Spectral Clustering & Graph Cuts

Normalized cut · Laplacian eigenvectors · k-means in spectral space

Data space — colored by spectral cluster assignment

k-NN graph — edge weight = Gaussian similarity

Laplacian eigenvectors (Fiedler vector + next)

Spectral embedding (2D eigenvector space)

Settings

Algorithm:
1. Build k-NN graph W
2. Compute L_norm = D^(-½)(D−W)D^(-½)
3. Find k smallest eigenvectors
4. k-means on rows of eigenvector matrix

Key insight: Fiedler vector (λ₂) captures connectivity — sign gives 2-way cut.