Revealing true subspace clusters in high dimensions

Subspace clustering is one of the best approaches for discovering meaningful clusters in high dimensional space. One cluster in high dimensional space may be transcribed into multiple distinct maximal clusters by projecting onto different subspaces. A direct consequence of clustering independently in each subspace is an overwhelmingly large set of overlapping clusters which may be significantly similar. To reveal the true underlying clusters, we propose a similarity measurement of the overlapping clusters. We adopt the model of Gaussian tailed hyper-rectangles to capture the distribution of any subspace cluster. A set of experiments on a synthetic dataset demonstrates the effectiveness of our approach. Application to real gene expression data also reveals impressive meta-clusters expected by biologists.