t-SNE, UMAP and manifold learning
High-dimensional data often lives near a curved, low-dimensional surface. Why PCA can't flatten it, how Isomap and t-SNE try, what t-SNE's perplexity and heavy tails do, where UMAP fits in, and how to read these beautiful plots without being fooled by them.
60 min
After this lesson you can
- State the manifold hypothesis and explain why a linear projection can't unroll a curved manifold
- Describe classical MDS and Isomap, and the short-circuit failure of neighbourhood graphs
- Derive the t-SNE objective, explain perplexity, and say why the embedding uses a heavy-tailed distribution
- Implement exact t-SNE in NumPy
- Read a t-SNE or UMAP plot correctly, knowing what cluster sizes, gaps and shapes can and cannot mean
In this lesson
- The manifold hypothesis
- t-SNE: match the neighbours, not the distances
- UMAP
- How to read (and misread) these plots
This lesson is part of Descent Pro
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