# Robust conditional dimension reduction for dissimilarity data

arXiv: https://arxiv.org/abs/2609.06284 · HTML: https://mlsanity.com/paper/2609.06284/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 30 references that are in the map.
- First posted on arXiv 5 Sep 2026.

## Builds on (most cited first, 5 of 5)

- [A State-of-the-Art Survey on Multidimensional Scaling Based Localization Techniques](https://mlsanity.com/paper/1906.03585/) (2019)
- [The Flag Median and FlagIRLS](https://mlsanity.com/paper/2203.04437/) (2022)
- [Dimension Reduction with Prior Information for Knowledge Discovery](https://mlsanity.com/paper/2111.13646/) (2021)
- [Robust Multi-Dimensional Scaling via Accelerated Alternating Projections](https://mlsanity.com/paper/2501.02208/) (2025)
- [l1-norm regularized l1-norm best-fit lines](https://mlsanity.com/paper/2402.16712/) (2024)

## Abstract (arXiv)

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