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Spectral clustering — the core idea.

hard

Answer

  • Build similarity graph on data (k-NN or ε-neighborhood).
  • Compute graph Laplacian L.
  • Find eigenvectors of the k smallest eigenvalues → embed points into RkR^{k}.
  • Run k-means in this embedding.
  • Captures non-convex, manifold-shaped clusters that k-means can't handle.
  • Cost: O(n3)O(n^{3}) eigendecomposition or O(n2)O(n^{2}) with Nyström — scales to ~50k.
  • Modern uses: community detection in graphs, image segmentation.
Check yourself — multiple choice
  • Same as k-means
  • Build similarity graph → eigenvectors of Laplacian → k-means in embedding; captures non-convex shapes; O(n3)O(n^{3}) or Nyström for scale
  • Random
  • Not real

Spectral clustering: Laplacian eigenvectors + k-means → non-convex clusters.

#clustering

Practise Unsupervised Learning

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