SPECTRAL CLUSTERING — Graph Laplacian Eigenmaps
Dataset
Concentric Rings
Two Moons
Blobs
Interleaved Spirals
k neighbors
8
Clusters
2
N points
120
Compute Clusters
INPUT DATA + k-NN GRAPH
SPECTRAL EMBEDDING (Fiedler vectors)
LAPLACIAN EIGENVALUES (spectral gap)
Spectral clustering
: Build graph Laplacian L=D−A, embed data using smallest eigenvectors (Fiedler vectors).
Spectral gap
λ₂ reveals cluster structure — near-zero = well-separated clusters. Works on non-convex shapes (rings, moons) where k-means fails. Eigenvectors capture global connectivity topology.