Semidefinite programming for assignment and partitioning problems
Semidefinite programming for assignment and partitioning problems
On the Rank of Extreme Matrices in Semidefinite Programs and the Multiplicity of Optimal Eigenvalues
Mathematics of Operations Research
Semidefinite programming and combinatorial optimization
HPOPT '96 Proceedings of the Stieltjes workshop on High performance optimization techniques
Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Min-max Cut Algorithm for Graph Partitioning and Data Clustering
ICDM '01 Proceedings of the 2001 IEEE International Conference on Data Mining
Segmentation Using Eigenvectors: A Unifying View
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Binary Partitioning, Perceptual Grouping, and Restoration with Semidefinite Programming
IEEE Transactions on Pattern Analysis and Machine Intelligence
Convex Optimization
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Multi-way partitioning of an undirected weighted graph where pairwise similarities are assigned as edge weights, provides an important tool for data clustering, but is an NP-hard problem. Spectral relaxation is a popular way of relaxation, leading to spectral clustering where the clustering is performed by the eigen-decomposition of the (normalized) graph Laplacian. On the other hand, semidefinite relaxation, is an alternative way of relaxing a combinatorial optimization, leading to a convex optimization. In this paper we employ a semidefinite programming (SDP) approach to the graph equipartitioning for clustering, where sufficient conditions for strong duality hold. The method is referred to as semidefinite spectral clustering, where the clustering is based on the eigen-decomposition of the optimal feasible matrix computed by SDP. Numerical experiments with several data sets, demonstrate the useful behavior of our semidefinite spectral clustering, compared to existing spectral clustering methods.