Subspace clustering aims to partition the data pointsuddrawn from a union of subspaces according to their underly-uding subspaces. For accurate semisupervised subspace clustering,all data that have a must-link constraint or the same label should be grouped into the same underlying subspace. However, this is not guaranteed in existing approaches. Moreover, these approaches require additional parameters for incorporating supervision information. In this paper, we propose a constrained low-rank representation (CLRR) for robust semisupervised sub-space clustering, based on a novel constraint matrix constructedudin this paper. While seeking the low-rank representation of data, CLRR explicitly incorporates supervision information as hard constraints for enhancing the discriminating power of optimal representation. This strategy can be further extended to other state-of-the-art methods, such as sparse subspace clustering. We theoretically prove that the optimal representation matrix has both a block-diagonal structure with clean data and a semisu-pervised grouping effect with noisy data. We have also developed an efficient optimization algorithm based on alternating the direction method of multipliers for CLRR. Our experimental results have demonstrated that CLRR outperforms existing methods.
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