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Leland McInnes, John Healy (2018). Based on topological data analysis. Faster than t-SNE, better at preserving global structure.
Why It Exists
t-SNE is slow on large datasets and doesn't preserve global structure well. UMAP is faster, scales better, and maintains both local and global relationships.
How It Works
Visual Intuition
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# Implementation sketch
The Math Inside
Builds a weighted k-nearest-neighbor graph in high-D. Optimizes a low-D layout that preserves the topological structure (fuzzy simplicial set).