Clustering has been traditionally viewed as an unsupervised method for data analysis. In real world application,however,some background prior knowledge can be easily obtained,such as pairwise constraints. It has been demonstrated that constraints can improve clustering performance. In this paper,the drawback of only incorporating pairwise constraints in clustering is firstly analyzed,and then an inherent prior knowledge in data sets,namely space consistency prior knowledge is exploited. The method of utilizing space consistency prior knowledge is also given. Incorporating the two types of prior knowledge into original spectral clustering,a density-sensitive semi-supervised spectral clustering algorithm (DS-SSC) is proposed. Experimental results on UCI (University of California Irvine) benchmark data,USPS (United States Postal Service) handwritten digits and text data from TREC (Text REtrieval Conference) show that the two types of prior knowledge can supplement each other in clustering process,leading to substantial performance enhancement of DS-SSC over other semi-supervised clustering methods which only incorporate pairwise constraints.