In general, semi-supervised clustering can outperform unsupervised clustering. Since 2001, pairwise constraints for semi-supervised clustering have been an important paradigm in this field. In this paper, we show that pairwise constraints (ECs) can affect the performance of clustering in certain situations and analyze the reasons for this in detail. To overcome these disadvantages, we first outline some exemplars constraints. Based on these constraints, we then describe a semi-supervised clustering framework, and design an exemplars constraints expectation-maximization algorithm. Finally, standard datasets are selected for experiments, and experimental results are presented, which show that the exemplars constraints outperform the corresponding unsupervised clustering and semi-supervised algorithms based on pairwise constraints.