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On Least Squares Euclidean Distance Matrix Approximation and Completion
"... The Euclidean distance matrix approximation problem as well as the completion problem have received a lot of attention in recent years because of their many important applications. In contrast to the many interesting but often sophisticated algorithms proposed in the literature, this paper o#ers a r ..."
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The Euclidean distance matrix approximation problem as well as the completion problem have received a lot of attention in recent years because of their many important applications. In contrast to the many interesting but often sophisticated algorithms proposed in the literature, this paper o#ers a
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
1 Euclidean Distance Matrix Completion for Adhoc Microphone Array Calibration
"... Abstract—This paper addresses application of missing data recovery via matrix completion for audio sensor network. We propose a method based on Euclidean distance matrix completion for adhoc microphone array location calibration. This method can calibrate a full network from partial connectivity in ..."
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Abstract—This paper addresses application of missing data recovery via matrix completion for audio sensor network. We propose a method based on Euclidean distance matrix completion for adhoc microphone array location calibration. This method can calibrate a full network from partial connectivity
Sensor Network Localization, Euclidean Distance Matrix. Completions, and Graph Realization
, 2008
"... ..."
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
Ad Hoc Microphone Array Calibration: Euclidean Distance Matrix Completion Algorithm and Theoretical Guarantees
, 2014
"... This paper addresses the problem of ad hoc microphone array calibration where only partial information about the distances between microphones is available. We construct a matrix consisting of the pairwise distances and propose to estimate the missing entries based on a novel Euclidean distance matr ..."
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This paper addresses the problem of ad hoc microphone array calibration where only partial information about the distances between microphones is available. We construct a matrix consisting of the pairwise distances and propose to estimate the missing entries based on a novel Euclidean distance
Universal Rigidity of Bar Frameworks in General Position: A Euclidean Distance Matrix Approach
"... ar ..."
On the Nonnegative Rank of Euclidean Distance Matrices
"... The Euclidean distance matrix for n distinct points in R r is generically of rank r + 2. It is shown in this paper via a geometric argument that its nonnegative rank for the case r = 1 is generically n. Key words: Euclidean distance matrix, nonnegative rank factorization, nonnegative rank 1. ..."
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Cited by 6 (0 self)
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The Euclidean distance matrix for n distinct points in R r is generically of rank r + 2. It is shown in this paper via a geometric argument that its nonnegative rank for the case r = 1 is generically n. Key words: Euclidean distance matrix, nonnegative rank factorization, nonnegative rank 1.
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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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
Results 1  10
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