# Hierarchical Nearest Neighbor Graph Embedding for Efficient Dimensionality Reduction

arXiv: https://arxiv.org/abs/2203.12997 · HTML: https://mlsanity.com/paper/2203.12997/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 40 references that are in the map.
- First posted on arXiv 24 Mar 2022.

## Builds on (most cited first, 11 of 11)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Efficient and robust approximate nearest neighbor search using Hierarchical Navigable Small World graphs](https://mlsanity.com/paper/1603.09320/) (2016)
- [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)
- [Parametric UMAP embeddings for representation and semi-supervised learning](https://mlsanity.com/paper/2009.12981/) (2020)
- [Efficient Parameter-free Clustering Using First Neighbor Relations](https://mlsanity.com/paper/1902.11266/) (2019)
- [Visualizing Large-scale and High-dimensional Data](https://mlsanity.com/paper/1602.00370/) (2016)
- [Efficient Algorithms for t-distributed Stochastic Neighborhood Embedding](https://mlsanity.com/paper/1712.09005/) (2017)
- [TriMap: Large-scale Dimensionality Reduction Using Triplets](https://mlsanity.com/paper/1910.00204/) (2019)
- [Empirical complexity of comparator-based nearest neighbor descent](https://mlsanity.com/paper/2202.00517/) (2022)

## Built on by (most cited first, 14 of 14)

- [Panoramic Panoptic Segmentation: Insights Into Surrounding Parsing for Mobile Agents via Unsupervised Contrastive Learning](https://mlsanity.com/paper/2206.10711/) (2022)
- [Dimension Reduction with Locally Adjusted Graphs](https://mlsanity.com/paper/2412.15426/) (2024)
- [Uncovering the Inner Workings of STEGO for Safe Unsupervised Semantic Segmentation](https://mlsanity.com/paper/2304.07314/) (2023)
- [DiffAug: Enhance Unsupervised Contrastive Learning with Domain-Knowledge-Free Diffusion-based Data Augmentation](https://mlsanity.com/paper/2309.07909/) (2023)
- [Interpretable Dimensionality Reduction by Feature Preserving Manifold Approximation and Projection](https://mlsanity.com/paper/2211.09321/) (2022)
- [Curvature Augmented Manifold Embedding and Learning](https://mlsanity.com/paper/2403.14813/) (2024)
- [Task2Box: Box Embeddings for Modeling Asymmetric Task Relationships](https://mlsanity.com/paper/2403.17173/) (2024)
- [MoE-Enhanced Explainable Deep Manifold Transformation for Complex Data Embedding and Visualization](https://mlsanity.com/paper/2410.19504/) (2024)
- [Muscles in Time: Learning to Understand Human Motion by Simulating Muscle Activations](https://mlsanity.com/paper/2411.00128/) (2024)
- [A survey of manifold learning and its applications for multimedia](https://mlsanity.com/paper/2310.12986/) (2023)
- [OmniFall: From Staged Through Synthetic to Wild, A Unified Multi-Domain Dataset for Robust Fall Detection](https://mlsanity.com/paper/2505.19889/) (2025)
- [LLM-Guided Taxonomy and Hierarchical Uncertainty for 3D Point Cloud Active Learning](https://mlsanity.com/paper/2505.18924/) (2025)
- [The Rashomon Effect for Visualizing High-Dimensional Data](https://mlsanity.com/paper/2604.00485/) (2026)
- [CosMAP: Contrastive Manifold Approximation and Projection for Dimensionality Reduction of Omics and Genealogical Data](https://mlsanity.com/paper/2608.11269/) (2026)

## Abstract (arXiv)

Dimensionality reduction is crucial both for visualization and preprocessing high dimensional data for machine learning. We introduce a novel method based on a hierarchy built on 1-nearest neighbor graphs in the original space which is used to preserve the grouping properties of the data distribution on multiple levels. The core of the proposal is an optimization-free projection that is competitive with the latest versions of t-SNE and UMAP in performance and visualization quality while being an order of magnitude faster in run-time. Furthermore, its interpretable mechanics, the ability to project new data, and the natural separation of data clusters in visualizations make it a general purpose unsupervised dimension reduction technique. In the paper, we argue about the soundness of the proposed method and evaluate it on a diverse collection of datasets with sizes varying from 1K to 11M samples and dimensions from 28 to 16K. We perform comparisons with other state-of-the-art methods on multiple metrics and target dimensions highlighting its efficiency and performance. Code is available at https://github.com/koulakis/h-nne