UMAP does not preserve global structure any better than t-SNE when using the same initialization

Abstract

One of the most ubiquitous analysis tools employed in single-cell transcriptomics and cytometry is t-distributed stochastic neighbor embedding (t-SNE) [1], used to visualize individual cells as points on a 2D scatter plot such that similar cells are positioned close together. Recently, a related algorithm, called uniform manifold approximation and projection (UMAP) [2] has attracted substantial attention in the single-cell community. In Nature Biotechnology, Becht et al. [3] argued that UMAP is preferable to t-SNE because it better preserves the global structure of the data and is more consistent across runs. Here we show that this alleged superiority of UMAP can be entirely attributed to different choices of initialization in the implementations used by Becht et al.: t-SNE implementations by default used random initialization, while the UMAP implementation used a technique called Laplacian eigenmaps [4] to initialize the embedding. We show that UMAP with random initialization preserves global structure as poorly as t-SNE with random initialization, while t-SNE with informative initialization performs as well as UMAP with informative initialization. Hence, contrary to the claims of Becht et al., their experiments do not demonstrate any advantage of the UMAP algorithm per se, but rather warn against using random initialization.