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Subspace clustering (also called projected clustering) addresses the problem that different sets of attributes may be relevant for different clusters in high dimensional feature spaces. In this paper, we propose the algorithm DiSH (Detecting Subspace cluster Hierarchies) that improves in the following points over existing approaches: First, DiSH can detect clusters in subspaces of significantly different dimensionality. Second, DiSH uncovers complex hierarchies of nested subspace clusters, i.e. clusters in lower-dimensional subspaces that are embedded within higher-dimensional subspace clusters. These hierarchies do not only consist of single inclusions, but may also exhibit multiple inclusions and thus, can only be modeled using graphs rather than trees. Third, DiSH is able to detect clusters of different size, shape, and density. Furthermore, we propose to visualize the complex hierarchies by means of an appropriate visualization model, the so-called subspace clustering graph, such that the relationships between the subspace clusters can be explored at a glance. Several comparative experiments show the performance and the effectivity of DiSH.