# A general framework for adaptive nonparametric dimensionality reduction

arXiv: https://arxiv.org/abs/2511.09486 · HTML: https://mlsanity.com/paper/2511.09486/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 30 references that are in the map.
- First posted on arXiv 12 Nov 2025.

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

- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [On Hyperparameter Optimization of Machine Learning Algorithms: Theory and Practice](https://mlsanity.com/paper/2007.15745/) (2020)
- [Deep Dimension Reduction for Supervised Representation Learning](https://mlsanity.com/paper/2006.05865/) (2020)
- [Locally Linear Embedding and its Variants: Tutorial and Survey](https://mlsanity.com/paper/2011.10925/) (2020)
- [A Survey of Dimension Estimation Methods](https://mlsanity.com/paper/2507.13887/) (2025)
- [Scale adaptive and robust intrinsic dimension estimation via optimal neighbourhood identification](https://mlsanity.com/paper/2405.15132/) (2024)

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

- [Psychosis involves a deficit of information compression in connected speech](https://mlsanity.com/paper/2609.15522/) (2026)

## Abstract (arXiv)

Dimensionality reduction is a fundamental task in modern data science. Several projection methods specifically tailored to take into account the non-linearity of the data via local embeddings have been proposed. Such methods are often based on local neighbourhood structures and require tuning the number of neighbours that define this local structure, and the dimensionality of the lower-dimensional space onto which the data are projected. Such choices critically influence the quality of the resulting embedding. In this paper, we exploit a recently proposed intrinsic dimension estimator which also returns the optimal locally adaptive neighbourhood sizes according to some desirable criteria. In principle, this adaptive framework can be employed to perform an optimal hyper-parameter tuning of any dimensionality reduction algorithm that relies on local neighbourhood structures. Numerical experiments on both real-world and simulated datasets show that the proposed method can be used to significantly improve well-known projection methods when employed for various learning tasks, with improvements measurable through both quantitative metrics and the quality of low-dimensional visualizations.