Robust Multi-Dimensional Scaling via Accelerated Alternating Projections
This work addresses robust localization in data analysis, offering an incremental improvement for handling outliers in distance-based methods.
The paper tackles the robust multi-dimensional scaling problem by localizing point locations from pairwise distances corrupted with outliers, proposing an alternating projection algorithm with tangent space acceleration that achieves linear convergence under sparse outliers and shows state-of-the-art performance in numerical experiments.
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.