
Lowrank Matrix Completion in a General Nonorthogonal Basis
This paper considers theoretical analysis of recovering a low rank matri...
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Inverse Kinematics as LowRank Euclidean Distance Matrix Completion
The majority of inverse kinematics (IK) algorithms search for solutions ...
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Localization from Incomplete Euclidean Distance Matrix: Performance Analysis for the SVDMDS Approach
Localizing a cloud of points from noisy measurements of a subset of pair...
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A Characterization of Deterministic Sampling Patterns for LowRank Matrix Completion
Lowrank matrix completion (LRMC) problems arise in a wide variety of ap...
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Nonlinear Mapping and Distance Geometry
Distance Geometry Problem (DGP) and Nonlinear Mapping (NLM) are two well...
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Image Tag Completion by Lowrank Factorization with Dual Reconstruction Structure Preserved
A novel tag completion algorithm is proposed in this paper, which is des...
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Exact Reconstruction of Euclidean Distance Geometry Problem Using Lowrank Matrix Completion
The Euclidean distance geometry problem arises in a wide variety of applications, from determining molecular conformations in computational chemistry to localization in sensor networks. When the distance information is incomplete, the problem can be formulated as a nuclear norm minimization problem. In this paper, this minimization program is recast as a matrix completion problem of a lowrank r Gram matrix with respect to a suitable basis. The well known restricted isometry property can not be satisfied in the scenario. Instead, a dual basis approach is introduced to theoretically analyze the reconstruction problem. If the Gram matrix satisfies certain coherence conditions with parameter ν, the main result shows that the underlying configuration of n points can be recovered with very high probability from O(nrν^2(n)) uniformly random samples. Computationally, simple and fast algorithms are designed to solve the Euclidean distance geometry problem. Numerical tests on different three dimensional data and protein molecules validate effectiveness and efficiency of the proposed algorithms.
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