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The sensitivity of the constrained K-means clustering algorithm (Cop-Kmeans) to the assignment order of instances is studied, and a novel assignment order learning method for Cop-Kmeans, termed as clustering Uncertainty-based Assignment order Learning Algorithm (UALA), is proposed in this paper. The main idea of UALA is to rank all instances in the data set according to their clustering uncertainties calculated by using the ensembles of multiple clustering algorithms. Experimental results on several real data sets with artificial instance-level constraints demonstrate that UALA can identify a good assignment order of instances for Cop-Kmeans. In addition, the effects of ensemble sizes on the performance of UALA are analyzed, and the generalization property of Cop-Kmeans is also studied.