Robust Multi-Dimensional Scaling via Accelerated Alternating Projections

TL;DR

This paper introduces an accelerated alternating projection algorithm for robust multi-dimensional scaling that effectively localizes points from potentially corrupted pairwise distances, demonstrating state-of-the-art performance.

Contribution

It proposes a novel accelerated alternating projection method for RMDS, inspired by classic MDS and RPCA theories, with proven linear convergence under certain conditions.

Findings

Algorithm achieves linear convergence when outliers are sparse.

Numerical experiments confirm state-of-the-art performance.

Method effectively localizes points from corrupted distance data.

Abstract

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.