# Consensus dimension reduction via multi-view learning

arXiv: https://arxiv.org/abs/2512.15802 · HTML: https://mlsanity.com/paper/2512.15802/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 67 references that are in the map.
- First posted on arXiv 16 Dec 2025.

## Builds on (most cited first, 12 of 12)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Understanding How Dimension Reduction Tools Work: An Empirical Approach to Deciphering t-SNE, UMAP, TriMAP, and PaCMAP for Data Visualization](https://mlsanity.com/paper/2012.04456/) (2020)
- [Stability](https://mlsanity.com/paper/1310.0150/) (2013)
- [Veridical Data Science](https://mlsanity.com/paper/1901.08152/) (2019)
- [Stop Misusing t-SNE and UMAP for Visual Analytics](https://mlsanity.com/paper/2506.08725/) (2025)
- [Integrated Principal Components Analysis](https://mlsanity.com/paper/1810.00832/) (2018)
- [Multi-view Data Visualisation via Manifold Learning](https://mlsanity.com/paper/2101.06763/) (2021)
- [A Spectral Method for Assessing and Combining Multiple Data Visualizations](https://mlsanity.com/paper/2210.13711/) (2022)
- [Multidimensional Scaling on Multiple Input Distance Matrices](https://mlsanity.com/paper/1605.00286/) (2016)
- [Unsupervised Manifold Alignment with Joint Multidimensional Scaling](https://mlsanity.com/paper/2207.02968/) (2022)
- [Unsupervised Machine Learning for Scientific Discovery: Workflow and Best Practices](https://mlsanity.com/paper/2506.04553/) (2025)
- [Uncovering smooth structures in single-cell data with PCS-guided neighbor embeddings](https://mlsanity.com/paper/2506.22228/) (2025)

## Built on by (most cited first, 1 of 1)

- [MEDAL: Manifold Embedding Distillation via Autoencoder Learning](https://mlsanity.com/paper/2605.24244/) (2026)

## Abstract (arXiv)

A plethora of dimension reduction methods have been developed to visualize high-dimensional data in low dimensions. However, different dimension reduction methods often output different and possibly conflicting visualizations of the same data. This problem is further exacerbated by the choice of hyperparameters, which may substantially impact the resulting visualization. To obtain a more robust and trustworthy dimension reduction output, we advocate for a consensus approach, which summarizes multiple visualizations into a single consensus dimension reduction visualization. Here, we leverage ideas from multi-view learning in order to identify the patterns that are most stable or shared across the many different dimension reduction visualizations, or views, and subsequently visualize this shared structure in a single low-dimensional plot. We demonstrate that this consensus visualization effectively identifies and preserves the shared low-dimensional data structure through both simulated and real-world case studies. We further highlight our method's robustness to the choice of dimension reduction method and hyperparameters -- a highly-desirable property when working towards trustworthy and reproducible data science.