# Opening the black-box of Neighbor Embedding with Hotelling's T2 statistic and Q-residuals

arXiv: https://arxiv.org/abs/2209.01984 · HTML: https://mlsanity.com/paper/2209.01984/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 16 references that are in the map.
- First posted on arXiv 5 Sep 2022.

## Builds on (most cited first, 5 of 5)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [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)
- [Embedding Projector: Interactive Visualization and Interpretation of Embeddings](https://mlsanity.com/paper/1611.05469/) (2016)
- [t-viSNE: Interactive Assessment and Interpretation of t-SNE Projections](https://mlsanity.com/paper/2002.06910/) (2020)
- [An Empirical Evaluation of the t-SNE Algorithm for Data Visualization in Structural Engineering](https://mlsanity.com/paper/2109.08795/) (2021)

## Abstract (arXiv)

In contrast to classical techniques for exploratory analysis of high-dimensional data sets, such as principal component analysis (PCA), neighbor embedding (NE) techniques tend to better preserve the local structure/topology of high-dimensional data. However, the ability to preserve local structure comes at the expense of interpretability: Techniques such as t-Distributed Stochastic Neighbor Embedding (t-SNE) or Uniform Manifold Approximation and Projection (UMAP) do not give insights into which input variables underlie the topological (cluster) structure seen in the corresponding embedding. We here propose different "tricks" from the chemometrics field based on PCA, Q-residuals and Hotelling's T2 contributions in combination with novel visualization approaches to derive local and global explanations of neighbor embedding. We show how our approach is capable of identifying discriminatory features between groups of data points that remain unnoticed when exploring NEs using standard univariate or multivariate approaches.