UMAP and t-SNE: Overview

Multivariate Statistics

umap

tsne

embedding

visualisation

Modern non-linear dimensionality reduction for visualisation: UMAP, t-SNE, and their caveats

Published

April 17, 2026

Introduction

UMAP (uniform manifold approximation and projection) and t-SNE (t-distributed stochastic neighbour embedding) are the dominant non-linear dimensionality-reduction techniques for visualising very high-dimensional data — single-cell RNA sequencing, large image embeddings, language-model representations. They produce striking 2D or 3D scatter plots in which similar observations cluster together, and they are now near-default visualisations in many computational-biology and machine-learning pipelines. They also have well-documented pitfalls, and learning what they do not show is as important as learning to apply them.

Prerequisites

A working understanding of principal components analysis, distance metrics, and the trade-off between preserving local and global structure in a low-dimensional embedding.

Theory

Both methods optimise a 2D or 3D embedding such that pairwise similarities computed in the original high-dimensional space are preserved as well as possible.

t-SNE computes Gaussian-weighted neighbour probabilities in the high-dimensional space, t-distributed neighbour probabilities in the low-dimensional space, and minimises the KL divergence between them. The Student-\(t\) distribution in low dimensions prevents the “crowding problem” (compressing many high-dimensional neighbours into a small low-dimensional area).
UMAP constructs a fuzzy topological representation of the high-dimensional data using local distance scaling, then optimises a similar fuzzy structure in low dimensions via a cross-entropy loss. UMAP is faster, scales better to large \(n\), and is often considered to preserve global structure better than t-SNE.

Both algorithms are stochastic; setting the random seed is required for reproducible figures.

Assumptions

A similarity-preserving 2D / 3D embedding is informative for the inferential question. Both algorithms assume meaningful local structure exists in the data; they do not assume Gaussianity, linearity, or any specific distance metric (UMAP’s metric is configurable).

R Implementation

library(umap); library(Rtsne)

set.seed(2026)
X <- as.matrix(iris[, 1:4])

# UMAP
u <- umap(X)
plot(u$layout, col = iris$Species, pch = 16,
     main = "UMAP of iris")

# t-SNE
t <- Rtsne(X, perplexity = 15, check_duplicates = FALSE)
plot(t$Y, col = iris$Species, pch = 16,
     main = "t-SNE of iris")

Output & Results

Both methods produce 2D coordinates per observation. UMAP and t-SNE both separate the three iris species clearly; differences in the layout (relative cluster positions, cluster sizes) reflect algorithm-specific choices rather than data-driven structure.

Interpretation

A reporting sentence: “UMAP and t-SNE embeddings of the four iris measurements both separate the three species, with setosa well-isolated and versicolor / virginica close but distinguishable; UMAP preserves the inter-cluster gap more faithfully than t-SNE, consistent with its better global-structure properties.” Always describe the algorithm and key hyperparameters in the figure caption; readers should not have to guess.

Practical Tips

Treat distances in the embedding as relative neighbourhoods only; absolute distances and cluster sizes are not meaningful, despite how the visualisation looks.
t-SNE’s perplexity parameter (typically 5–50) sets the effective neighbourhood scale; vary it across at least three values to confirm the structure is robust.
UMAP’s n_neighbors and min_dist control the same trade-offs; defaults work for most data but should be tuned for very small or very large \(n\).
For very high-dimensional input, run PCA first to reduce noise to the top 50 components, then UMAP/t-SNE on the PCA scores; this is the standard pipeline in single-cell analysis.
Cluster sizes in the embedding are meaningless; do not interpret a “small cluster” or “large cluster” as biologically real.
Reproducibility requires a fixed seed and fixed software versions; UMAP results in particular can shift between releases.

R Packages Used

umap for the canonical UMAP implementation; uwot for a faster UMAP variant with more options; Rtsne for the standard t-SNE; M3C and embed for tidymodels-flavoured wrappers; dimRed for a unified interface across UMAP, t-SNE, Isomap, and other non-linear embeddings.