  Neighbor embeddings are a family of methods for visualizing complex
high-dimensional datasets using $k$NN graphs. To find the low-dimensional
embedding, these algorithms combine an attractive force between neighboring
pairs of points with a repulsive force between all points. One of the most
popular examples of such algorithms is t-SNE. Here we empirically show that
changing the balance between the attractive and the repulsive forces in t-SNE
using the exaggeration parameter yields a spectrum of embeddings, which is
characterized by a simple trade-off: stronger attraction can better represent
continuous manifold structures, while stronger repulsion can better represent
discrete cluster structures and yields higher $k$NN recall. We find that UMAP
embeddings correspond to t-SNE with increased attraction; mathematical analysis
shows that this is because the negative sampling optimisation strategy employed
by UMAP strongly lowers the effective repulsion. Likewise, ForceAtlas2,
commonly used for visualizing developmental single-cell transcriptomic data,
yields embeddings corresponding to t-SNE with the attraction increased even
more. At the extreme of this spectrum lie Laplacian Eigenmaps. Our results
demonstrate that many prominent neighbor embedding algorithms can be placed
onto the attraction-repulsion spectrum, and highlight the inherent trade-offs
between them.
