  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
