Robust conditional dimension reduction for dissimilarity data

• URL: http://arxiv.org/abs/2609.06284v1
• Date: Sat, 05 Sep 2026 22:36:29 GMT
• Title: Robust conditional dimension reduction for dissimilarity data
• Abstract summary: Conditional MultidimensionalScaling (cMDS) is a cDR technique that works directly with dissimilarity data.<n>We proposed Robust Multidimensional Scaling (rcMDS) by replacing the squared-stress criterion with a Fair M-estimation objective.<n>We developed a reweighted conditional SMACOF algorithm to optimize this objective.
• Score: 2.361342322155422
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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