Robust Multi-Dimensional Scaling via Accelerated Alternating Projections

• URL: http://arxiv.org/abs/2501.02208v1
• Date: Sat, 04 Jan 2025 06:28:10 GMT
• Title: Robust Multi-Dimensional Scaling via Accelerated Alternating Projections
• Authors: Tong Deng, Tianming Wang,
• Abstract summary: We consider the robust multi-dimensional (RMDS) problem in this paper. Inspired by classic MDSA theories, we propose an alternating projection technique.
• Score: 5.778024594615575
• License:
• 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.

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