t-SNE and UMAP: When Linear Methods Aren't Enough

In Part 2, we covered PCA - the workhorse of dimensionality reduction. It's fast, interpretable, and it finds the axes of greatest variation in your data. But we ended on its biggest limitation: PCA only sees straight lines. Biology doesn't work in straight lines.

Cell differentiation bends. Activation states form gradients that curve through gene expression space. A T cell moving from naive to effector to exhausted doesn't travel in a single direction, it follows a trajectory that twists and branches. PCA flattens all of that into a linear projection, and the result is often a blobby mess where real structure gets lost.

That's where t-SNE and UMAP come in. They're built to find exactly the kind of curved, branching, nonlinear structure that PCA misses.

The neighborhood principle

Both t-SNE and UMAP work on the same core idea, and it's surprisingly intuitive.

Forget about preserving global distances or finding axes of variation. Instead, think about neighborhoods. For every cell in your dataset, these methods ask: who are this cell's closest neighbors in the original high-dimensional space? Then they try to arrange all the cells on a 2D plot so that those neighborhood relationships are preserved as faithfully as possible.

Think of it like seating a wedding reception. You have 200 guests. In the “real world” (high-dimensional space), you know who's close to whom - family clusters, friend groups, work colleagues. Your job is to arrange tables in a room (2D space) so that people who are close in real life end up sitting near each other. You can't perfectly preserve every relationship, the room is smaller than reality, but you can make sure that tight-knit groups stay together.

That's what these methods do. Cells that are similar across thousands of genes end up near each other on the plot. Cells that are different end up far apart. And because the algorithm doesn't insist on straight-line axes, it can capture curves, branches, and clusters of any shape.

t-SNE vs. UMAP: the practical differences

Both methods use the neighborhood principle, but they differ in ways that matter for your analysis.

t-SNE was the standard for years. It produces beautiful, well-separated clusters and has a distinctive look, tight islands with clear gaps between them. But it has real drawbacks. It's slow on large datasets. It doesn't preserve global structure well, meaning the relative positions of clusters on the plot are essentially arbitrary. Two clusters being close together on a t-SNE doesn't mean those cell types are biologically related. And running t-SNE twice on the same data with different random seeds can give you plots that look completely different.

UMAP has largely replaced t-SNE in most single-cell workflows, and for good reason. It's faster, it scales better to large datasets, and it does a better job preserving global structure, meaning that if two clusters are near each other on a UMAP, there's some reason to think those populations are related (though you should still verify this biologically). UMAP also tends to preserve continuous trajectories better, which matters if you're studying differentiation or activation states.