Smoothed Least-Absolute Conditional Multidimensional Scaling via Iteratively Reweighted Majorization

Abstract

Conditional multidimensional scaling combines latent coordinates with observed covariates to fit pairwise dissimilarities. We develop a smoothed l1 formulation using the shifted Charbonnier loss. We prove residualwise sharpness of the quadratic loss majorizer, monotonicity, compact containment, and stationarity of noncollapsed accumulation points. A uniform additive bound quantifies approximation to exact least-absolute conditional stress. The experiments use paired contamination, separately calibrated loss parameters, combined-configuration recovery, and direct checks of the theorem's inequalities.

arXiv comment33 pages, 6 figures, 8 tables