Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Deng, Tong, Wang, Tianming
Institution: Southwestern University of Finance and Economics
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4406133551