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Subspace clustering finds sets of objects that are homogeneous in subspaces of high-dimensional datasets, and has been successfully applied in many domains. In recent years, a new breed of subspace clustering algorithms, which we denote as enhanced subspace clustering algorithms, have been proposed to (1) handle the increasing abundance and complexity of data and to (2) improve the clustering results. In this survey, we present these enhanced approaches to subspace clustering by discussing the problems they are solving, their cluster definitions and algorithms. Besides enhanced subspace clustering, we also present the basic subspace clustering and the related works in high-dimensional clustering.