5.15 Dimensionality reduction
You can compress and visualize high-dimensional data.
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Dimensionality reduction compresses many features into few: PCA for a faithful linear summary with variance-explained as its receipt, t-SNE and UMAP for visualisation. It sits in the unsupervised run because compression is structure-finding. The over-reading of t-SNE plots gets named directly — cluster sizes and between-cluster distances there are artefacts of perplexity settings, and treating the picture as geometry rather than suggestion is how false stories start.
Work through these
PCA: derivation, variance explained, whitening
Finding the directions of greatest variation and keeping the strongest few, with a clear statement of how much information was kept. It is the workhorse and it is linear, which is both its strength and its limit.
t-SNE: perplexity and how to not over-read it
A nonlinear method for visualisation, with one setting that changes the picture substantially and results that must not be over-interpreted. Distances between well-separated groups in the output mean very little.
UMAP and its trade-offs
A more recent alternative that is faster and preserves more of the large-scale structure, with its own settings and its own caveats. It has largely become the default for visualisation.
Feature selection vs. feature extraction
Choosing a subset of existing features and constructing new combined ones are different operations with different consequences for interpretability. Knowing which you need comes before choosing a method.
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Links last checked 29 Aug 2026.
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