In high dimensional data, the general performance of traditional clustering algorithms decreases. This is partly because the similarity criterion used by these algorithms becomes inadequate in high dimensional space. Another reason is that some dimensions are likely to be irrelevant or contain noisy data, thus hiding a possible clustering. To overcome these problems, subspace clustering techniques, which can automatically find clusters in relevant subsets of dimensions, have been developed. However, due to the huge number of subspaces to consider, these techniques often lack efficiency. In this paper we propose to extend the framework of bottom up subspace clustering algorithms by integrating background knowledge and, in particular, instance-level constraints to speed up the enumeration of subspaces. We show how this new framework can be applied to both density and distance based bottom-up subspace clustering techniques. Our experiments on real datasets show that instance-level constraints cannot only increase the efficiency of the clustering process but also the accuracy of the resultant clustering.