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Subspace clustering

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Abstract Subspace clustering refers to the task of identifying clusters of similar objects or data records (vectors) where the similarity is defined with respect to a subset of the attributes (i.e., a subspace of the data space). The subspace is not necessarily (and actually is usually not) the same for different clusters within one clustering solution. In this article, the problems motivating subspace clustering are sketched, different definitions and usages of subspaces for clustering are described, and exemplary algorithmic solutions are discussed. Finally, we sketch current research directions. © 2012 Wiley Periodicals, Inc. This article is categorized under: Technologies > Structure Discovery and Clustering

Local feature relevance: three clusters, each cluster defined in two attributes, yet no any two clusters share two relevant attributes. Figures created with ELKI 0.4.27

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Hough transform: points in the picture space map to functions in the parameter space, an intersection of functions in the parameter space maps to a linear manifold shared by all points mapping to these functions.

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Grid‐based bottom‐up subspace clustering. Dense one‐dimensional and two‐dimensional units (for τ > 3) are highlighted. All one‐dimensional projections of each dense two‐dimensional unit are also dense, although not all two‐dimensional combinations of dense one‐dimensional units are dense.

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Frequent itemset mining and subspace mining: the search space of all possible itemsets over four items {A, B, C, D} and of all possible subspaces of a four‐dimensional data space where each subspace is encoded as a four‐dimensional vector recording 1 for those attributes spanning the subspace and 0 for the remaining attributes.

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Arbitrarily oriented subspace cluster.

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Axis‐parallel subspace cluster.

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