Spectral Clustering via Graph Laplacian

Cluster points using eigenvectors of L = D − A; the graph structure reveals community structure

2D Points + k-NN graph
Eigenvalue spectrum of Laplacian
Points: 45 λ₂ (Fiedler): -- Accuracy: --
About: Spectral clustering builds a k-nearest-neighbor graph, computes the normalized graph Laplacian L = D − A, and uses the k smallest non-trivial eigenvectors to embed points in a low-dimensional space where k-means clustering becomes effective. The Fiedler value (λ₂) measures graph connectivity — near zero means the graph is weakly connected. This approach succeeds on non-convex clusters where standard k-means fails.