Multiclass spectral clustering

We propose a principled account on multiclass spectral clustering. Given a discrete clustering formulation, we first solve a relaxed continuous optimization problem by eigen-decomposition. We clarify the role of eigenvectors as a generator of all optimal solutions through orthonormal transforms. We then solve an optimal discretization problem, which seeks a discrete solution closest to the continuous optima. The discretization is efficiently computed in an iterative fashion using singular value decomposition and nonmaximum suppression. The resulting discrete solutions are nearly global-optimal. Our method is robust to random initialization and converges faster than other clustering methods. Experiments on real image segmentation are reported.