Robust conditional dimension reduction for dissimilarity data

Xiao Ling; Anh Bui

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arXiv · 2609.06284

Robust conditional dimension reduction for dissimilarity data

Xiao Ling·Anh Bui

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Abstract

Conditional dimension reduction (cDR) learns low-dimensional latent coordinates while accounting for observed covariates that represent known sources of variation in the data. Conditional Multidimensional Scaling (cMDS) is a cDR technique that works directly with dissimilarity data. Its standard squared-stress formulation, however, is sensitive to contaminated dissimilarity, since outliers can dominate the objective and distort the learned configuration. We proposed Robust Conditional Multidimensional Scaling (rcMDS) by replacing the squared-stress criterion with a Fair M-estimation objective. We developed a reweighted conditional SMACOF algorithm to optimize this objective. The proposed algorithm admits computationally tractable updates, and its stabilized objective values decrease monotonically and converge to a finite limit. Experiments on synthetic and real data show that the pro

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Xiao Ling, Anh Bui. 2026-09-05. Robust conditional dimension reduction for dissimilarity data. https://arxiv.org/abs/2609.06284

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