# Modern Dimension Reduction

arXiv: https://arxiv.org/abs/2103.06885 · HTML: https://mlsanity.com/paper/2103.06885/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 30 references that are in the map.
- First posted on arXiv 11 Mar 2021.

## Builds on (most cited first, 3 of 3)

- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Exploratory Analysis of Covid-19 Tweets using Topic Modeling, UMAP, and DiGraphs](https://mlsanity.com/paper/2005.03082/) (2020)

## Built on by (most cited first, 2 of 2)

- [Identifying Chemicals Through Dimensionality Reduction](https://mlsanity.com/paper/2211.14708/) (2022)
- [NOFE - Neural Operator Function Embedding](https://mlsanity.com/paper/2605.11970/) (2026)

## Abstract (arXiv)

Data are not only ubiquitous in society, but are increasingly complex both in size and dimensionality. Dimension reduction offers researchers and scholars the ability to make such complex, high dimensional data spaces simpler and more manageable. This Element offers readers a suite of modern unsupervised dimension reduction techniques along with hundreds of lines of R code, to efficiently represent the original high dimensional data space in a simplified, lower dimensional subspace. Launching from the earliest dimension reduction technique principal components analysis and using real social science data, I introduce and walk readers through application of the following techniques: locally linear embedding, t-distributed stochastic neighbor embedding (t-SNE), uniform manifold approximation and projection, self-organizing maps, and deep autoencoders. The result is a well-stocked toolbox of unsupervised algorithms for tackling the complexities of high dimensional data so common in modern society. All code is publicly accessible on Github.