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 eigendecomposition. 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. Spectral graph partitioning methods have been successfully applied to circuit layout [3, 1], load balancing [4] and image segmentation [10, 6]. As a discriminative approach, they do not make assumptions about the global structure of data. Instead,...

• Type: Conference
• Year: 2003
• Where: ICCV
• Authors: Stella X. Yu, Jianbo Shi
• Keywords: Clustering Problem, Computer Vision, Discrete Clustering Formulation, ICCV 2003, Multiclass Spectral Clustering, Optimal Discretization Problem, Various Clustering Heuristics