t-SNE

What is t-SNE?

t-SNE places each observation in 2D such that the probability of being a 'neighbour' to other points matches the same probability in high-dim space. The result is a layout where clusters in the original space stay clusters in 2D, but distances *between* clusters are not preserved — so '5cm apart' in t-SNE means nothing.

Two key knobs: perplexity controls the effective number of neighbours per point (default 30); larger perplexity ⇒ more global structure preserved at the cost of local detail. Iterations control convergence.

Compared to PCA: t-SNE handles non-linear structure that PCA misses (curved manifolds, well-separated clusters in high dim). Compared to UMAP: t-SNE has a stronger 'local-focus' bias; UMAP is faster and preserves more global structure.

Important: re-running t-SNE with a different seed gives a different 2D layout. The cluster structure is reproducible but specific point positions are not.

When should I use t-SNE?

• Visualising clusters in high-dimensional data (single-cell RNA-seq, embeddings).
• Discovering whether your data has structure before formal clustering.
• Switch to UMAP for faster runs on large data with similar quality.

What data does it need?

≥ 3 numeric columns + perplexity + optional grouping factor.

What does it report?

2D scatter of t-SNE coordinates, coloured by group when provided.

What does it assume?

• Distance is meaningful in the original space (consider scaling).
• The data has cluster structure (random data gives random-looking layouts).

How do I interpret the result?

Do not interpret distance between clusters as meaningful — only within-cluster compactness and between-cluster separation count.

Cluster sizes in the t-SNE plot don't reflect cluster sizes in the data — t-SNE expands sparse regions and compresses dense ones.

See also

• PCA
• UMAP
• MDS (classical)
• K-means clustering
• Hierarchical clustering (with dendrogram)

References

• van der Maaten & Hinton (2008). Visualizing data using t-SNE. JMLR 9.