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This paper defines and discusses a new problem in the area of subspace clustering. It defines the problem of mining closed subspace clusters. This new concept allows for the culling of more high quality and less redundant clusters, than that of traditional clustering algorithms. In addition, our method contains a relaxation parameter, which allows for the classification of qualifying clusters into mutually exclusive bins of varying quality---extending the problem to mining relaxed closed subspace clusters. These concepts culminate in a new algorithm called Relaxed Closed Subspace Clustering (RCSC).