Isomap — what does it do?
hardAnswer
- Non-linear DR that preserves geodesic (manifold) distances.
- Steps: (1) k-NN graph, (2) all-pairs shortest paths (Dijkstra / Floyd-Warshall) → geodesic distance matrix, (3) MDS on geodesic distances → low-dim embedding.
- Discovers curved manifolds where Euclidean distance fails (roll, sphere).
- Precursor to UMAP; still useful for interpretability and small datasets.
Check yourself — multiple choice
- Random
- k-NN graph → shortest-path geodesic distances → MDS embedding; discovers curved manifolds where Euclidean fails
- Same as PCA
- Not real
Isomap: geodesic distances via k-NN shortest paths + MDS.
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