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Multi-way constrained spectral clustering by nonnegative restriction

Clustering often benefits from side information. In this paper, we consider the problem of multi-way constrained spectral clustering with pairwise constraints which encode whether two nodes belong to the same cluster or not. Due to the nontransitive property of cannot-link constraints, it is hard to incorporate cannot-link constraints into the framework. We settle this difficulty by restricting the spectral vectors with nonnegative elements. An iterative method is proposed to optimize the objective. Experiments on several publicly available datasets demonstrate the effectiveness of our algorithm.