# Robust Multi-Dimensional Scaling via Accelerated Alternating Projections

arXiv: https://arxiv.org/abs/2501.02208 · HTML: https://mlsanity.com/paper/2501.02208/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jan 2025.

## Built on by (most cited first, 3 of 3)

- [A Dual Basis Approach for Structured Robust Euclidean Distance Geometry](https://mlsanity.com/paper/2505.18414/) (2025)
- [Optimizing Multidimensional Scaling in Gini Metric Spaces](https://mlsanity.com/paper/2605.25124/) (2026)
- [Robust conditional dimension reduction for dissimilarity data](https://mlsanity.com/paper/2609.06284/) (2026)

## Abstract (arXiv)

We consider the robust multi-dimensional scaling (RMDS) problem in this paper. The goal is to localize point locations from pairwise distances that may be corrupted by outliers. Inspired by classic MDS theories, and nonconvex works for the robust principal component analysis (RPCA) problem, we propose an alternating projection based algorithm that is further accelerated by the tangent space projection technique. For the proposed algorithm, if the outliers are sparse enough, we can establish linear convergence of the reconstructed points to the original points after centering and rotation alignment. Numerical experiments verify the state-of-the-art performances of the proposed algorithm.