This paper addresses the problem of low-rank distance matrix completion. Thisproblem amounts to recover the missing entries of a distance matrix when thedimension of the data embedding space is possibly unknown but small compared tothe number of considered data points. The focus is on high-dimensionalproblems. We recast the considered problem into an optimization problem overthe set of low-rank positive semidefinite matrices and propose two efficientalgorithms for low-rank distance matrix completion. In addition, we propose astrategy to determine the dimension of the embedding space. The resultingalgorithms scale to high-dimensional problems and monotonically converge to aglobal solution of the problem. Finally, numerical experiments illustrate thegood performance of the proposed algorithms on benchmarks.
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