Hierarchical Nearest Neighbor Graph Embedding for Efficient Dimensionality Reduction

TL;DR

The paper introduces a hierarchical, optimization-free dimensionality reduction method based on nearest neighbor graphs, offering competitive visualization quality and speed, with interpretability and scalability advantages.

Contribution

It presents a novel hierarchical graph-based approach that is faster and more interpretable than existing methods like t-SNE and UMAP.

Findings

Achieves comparable visualization quality to t-SNE and UMAP.

Runs an order of magnitude faster than existing methods.

Effectively scales to datasets with up to 11 million samples.

Abstract

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