# Low-rank optimization for distance matrix completion

arXiv: https://arxiv.org/abs/1304.6663 · HTML: https://mlsanity.com/paper/1304.6663/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Apr 2013.

## Built on by (most cited first, 2 of 2)

- [Advancements in Federated Learning: Models, Methods, and Privacy](https://mlsanity.com/paper/2302.11466/) (2023)
- [On Geometric Connections of Embedded and Quotient Geometries in Riemannian Fixed-rank Matrix Optimization](https://mlsanity.com/paper/2110.12121/) (2021)

## Abstract (arXiv)

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.