# Conditional Multidimensional Scaling with Incomplete Conditioning Data

arXiv: https://arxiv.org/abs/2509.16627 · HTML: https://mlsanity.com/paper/2509.16627/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 39 references that are in the map.
- First posted on arXiv 20 Sep 2025.

## Builds on (most cited first, 7 of 7)

- [Parametric UMAP embeddings for representation and semi-supervised learning](https://mlsanity.com/paper/2009.12981/) (2020)
- [New Bounds for Matrix Multiplication: from Alpha to Omega](https://mlsanity.com/paper/2307.07970/) (2023)
- [Impact of signal-to-noise ratio and bandwidth on graph Laplacian spectrum from high-dimensional noisy point cloud](https://mlsanity.com/paper/2011.10725/) (2020)
- [Interactive Dimensionality Reduction for Comparative Analysis](https://mlsanity.com/paper/2106.15481/) (2021)
- [Learning Low-Dimensional Nonlinear Structures from High-Dimensional Noisy Data: An Integral Operator Approach](https://mlsanity.com/paper/2203.00126/) (2022)
- [SLISEMAP: Supervised dimensionality reduction through local explanations](https://mlsanity.com/paper/2201.04455/) (2022)
- [Dimension Reduction with Prior Information for Knowledge Discovery](https://mlsanity.com/paper/2111.13646/) (2021)

## Abstract (arXiv)

Conditional multidimensional scaling seeks for a low-dimensional configuration from pairwise dissimilarities, in the presence of other known features. By taking advantage of available data of the known features, conditional multidimensional scaling improves the estimation quality of the low-dimensional configuration and simplifies knowledge discovery tasks. However, existing conditional multidimensional scaling methods require full data of the known features, which may not be always attainable due to time, cost, and other constraints. This paper proposes a conditional multidimensional scaling method that can learn the low-dimensional configuration when there are missing values in the known features. The method can also impute the missing values, which provides additional insights of the problem. Computer codes of this method are maintained in the cml R package on CRAN.