
 Journal of Machine Learning Research,
, 2004
"... Abstract Nonnegative matrix factorization (NMF) is a recently developed technique for finding partsbased, linear representations of nonnegative data. Although it has successfully been applied in several applications, it does not always result in partsbased representations. In this paper, we sho ..."
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Cited by 498 (0 self)
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Abstract Nonnegative matrix factorization (NMF) is a recently developed technique for finding partsbased, linear representations of nonnegative data. Although it has successfully been applied in several applications, it does not always result in partsbased representations. In this paper, we
Results 1  10
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