Constrained clustering via spectral regularization

• Published in: 2009 IEEE Conference on Computer Vision and Pattern Recognition pp. 421 - 428
• Main Authors: Zhenguo Li, Jianzhuang Liu, Xiaoou Tang
• Format: Conference Proceeding
• Language: English; Japanese
• Published: IEEE 01.06.2009
• Subjects: Clustering algorithms; Computer vision; Current measurement; Data analysis; Data mining; Feature extraction; Glass; Kernel; Large-scale systems; Pattern recognition
• DOI: 10.1109/CVPR.2009.5206852
• ISBN: 1424439922; 9781424439928
• ISSN: 1063-6919

We propose a novel framework for constrained spectral clustering with pairwise constraints which specify whether two objects belong to the same cluster or not. Unlike previous methods that modify the similarity matrix with pairwise constraints, we adapt the spectral embedding towards an ideal embedding as consistent with the pairwise constraints as possible. Our formulation leads to a small semidefinite program whose complexity is independent of the number of objects in the data set and the number of pairwise constraints, making it scalable to large-scale problems. The proposed approach is applicable directly to multi-class problems, handles both must-link and cannot-link constraints, and can effectively propagate pairwise constraints. Extensive experiments on real image data and UCI data have demonstrated the efficacy of our algorithm.