# A general framework for adaptive nonparametric dimensionality reduction

## TL;DR

This paper introduces a framework that adapts dimensionality reduction methods by automatically choosing optimal local structures, improving data projections.

## Contribution

The novel contribution is using an intrinsic dimension estimator to automatically tune neighborhood sizes in nonparametric dimensionality reduction.

## Key findings

- The adaptive framework significantly improves projection methods on real and simulated datasets.
- Improvements are measurable via quantitative metrics and visualization quality.
- The method optimizes hyperparameters for algorithms relying on local neighborhood structures.

## Abstract

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.