over the last few years, manifold clustering has attracted considerable interest in high-dimensional data clustering. However achieving accurate clustering results that match user desires and data structure is still an open problem. One way to do so is incorporating additional information that indicate relation between data objects. In this paper we propose a method for constrained clustering that take advantage of pairwise constraints. It first solves an optimization program to construct an affinity matrix according to pairwise constraints and manifold structure of data, then applies spectral clustering to find data clusters. Experiments demonstrated that our algorithm outperforms other related algorithms in face image datasets and has comparable results on hand-written digit datasets.

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