# Dimension Reduction with Prior Information for Knowledge Discovery

arXiv: https://arxiv.org/abs/2111.13646 · HTML: https://mlsanity.com/paper/2111.13646/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 64 references that are in the map.
- First posted on arXiv 26 Nov 2021.

## Builds on (most cited first, 4 of 4)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Parametric UMAP embeddings for representation and semi-supervised learning](https://mlsanity.com/paper/2009.12981/) (2020)
- [Interactive Dimensionality Reduction for Comparative Analysis](https://mlsanity.com/paper/2106.15481/) (2021)
- [Explaining dimensionality reduction results using Shapley values](https://mlsanity.com/paper/2103.05678/) (2021)

## Built on by (most cited first, 3 of 3)

- [MoE-Enhanced Explainable Deep Manifold Transformation for Complex Data Embedding and Visualization](https://mlsanity.com/paper/2410.19504/) (2024)
- [Conditional Multidimensional Scaling with Incomplete Conditioning Data](https://mlsanity.com/paper/2509.16627/) (2025)
- [Robust conditional dimension reduction for dissimilarity data](https://mlsanity.com/paper/2609.06284/) (2026)

## Abstract (arXiv)

This paper addresses the problem of mapping high-dimensional data to a low-dimensional space, in the presence of other known features. This problem is ubiquitous in science and engineering as there are often controllable/measurable features in most applications. To solve this problem, this paper proposes a broad class of methods, which is referred to as conditional multidimensional scaling (MDS). An algorithm for optimizing the objective function of conditional MDS is also developed. The convergence of this algorithm is proven under mild assumptions. Conditional MDS is illustrated with kinship terms, facial expressions, textile fabrics, car-brand perception, and cylinder machining examples. These examples demonstrate the advantages of conditional MDS over conventional dimension reduction in improving the estimation quality of the reduced-dimension space and simplifying visualization and knowledge discovery tasks. Computer codes for this work are available in the open-source cml R package.