  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.
