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Issue No. 05 - May (2012 vol. 24)
ISSN: 1041-4347
pp: 926-939
Hong Zeng , Sch. of Instrum. Sci. & Eng., Southeast Univ., Nanjing, China
Yiu-Ming Cheung , Dept. of Comput. Sci., Hong Kong Baptist Univ., Hong Kong, China
The pairwise constraints specifying whether a pair of samples should be grouped together or not have been successfully incorporated into the conventional clustering methods such as k-means and spectral clustering for the performance enhancement. Nevertheless, the issue of pairwise constraints has not been well studied in the recently proposed maximum margin clustering (MMC), which extends the maximum margin framework in supervised learning for clustering and often shows a promising performance. This paper therefore proposes a pairwise constrained MMC algorithm. Based on the maximum margin idea in MMC, we propose a set of effective loss functions for discouraging the violation of given pairwise constraints. For the resulting optimization problem, we show that the original nonconvex problem in our approach can be decomposed into a sequence of convex quadratic program problems via constrained concave-convex procedure (CCCP). Subsequently, we present an efficient subgradient projection optimization method to solve each convex problem in the CCCP sequence. Experiments on a number of real-world data sets show that the proposed constrained MMC algorithm is scalable and outperforms the existing constrained MMC approach as well as the typical semi-supervised clustering counterparts.
quadratic programming, concave programming, convex programming, gradient methods, learning (artificial intelligence), pattern clustering, semisupervised maximum margin clustering, pairwise constraint, k-means clustering method, spectral clustering method, performance enhancement, maximum margin framework, supervised learning, maximum margin idea, loss function, optimization problem, nonconvex problem, constrained concave-convex procedure, convex quadratic program, subgradient projection optimization method, Clustering algorithms, Robustness, Estimation, Labeling, Partitioning algorithms, Optimization methods, constrained concave-convex procedure., Semi-supervised clustering, pairwise constraints, maximum margin clustering

Hong Zeng and Yiu-Ming Cheung, "Semi-Supervised Maximum Margin Clustering with Pairwise Constraints," in IEEE Transactions on Knowledge & Data Engineering, vol. 24, no. , pp. 926-939, 2012.
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