: In this article, we propose an efficient and effective method for finding arbitrarily oriented subspace clusters by mapping the data space to a parameter space defining the set of possible arbitrarily oriented subspaces. The objective of a clustering algorithm based on this principle is to find those among all the possible subspaces that accommodate many database objects. In contrast to existing approaches, our method can find subspace clusters of different dimensionality even if they are sparse or are intersected by other clusters within a noisy environment. A broad experimental evaluation demonstrates the robustness and effectiveness of our method. 2008 Wiley Periodicals, Inc. Statistical Analysis and Data Mining 1: 111