Finding non-Redundant, Statistically Significant Regions in High Dimensional Data: a Novel Approach to Projected and Subspace Clustering

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  • Technical report TR08-03. Projected and subspace clustering algorithms search for clusters of objects in subsets of attributes. Projected clustering computes several disjoint clusters, plus outliers, so that each cluster exists in its own subset of attributes. Subspace clustering enumerates clusters of objects in all subsets of attributes, and it produces many overlapping clusters. One problem of existing approaches is that their objectives are stated in a way that is not independent of the particular algorithm proposed to detect such clusters. A second problem is the definition of cluster density based on user-defined parameters, which makes it hard to assess whether the reported clusters are an artifact of the algorithm or they actually stand out in the data in a statistical sense. We propose a novel problem formulation that aims at extracting axis-parallel regions that stand out in the data in a statistical sense. The set of axis-parallel, statistically significant regions that exist in a given data set is typically highly redundant. Therefore, we formulate the problem of representing this set through a reduced, non-redundant set of axis-parallel, statistically significant regions as an optimization problem. Exhaustive search is not a viable solution to the optimization problem due to computational infeasibility. Consequently, we propose the approximation algorithm STATPC. Our comprehensive experimental evaluation shows that STATPC significantly outperforms existing projected and subspace clustering algorithms. | TRID-ID TR08-03

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    Attribution 3.0 International