A Performance Guarantee for Spectral Clustering

The two-step spectral clustering method, which consists of the Laplacian eigenmap and a rounding step, is widely used method for graph partitioning. It can be seen as natural relaxation to NP-hard minimum ratio cut problem. In this paper, we study following central question: When able find global solution problem? First, provide condition that naturally depends on intra- intercluster connectivities given partition under may certify Then, develop deterministic two-to-infinity norm perturbation bound invariant subspace corresponds $k$ smallest eigenvalues. Finally, by combining these two results give guaranteed output problem, serves performance guarantee clustering.