Low-rank optimization for distance matrix completion
This work addresses distance matrix completion for high-dimensional data analysis, but it appears incremental as it builds on existing low-rank optimization methods.
The paper tackles the problem of recovering missing entries in distance matrices when the embedding space dimension is unknown but small, focusing on high-dimensional settings, and proposes two efficient algorithms that monotonically converge to a global solution, with numerical experiments showing good performance on benchmarks.
This paper addresses the problem of low-rank distance matrix completion. This problem amounts to recover the missing entries of a distance matrix when the dimension of the data embedding space is possibly unknown but small compared to the number of considered data points. The focus is on high-dimensional problems. We recast the considered problem into an optimization problem over the set of low-rank positive semidefinite matrices and propose two efficient algorithms for low-rank distance matrix completion. In addition, we propose a strategy to determine the dimension of the embedding space. The resulting algorithms scale to high-dimensional problems and monotonically converge to a global solution of the problem. Finally, numerical experiments illustrate the good performance of the proposed algorithms on benchmarks.