Subspace correlation clustering: Finding locally correlated dimensions in subspace projections of the data

The necessity to analyze subspace projections of complex data is a well-known fact in the clustering community. While the full space may be obfuscated by overlapping patterns and irrelevant dimensions, only certain subspaces are able to reveal the clustering structure. Subspace clustering discards irrelevant dimensions and allows objects to belong to multiple, overlapping clusters due to individual subspace projections for each set of objects. As we will demonstrate, the observations, which originate the need to consider subspace projections for traditional clustering, also apply for the task of correlation analysis. In this work, we introduce the novel paradigm of subspace correlation clustering: we analyze subspace projections to find subsets of objects showing linear correlations among this subset of dimensions. In contrast to existing techniques, which determine correlations based on the full-space, our method is able to exclude locally irrelevant dimensions, enabling more precise detection of the correlated features. Since we analyze subspace projections, each object can contribute to several correlations. Our model allows multiple overlapping clusters in general but simultaneously avoids redundant clusters deducible from already known correlations. We introduce the algorithm SSCC that exploits different pruning techniques to efficiently generate a subspace correlation clustering. In thorough experiments we demonstrate the strength of our novel paradigm in comparison to existing methods.